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Open Mathematics

Subject:
Mathematics (miscellaneous)
Publisher:
De Gruyter —
de Gruyter
ISSN:
2391-5455
Scimago Journal Rank:
28

2023

Volume 21
Issue 1 (Jan)
Volume 20
Issue 1 (Jan)

2022

Volume 20
Issue 1 (Jan)

2021

Volume 19
Issue 1 (Dec)

2020

Volume 18
Issue 1 (Dec)

2019

Volume 17
Issue 1 (Dec)

2018

Volume 2020
Issue 1803 (Mar)
Volume 16
Issue 1 (Dec)

2017

Volume 2020
Issue 1705 (Apr)
Volume 15
Issue 1 (Dec)

2016

Volume 14
Issue 1 (Jan)

2015

Volume N/A
Issue 1 (Oct)
Volume 13
Issue 1 (Jan)

2014

Volume 13
Issue 1 (Dec)

2013

Volume 11
Issue 10 (Oct)Issue 7 (Jul)Issue 6 (Jun)Issue 3 (Mar)

2012

Volume 10
Issue 6 (Dec)

2010

Volume 8
Issue 4 (Aug)

2009

Volume 7
Issue 4 (Dec)Issue 2 (Jun)Issue 1 (Mar)
journal article
LitStream Collection
Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras

Zuevsky, A.

2018 Open Mathematics

doi: 10.1515/math-2018-0002

AbstractWe prove new theorems related to the construction of the shallow water bi-Hamiltonian systems associated to the semi-direct product of Virasoro and affine Kac–Moody Lie algebras. We discuss associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems.
journal article
LitStream Collection
On a viscous two-fluid channel flow including evaporation

Socolowsky, Jürgen

2018 Open Mathematics

doi: 10.1515/math-2018-0001

AbstractIn this contribution a particular plane steady-state channel flow including evaporation effects is investigated from analytical point of view. The channel is assumed to be horizontal. The motion of two heavy viscous immiscible fluids is governed by a free boundary value problem for a coupled system of Navier-Stokes and Stephan equations. The flow domain is unbounded in two directions and the free interface separating partially both liquids is semi-infinite, i.e. infinite in one direction. The free interface begins in some point Q where the half-line Σ1 separating the two parts of the channel in front of Q ends. Existence and uniqueness of a suitable solution in weighted HÖLDER spaces can be proved for small data (i.e. small fluxes) of the problem.
journal article
LitStream Collection
Generation of pseudo-random numbers with the use of inverse chaotic transformation

Lawnik, Marcin

2018 Open Mathematics

doi: 10.1515/math-2018-0004

AbstractIn (Lawnik M., Generation of numbers with the distribution close to uniform with the use of chaotic maps, In: Obaidat M.S., Kacprzyk J., Ören T. (Ed.), International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) (28-30 August 2014, Vienna, Austria), SCITEPRESS, 2014) Lawnik discussed a method of generating pseudo-random numbers from uniform distribution with the use of adequate chaotic transformation. The method enables the “flattening” of continuous distributions to uniform one. In this paper a inverse process to the above-mentioned method is presented, and, in consequence, a new manner of generating pseudo-random numbers from a given continuous distribution. The method utilizes the frequency of the occurrence of successive branches of chaotic transformation in the process of “flattening”. To generate the values from the given distribution one discrete and one continuous value of a random variable are required. The presented method does not directly involve the knowledge of the density function or the cumulative distribution function, which is, undoubtedly, a great advantage in comparison with other well-known methods. The described method was analysed on the example of the standard normal distribution.
journal article
LitStream Collection
Singular Cauchy problem for the general Euler-Poisson-Darboux equation

Shishkina, E.L.

2018 Open Mathematics

doi: 10.1515/math-2018-0005

AbstractIn this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.
journal article
LitStream Collection
Ternary and n-ary f-distributive structures

Churchill, Indu R. U.; Elhamdadi, M.; Green, M.; Makhlouf, A.

2018 Open Mathematics

doi: 10.1515/math-2018-0006

AbstractWe introduce and study ternary f-distributive structures, Ternary f-quandles and more generally their higher n-ary analogues. A classification of ternary f-quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n-ary, f-quandles. Furthermore, we give some computational examples.
journal article
LitStream Collection
On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics

Iena, Oleksandr

2018 Open Mathematics

doi: 10.1515/math-2018-0003

AbstractA parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M4m ± 1(ℙ2) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. Two different proofs of this statement are given.
journal article
LitStream Collection
Evaluation of integrals with hypergeometric and logarithmic functions

Sofo, Anthony

2018 Open Mathematics

doi: 10.1515/math-2018-0008

AbstractWe provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.
journal article
LitStream Collection
Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Encinas, A.M.; Jiménez, M.J.

2018 Open Mathematics

doi: 10.1515/math-2018-0007

AbstractIn this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.
journal article
LitStream Collection
Oscillation of first order linear differential equations with several non-monotone delays

Attia, E.R.; Benekas, V.; El-Morshedy, H.A.; Stavroulakis, I.P.

2018 Open Mathematics

doi: 10.1515/math-2018-0010

AbstractConsider the first-order linear differential equation with several retarded argumentsx′(t)+∑k=1npk(t)x(τk(t))=0,t≥t0,$$\begin{array}{}\displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0},\end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.
journal article
LitStream Collection
Review of Cryptographic Schemes applied to Remote Electronic Voting systems: remaining challenges and the upcoming post-quantum paradigm

Marcos del Blanco, David Yeregui; Panizo Alonso, Luis; Hermida Alonso, Jose Angel

2018 Open Mathematics

doi: 10.1515/math-2018-0013

AbstractThe implantation of Remote Electronic Voting (REV) systems to Electoral Processes is happening at a slower pace than anticipated. One of the relevant factors explaining that reality is the lack of studies about the Cryptographic Schemes and Primitives applied to the existing REV solutions. In this paper, the authors review the main cryptographic schemes applied to date, as well as the most relevant Post Quantum research in the field. The aim is twofold: contribute to clarify the strengths and weaknesses of each scheme as well as expose the remaining challenges, as a necessary step towards a broader introduction of REV solutions in binding elections.
journal article
LitStream Collection
Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Zhang, Xuping; Chen, Qiyu; Li, Yongxiang

2018 Open Mathematics

doi: 10.1515/math-2018-0012

AbstractThis paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.
journal article
LitStream Collection
The log-concavity of the q-derangement numbers of type B

Liu, Eric H.; Du, Wenjing

2018 Open Mathematics

doi: 10.1515/math-2018-0009

AbstractRecently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn(q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation forDnB(q) $\begin{array}{}\displaystyle D^B_n(q)\end{array}$ discovered by Chow, we show that for n ≥ 4, the q-derangement numbers of type BDnB(q) $\begin{array}{}\displaystyle D^B_n(q)\end{array}$ are also log-concave.
journal article
LitStream Collection
Generalized state maps and states on pseudo equality algebras

Cheng, Xiao Yun; Xin, Xiao Long; He, Peng Fei

2018 Open Mathematics

doi: 10.1515/math-2018-0014

AbstractIn this paper, we attempt to cope with states in a universal algebraic setting, that is, introduce a notion of generalized state map from a pseudo equality algebra X to an arbitrary pseudo equality algebra Y. We give two types of special generalized state maps, namely, generalized states and generalized internal states. Also, we study two types of states, namely, Bosbach states and Riečan states. Finally, we discuss the relations among generalized state maps, states and internal states (or state operators) on pseudo equality algebras. We verify the results that generalized internal states are the generalization of internal states, and generalized states are the generalization of state-morphisms on pseudo equality algebras. Furthermore, we obtain that generalized states are the generalization of Bosbach states and Riečan states on linearly ordered and involutive pseudo equality algebras, respectively. Hence we can come to the conclusion that, in a sense, generalized state maps can be viewed as a possible united framework of the states and the internal states, the state-morphisms and the internal state-morphisms on pseudo equality algebras.
journal article
LitStream Collection
Monotone subsequence via ultrapower

Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Nowik, Tahl

2018 Open Mathematics

doi: 10.1515/math-2018-0015

AbstractAn ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications.
journal article
LitStream Collection
Note on group irregularity strength of disconnected graphs

Anholcer, Marcin; Cichacz, Sylwia; Jura, Rafał; Marczyk, Antoni

2018 Open Mathematics

doi: 10.1515/math-2018-0017

AbstractWe investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group 𝓖 of order s, there exists a function f : E(G) → 𝓖 such that the sums of edge labels at every vertex are distinct. So far it was not known if sg(G) is finite for disconnected graphs. In the paper we present some upper bound for all graphs. Moreover we give the exact values and bounds on sg(G) for disconnected graphs without a star as a component.
journal article
LitStream Collection
On the security of the Courtois-Finiasz-Sendrier signature

Morozov, Kirill; Roy, Partha Sarathi; Steinwandt, Rainer; Xu, Rui

2018 Open Mathematics

doi: 10.1515/math-2018-0011

AbstractWe prove that a variant of the Courtois-Finiasz-Sendrier signature is strongly existentially unforgeable under chosen message attack in the random oracle model, assuming hardness of the Permuted Goppa Syndrome Decoding Problem (also known as the Niederreiter problem). In addition, we explicitly show that security against key substitution attacks can be arranged by a standard technique of Menezes and Smart, hashing the public key.
journal article
LitStream Collection
A further study on ordered regular equivalence relations in ordered semihypergroups

Tang, Jian; Feng, Xinyang; Davvaz, Bijan; Xie, Xiang-Yun

2018 Open Mathematics

doi: 10.1515/math-2018-0016

AbstractIn this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.
journal article
LitStream Collection
On the structure vector field of a real hypersurface in complex quadric

Dios Pérez, Juan de

2018 Open Mathematics

doi: 10.1515/math-2018-0021

AbstractFrom the notion of Jacobi type vector fields for a real hypersurface in complex quadric Qm we prove that if the structure vector field is of Jacobi type it is Killing when the real hypersurface is either Hopf or compact. In such cases we classify real hypersurfaces whose structure vector field is of Jacobi type.
journal article
LitStream Collection
Rank relations between a {0, 1}-matrix and its complement

Ma, Chao; Zhong, Jin

2018 Open Mathematics

doi: 10.1515/math-2018-0020

AbstractLet A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1. In particular, when A is a square {0, 1}-matrix with each diagonal entry being 0, another kind of complement matrix of A is defined and denoted by A = J − I − A, where I is the identity matrix. We determine the possible values of r(A) ± r(Ac) and r(A) ± r(A) in the general case and in the symmetric case. Our proof is constructive.
journal article
LitStream Collection
Lie n superderivations and generalized Lie n superderivations of superalgebras

Yuan, He; Chen, Liangyun

2018 Open Mathematics

doi: 10.1515/math-2018-0018

AbstractIn the paper, we study Lie n superderivations and generalized Lie n superderivations of superalgebras, using the theory of functional identities in superalgebras. We prove that if A = A0 ⊕ A1 is a prime superalgebra with deg(A1) ≥ 2n + 5, n ≥ 2, then any Lie n superderivation of A is the sum of a superderivation and a linear mapping, and any generalized Lie n superderivation of A is the sum of a generalized superderivation and a linear mapping.
journal article
LitStream Collection
Time parallelization scheme with an adaptive time step size for solving stiff initial value problems

Bu, Sunyoung

2018 Open Mathematics

doi: 10.1515/math-2018-0022

AbstractIn this paper, we introduce a practical strategy to select an adaptive time step size suitable for the parareal algorithm designed to parallelize a numerical scheme for solving stiff initial value problems. For the adaptive time step size, a technique to detect stiffness of a given system is first considered since the step size will be chosen according to the extent of stiffness. Finally, the stiffness detection technique is applied to an initial prediction step of the parareal algorithm, and select an adaptive step size to each time interval according to the stiffness. Several numerical experiments demonstrate the efficiency of the proposed method.
journal article
LitStream Collection
Stability problems and numerical integration on the Lie group SO(3) × R3 × R3

Pop, Camelia; Ene, Remus-Daniel

2018 Open Mathematics

doi: 10.1515/math-2018-0019

AbstractThe paper is dealing with stability problems for a nonlinear system on the Lie group SO(3) × R3 × R3. The approximate analytic solutions of the considered system via Optimal Homotopy Asymptotic Method are presented, too.
journal article
LitStream Collection
On some fixed point results for (s, p, α)-contractive mappings in b-metric-like spaces and applications to integral equations

Zoto, Kastriot; Radenović, Stojan; Ansari, Arslan H.

2018 Open Mathematics

doi: 10.1515/math-2018-0024

AbstractIn this work, we introduce the notions of (s, p, α)-quasi-contractions and (s, p)-weak contractions and deduce some fixed point results concerning such contractions, in the setting of b-metric-like spaces. Our results extend and generalize some recent known results in literature to more general metric spaces. Moreover, some examples and applications support the results.
journal article
LitStream Collection
On algebraic characterization of SSC of the Jahangir’s graph 𝓙n,m

Raza, Zahid; Kashif, Agha; Anwar, Imran

2018 Open Mathematics

doi: 10.1515/math-2018-0025

AbstractIn this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex Δs(𝓙n,m) of the Jahangir’s graph 𝓙n,m are explored. We show that Δs(𝓙n,m) is pure, present the formula for f-vectors associated to it and hence deduce a recipe for computing the Hilbert series of the Face ring k[Δs(𝓙n,m)]. Finally, we show that the face ring of Δs(𝓙n,m) is Cohen-Macaulay and give some open scopes of the current work.
journal article
LitStream Collection
A greedy algorithm for interval greedoids

Mao, Hua

2018 Open Mathematics

doi: 10.1515/math-2018-0026

AbstractWe show that the greedy algorithm provided in this paper works for interval greedoids with positive weights under some conditions, and also characterize an exchangeable system to be an interval greedoid with the assistance of the greedy algorithm.
journal article
LitStream Collection
On nonlinear evolution equation of second order in Banach spaces

Soltanov, Kamal N.

2018 Open Mathematics

doi: 10.1515/math-2018-0023

AbstractHere we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the special case, is the equation of the type of equation of traffic flow.
journal article
LitStream Collection
A primal-dual approach of weak vector equilibrium problems

László, Szilárd

2018 Open Mathematics

doi: 10.1515/math-2018-0028

AbstractIn this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we provide conditions that assure the solution set of the original problem and its dual coincide. We show that many known problems from the literature can be treated in our primal-dual model. We provide several coercivity conditions in order to obtain the existence of the solution of the primal-dual problems without compactness assumption. We apply the obtained results to perturbed vector equilibrium problems.
journal article
LitStream Collection
On new strong versions of Browder type theorems

Sanabria, José; Carpintero, Carlos; Rodríguez, Jorge; Rosas, Ennis; García, Orlando

2018 Open Mathematics

doi: 10.1515/math-2018-0029

AbstractAn operator T acting on a Banach space X satisfies the property (UWΠ) if σa(T)∖σSF+−$\begin{array}{}\sigma_{SF_{+}^{-}}\end{array} $(T) = Π(T), where σa(T) is the approximate point spectrum of T, σSF+−$\begin{array}{}\sigma_{SF_{+}^{-}}\end{array} $(T) is the upper semi-Weyl spectrum of T and Π(T) the set of all poles of T. In this paper we introduce and study two new spectral properties, namely (VΠ) and (VΠa), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property (VΠ) if and only if T satisfies property (UWΠ) and σ(T) = σa(T).
journal article
LitStream Collection
A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Wang, Xiaoxiao; Li, Chaoqian; Li, Yaotang

2018 Open Mathematics

doi: 10.1515/math-2018-0030

AbstractA set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.
journal article
LitStream Collection
Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖i| ≤ 7)

Cruz, Catarina N.; ďAzevedo Breda, Ana M.

2018 Open Mathematics

doi: 10.1515/math-2018-0027

AbstractThe Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over ℤ for n ≥ 3 and r ≥ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.
journal article
LitStream Collection
Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents

Yang, Yanqi; Tao, Shuangping

2018 Open Mathematics

doi: 10.1515/math-2018-0036

AbstractLet T be the singular integral operator with variable kernel defined byTf(x)=p.v.∫RnΩ(x,x−y)|x−y|nf(y)dy$$\begin{array}{}\displaystyle Tf(x)= p.v. \int\limits_{\mathbb{R}^{n}}\frac{{\it\Omega}(x,x-y)}{|x-y|^{n}}f(y)\text{d}y\end{array} $$and Dγ(0 ≤ γ ≤ 1) be the fractional differentiation operator. Let T∗ and T♯ be the adjoint of T and the pseudo-adjoint of T, respectively. The aim of this paper is to establish some boundedness for TDγ − DγT and (T∗ − T♯)Dγ on the homogeneous Morrey-Herz-type Hardy spaces with variable exponentsHMK˙p(⋅),λα(⋅),q$\begin{array}{}HM\dot{K}^{\alpha(\cdot),q}_{p(\cdot),\lambda}\end{array} $ via the convolution operator Tm, j and Calderón-Zygmund operator, and then establish their boundedness on these spaces. The boundedness onHMK˙p(⋅),λα(⋅),q$\begin{array}{}HM\dot{K}^{\alpha(\cdot),q}_{p(\cdot),\lambda}\end{array} $(ℝn) is shown to hold forTDγ − DγT and (T∗ − T♯)Dγ. Moreover, the authors also establish various norm characterizations for the product T1T2 and the pseudo-product T1 ∘ T2.
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LitStream Collection
Introduction to disoriented knot theory

Altıntaş, İsmet

2018 Open Mathematics

doi: 10.1515/math-2018-0032

AbstractThis paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot, disoriented crossing and Reidemesiter moves for disoriented diagrams, numerical invariants such as the linking number and the complete writhe, the polynomial invariants such as the bracket polynomial, the Jones polynomial for the disoriented knots and links.
journal article
LitStream Collection
Restricted triangulation on circulant graphs

Ali, Niran Abbas; Kilicman, Adem; Trao, Hazim Michman

2018 Open Mathematics

doi: 10.1515/math-2018-0033

AbstractThe restricted triangulation existence problem on a given graph decides whether there exists a triangulation on the graph’s vertex set that is restricted with respect to its edge set. Let G = C(n, S) be a circulant graph on n vertices with jump value set S. We consider the restricted triangulation existence problem for G. We determine necessary and sufficient conditions on S for which G admitting a restricted triangulation. We characterize a set of jump values S(n) that has the smallest cardinality with C(n, S(n)) admits a restricted triangulation. We present the measure of non-triangulability of Kn − G for a given G.
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LitStream Collection
Boundedness control sets for linear systems on Lie groups

Ayala, Víctor; Todco, María Torreblanca

2018 Open Mathematics

doi: 10.1515/math-2018-0035

AbstractLet Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e. We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.
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LitStream Collection
Chen’s inequalities for submanifolds in (κ, μ)-contact space form with a semi-symmetric metric connection

Ahmad, Asif; Guoqing, He; Wanxiao, Tang; Peibiao, Zhao

2018 Open Mathematics

doi: 10.1515/math-2018-0034

AbstractIn this paper, we obtain Chen’s inequalities for submanifolds in (κ, μ)-contact space form endowed with a semi-symmetric metric connection.
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LitStream Collection
Disjointed sum of products by a novel technique of orthogonalizing ORing

Can, Yavuz

2018 Open Mathematics

doi: 10.1515/math-2018-0038

AbstractThis work presents a novel combining method called ‘orthogonalizing ORing ◯∨$\bigcirc\!\!\!\!\!\!\vee $’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation.
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LitStream Collection
A parametric linearizing approach for quadratically inequality constrained quadratic programs

Jiao, Hongwei; Chen, Rongjiang

2018 Open Mathematics

doi: 10.1515/math-2018-0037

AbstractIn this paper we propose a new parametric linearizing approach for globally solving quadratically inequality constrained quadratic programs. By utilizing this approach, we can derive the parametric linear programs relaxation problem of the investigated problem. To accelerate the computational speed of the proposed algorithm, an interval deleting rule is used to reduce the investigated box. The proposed algorithm is convergent to the global optima of the initial problem by subsequently partitioning the initial box and solving a sequence of parametric linear programs relaxation problems. Finally, compared with some existing algorithms, numerical results show higher computational efficiency of the proposed algorithm.
journal article
LitStream Collection
Generalizations of Steffensen’s inequality via the extension of Montgomery identity

Aljinović, Andrea Aglić; Pečarić, Josip; Pribanić, Anamarija Perušić

2018 Open Mathematics

doi: 10.1515/math-2018-0039

AbstractIn this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s inequality. Related Ostrowski type inequalities are also provided. Bounds for the reminders in new identities are given by using the Chebyshev and Grüss type inequalities.
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LitStream Collection
Vector fields satisfying the barycenter property

Lee, Manseob

2018 Open Mathematics

doi: 10.1515/math-2018-0040

AbstractWe show that if a vector field X has the C1 robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a generic C1-vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].
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LitStream Collection
On the freeness of hypersurface arrangements consisting of hyperplanes and spheres

Gao, Ruimei; Dai, Qun; Li, Zhe

2018 Open Mathematics

doi: 10.1515/math-2018-0041

AbstractLet V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements. In this paper, we use Saito’s criterion to study the freeness of hypersurface arrangements consisting of hyperplanes and spheres, and construct the bases for the derivation modules explicitly.
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LitStream Collection
Biderivations of the higher rank Witt algebra without anti-symmetric condition

Tang, Xiaomin; Yang, Yu

2018 Open Mathematics

doi: 10.1515/math-2018-0042

AbstractThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.
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LitStream Collection
Some remarks on spectra of nuclear operators

Reinov, Oleg I.

2018 Open Mathematics

doi: 10.1515/math-2018-0043

AbstractWe give criteria for the spectra of some nuclear operators in subspaces of quotients of Lp-spaces to be central-symmetric, as well as for the spectra of linear operators in Banach spaces to be Zd-symmetric in the sense of B. Mityagin. Also, we present a short proof of a corresponding Mityagin’s theorem.
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LitStream Collection
Recursive interpolating sequences

Tugores, Francesc

2018 Open Mathematics

doi: 10.1515/math-2018-0044

AbstractThis paper is devoted to pose several interpolation problems on the open unit disk 𝔻 of the complex plane in a recursive and linear way. We look for interpolating sequences (zn) in 𝔻 so that given a bounded sequence (an) and a suitable sequence (wn), there is a bounded analytic function f on 𝔻 such that f(z1) = w1 and f(zn+1) = anf(zn) + wn+1. We add a recursion for the derivative of the type: f′(z1) = w1′$\begin{array}{}w_1'\end{array} $ and f′(zn+1) = an′$\begin{array}{}a_n'\end{array} $ [(1 − |zn|2)/(1 − |zn+1|2)] f′(zn) + wn+1′,$\begin{array}{}w_{n+1}',\end{array} $ where (an′$\begin{array}{}a_n'\end{array} $) is bounded and (wn′$\begin{array}{}w_n'\end{array} $) is an appropriate sequence, and we also look for zero-sequences verifying the recursion for f′. The conditions on these interpolating sequences involve the Blaschke product with zeros at their points, one of them being the uniform separation condition.
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Involutory biquandles and singular knots and links

Bataineh, Khaled; Ghaith, Hadeel

2018 Open Mathematics

doi: 10.1515/math-2018-0031

AbstractWe define a new algebraic structure for singular knots and links. It extends the notion of a bikei (or involutory biquandle) from regular knots and links to singular knots and links. We call this structure a singbikei. This structure results from the generalized Reidemeister moves representing singular isotopy. We give several examples on singbikei and we use singbikei to distinguish several singular knots and links.
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Constacyclic codes over 𝔽pm[u1, u2,⋯,uk]/〈 ui2 = ui, uiuj = ujui〉

Zheng, Xiying; Kong, Bo

2018 Open Mathematics

doi: 10.1515/math-2018-0045

AbstractIn this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈ui2$\begin{array}{}u^{2}_{i}\end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k. We define a Gray map from RkntoFpm2kn$\begin{array}{}R_{k}^n\,\,\text{to}\,\,{\mathbb F}_{p^m}^{2^kn}\end{array} $ and give the generator polynomials of constacyclic codes over Rk. We also study the MacWilliams identities of linear codes over Rk.
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Topological entropy for positively weak measure expansive shadowable maps

Lee, Manseob; Oh, Jumi

2018 Open Mathematics

doi: 10.1515/math-2018-0046

AbstractIn this paper, we consider positively weak measure expansive homeomorphisms and flows with the shadowing property on a compact metric space X. Moreover, we prove that if a homeomorphism (or flow) has a positively weak expansive measure and the shadowing property on its nonwandering set, then its topological entropy is positive.
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Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

Hasil, Petr; Veselý, Michal

2018 Open Mathematics

doi: 10.1515/math-2018-0047

AbstractThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.
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On 𝓠-regular semigroups

Feng, Xinyang

2018 Open Mathematics

doi: 10.1515/math-2018-0048

AbstractIn this paper, we give some characterizations of 𝓠-regular semigroups and show that the class of 𝓠-regular semigroups is closed under the direct product and homomorphic images. Furthermore, we characterize the 𝓠-subdirect products of this class of semigroups and study the E-unitary 𝓠-regular covers for 𝓠-regular semigroups, in particular for those whose maximum group homomorphic image is a given group. As an application of these results, we claim that the similar results on V-regular semigroups also hold.
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One kind power mean of the hybrid Gauss sums

Lan, Qi; Wenpeng, Zhang

2018 Open Mathematics

doi: 10.1515/math-2018-0052

AbstractIn this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation mod p, where p be an odd prime.
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A reduced space branch and bound algorithm for a class of sum of ratios problems

Zhao, Yingfeng; Zhao, Ting

2018 Open Mathematics

doi: 10.1515/math-2018-0049

AbstractSum of ratios problem occurs frequently in various areas of engineering practice and managementscience, but most solution methods for this kind of problem are often designed for determining local solutions . In this paper, we develop a reduced space branch and bound algorithm for globally solving sum of convex-concave ratios problem. By introducing some auxiliary variables, the initial problem is converted into an equivalent problem where the objective function is linear. Then the convex relaxation problem of the equivalent problem is established by relaxing auxiliary variables only in the outcome space. By integrating some acceleration and reduction techniques into branch and bound scheme, the presented global optimization algorithm is developed for solving these kind of problems. Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib are carried out to validate the performance of the proposed algorithm.
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Some recurrence formulas for the Hermite polynomials and their squares

He, Yuan; Yang, Fengzao

2018 Open Mathematics

doi: 10.1515/math-2018-0050

AbstractIn this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares. These results presented here are the corresponding extensions of some known formulas.
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A relaxed block splitting preconditioner for complex symmetric indefinite linear systems

Huang, Yunying; Chen, Guoliang

2018 Open Mathematics

doi: 10.1515/math-2018-0051

AbstractIn this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of the relaxed splitting preconditioner.
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On f - prime radical in ordered semigroups

Gu, Ze

2018 Open Mathematics

doi: 10.1515/math-2018-0053

AbstractIn this paper, we introduce the concepts of f-prime ideals, f-semiprime ideals and f-prime radicals in ordered semigroups. Furthermore, some results on f-prime radicals and f-primary decomposition of an ideal in an ordered semigroup are obtained.
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Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions

Hao, Xinan; Wang, Huaqing

2018 Open Mathematics

doi: 10.1515/math-2018-0055

AbstractIn this paper, the existence of positive solutions for systems of semipositone singular fractional differential equations with a parameter and integral boundary conditions is investigated. By using fixed point theorem in cone, sufficient conditions which guarantee the existence of positive solutions are obtained. An example is given to illustrate the results.
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Disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators

Ma, Yingbin; Wang, Cui

2018 Open Mathematics

doi: 10.1515/math-2018-0054

AbstractWe characterize disjointness of supercyclic operators which map a holomorphic function to a partial sum of the Taylor expansion. In particular, we show that disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators. Moreover, we give a sufficient condition to yield the disjoint supercyclicity for families of Taylor-type operators.
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A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment

Yin, Shi; Li, Baizhou

2018 Open Mathematics

doi: 10.1515/math-2018-0056

AbstractConsidering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.
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Dynamic behavior analysis of a prey-predator model with ratio-dependent Monod-Haldane functional response

Feng, Xiaozhou; Song, Yi; An, Xiaomin

2018 Open Mathematics

doi: 10.1515/math-2018-0060

AbstractThis paper investigates the dynamic behavior analysis on the prey-predator model with ratio-dependent Monod-Haldane response function under the homogeneous Dirichlet boundary conditions, which is used to simulate a class of biological system. Firstly, the sufficient and necessary conditions on existence and non-existence of coexistence states of this model are discussed by comparison principle and fixed point index theory. Secondly, taking a as a main bifurcation parameter, the structure of global bifurcation curve on positive solutions is established by using global bifurcation theorem and properties of principal eigenvalue. Finally, the stability of coexistence states is obtained by the eigenvalue perturbation theory; the multiplicity of coexistence states is investigated when a satisfies some condition by the fixed point index theory.
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The points and diameters of quantales

Liang, Shaohui

2018 Open Mathematics

doi: 10.1515/math-2018-0057

AbstractIn this paper, we investigate some properties of points on quantales. It is proved that the two sided prime elements are in one to one correspondence with points. By using points of quantales, we give the concepts of p-spatial quantales, and some equivalent characterizations for P-spatial quantales are obtained. It is shown that two sided quantale Q is a spatial quantale if and only if Q is a P-spatial quantale. Based on a quantale Q, we introduce the definition of diameters. We also prove that the induced topology by diameter coincides with the topology of the point spaces.
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Linearity in decimation-based generators: an improved cryptanalysis on the shrinking generator

Cardell, Sara D.; Fúster-Sabater, Amparo; Ranea, Adrián H.

2018 Open Mathematics

doi: 10.1515/math-2018-0058

AbstractDecimation-based sequence generators are a class of non-linear cryptographic generators designed to be used in hardware implementations. An inherent characteristic of such generators is that their output sequences are interleaved sequences. This profitable characteristic can be used in the cryptanalysis of those generators. In this work, emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems. Compared with previous cryptanalysis, computational complexity and intercepted sequence requirements are dramatically reduced. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analyzed in terms of simple linear structures.
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On dynamic network security: A random decentering algorithm on graphs

Trobajo, M.T.; Cifuentes-Rodríguez, J.; Carriegos, M.V.

2018 Open Mathematics

doi: 10.1515/math-2018-0059

AbstractRandom Decentering Algorithm (RDA) on a undirected unweighted graph is defined and tested over several concrete scale-free networks. RDA introduces ancillary nodes to the given network following basic principles of minimal cost, density preservation, centrality reduction and randomness. First simulations over scale-free networks show that RDA gives a significant decreasing of both betweenness centrality and closeness centrality and hence topological protection of network is improved. On the other hand, the procedure is performed without significant change of the density of connections of the given network. Thus ancillae are not distinguible from real nodes (in a straightforward way) and hence network is obfuscated to potential adversaries by our manipulation.
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Directed colimits of some flatness properties and purity of epimorphisms in S-posets

Liang, Xingliang; Khosravi, Roghaieh

2018 Open Mathematics

doi: 10.1515/math-2018-0061

AbstractLet S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S-posets, such as strong flatness, Conditions (E), (E′), (P), (Pw), (WP), (WP)w, (PWP) and (PWP)w. Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S-posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S-posets can be transferred to their directed colimit. Finally, we prove that every class of S-posets having a flatness property is closed under directed colimits.
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Super (a, d)-H-antimagic labeling of subdivided graphs

Taimur, Amir; Numan, Muhammad; Ali, Gohar; Mumtaz, Adeela; Semaničová-Feňovčíková, Andrea

2018 Open Mathematics

doi: 10.1515/math-2018-0062

AbstractA simple graph G = (V, E) admits an H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called an (a, d)-H-antimagic if there exists a bijective function f : V(G) ∪ E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H the sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a, a + d, …, a + (t − 1)d}, where a > 0 and d ≥ 0 are integers and t is the number of all subgraphs of G isomorphic to H. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a, d)-cycle-antimagic labeling for some d.
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On the power sum problem of Lucas polynomials and its divisible property

Xiao, Wang

2018 Open Mathematics

doi: 10.1515/math-2018-0063

AbstractThe main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.
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Existence of solutions for a shear thickening fluid-particle system with non-Newtonian potential

Song, Yukun; Liu, Fengming

2018 Open Mathematics

doi: 10.1515/math-2018-0064

AbstractThis paper is concerned with a compressible shear thickening fluid-particle interaction model for the evolution of particles dispersed in a viscous non-Newtonian fluid. Taking the influence of non-Newtonian gravitational potential into consideration, the existence and uniqueness of strong solutions are established.
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On generalized P-reducible Finsler manifolds

Zamanzadeh, Seyyed Mohammad; Najafi, Behzad; Toomanian, Megerdich

2018 Open Mathematics

doi: 10.1515/math-2018-0065

AbstractThe class of generalized P-reducible manifolds (briefly GP-reducible manifolds) was first introduced by Tayebi and his collaborates [1]. This class of Finsler manifolds contains the classes of P-reducible manifolds, C-reducible manifolds and Landsberg manifolds. We prove that every compact GP-reducible manifold with positive or negative character is a Randers manifold. The norm of Cartan torsion plays an important role for studying immersion theory in Finsler geometry. We find the relation between the norm of Cartan torsion, mean Cartan torsion, Landsberg and mean Landsberg curvatures of the class of GP-reducible manifolds. Finally, we prove that every GP-reducible manifold admitting a concurrent vector field reduces to a weakly Landsberg manifold.
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On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences

Jureczko, Joanna

2018 Open Mathematics

doi: 10.1515/math-2018-0066

AbstractIn 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory. They showed that the existence of the so called BK-matrix related to Banach and Kuratowski theorem is equivalent to the existence of a K-Lusin set of cardinality continuum. On the other hand, in 1965 Efimov introduced the strong sequences method and using this method proved some well-known theorems in dyadic spaces. The goal of this paper is to show that the existence of such a K-Lusin set is equivalent to the existence of strong sequences of the same cardinality. Some applications of this results are also shown.
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On the boundedness of square function generated by the Bessel differential operator in weighted Lebesque Lp,α spaces

Bayrakci, Simten

2018 Open Mathematics

doi: 10.1515/math-2018-0067

AbstractIn this paper, we consider the square function(Sf)(x)=(∫0∞|(f⊗Φt)(x)|2dtt)1/2$$\begin{array}{} \displaystyle (\mathcal{S}f)(x)=\left( \int\limits_{0}^{\infty }|(f\otimes {\it\Phi}_{t})\left( x\right) |^{2}\frac{dt}{t}\right) ^{1/2}\end{array} $$associated with the Bessel differential operator Bt=d2dt2+(2α+1)tddt,$\begin{array}{} B_{t}=\frac{d^{2}}{dt^{2}}+\frac{(2\alpha+1)}{t}\frac{d}{dt},\end{array} $α > −1/2, t > 0 on the half-line ℝ+ = [0, ∞). The aim of this paper is to obtain the boundedness of this function in Lp,α, p > 1. Firstly, we proved L2,α-boundedness by means of the Bessel-Plancherel theorem. Then, its weak-type (1, 1) and Lp,α, p > 1 boundedness are proved by taking into account vector-valued functions.
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On the different kinds of separability of the space of Borel functions

Osipov, Alexander V.

2018 Open Mathematics

doi: 10.1515/math-2018-0070

AbstractIn paper we prove that:a space of Borel functions B(X) on a set of reals X, with pointwise topology, to be countably selective sequentially separable if and only if X has the property S1(BΓ, BΓ);there exists a consistent example of sequentially separable selectively separable space which is not selective sequentially separable. This is an answer to the question of A. Bella, M. Bonanzinga and M. Matveev;there is a consistent example of a compact T2 sequentially separable space which is not selective sequentially separable. This is an answer to the question of A. Bella and C. Costantini;min{𝔟, 𝔮} = {κ : 2κ is not selective sequentially separable}. This is a partial answer to the question of A. Bella, M. Bonanzinga and M. Matveev.
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Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers

Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesús

2018 Open Mathematics

doi: 10.1515/math-2018-0069

AbstractThis article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 𝕃2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.
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Functional analysis method for the M/G/1 queueing model with single working vacation

Kasim, Ehmet; Gupur, Geni

2018 Open Mathematics

doi: 10.1515/math-2018-0074

AbstractIn this paper, we study the asymptotic property of underlying operator corresponding to the M/G/1 queueing model with single working vacation, where both service times in a regular busy period and in a working vacation period are function. We obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of both the operator and its adjoint operator with geometric multiplicity one. Therefore, we deduce that the time-dependent solution of the queueing model strongly converges to its steady-state solution. We also study the asymptotic behavior of the time-dependent queueing system’s indices for the model.
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Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

Cao, Junfei; Huang, Zaitang

2018 Open Mathematics

doi: 10.1515/math-2018-0068

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.
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The existence of solutions to certain type of nonlinear difference-differential equations

Lü, Weiran; Wu, Linlin; Wang, Dandan; Yang, Chungchun

2018 Open Mathematics

doi: 10.1515/math-2018-0071

AbstractIn this paper we study the entire solutions to a certain type of difference-differential equations. We also give an affirmative answer to the conjecture of Zhang et al. In addition, our results improve and complement earlier ones due to Yang-Laine, Latreuch, Liu-Lü et al. and references therein.
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Domination in 4-regular Knödel graphs

Mojdeh, Doost Ali; Musawi, S.R.; Nazari, E.

2018 Open Mathematics

doi: 10.1515/math-2018-0072

AbstractA subset D of vertices of a graph G is a dominating set if for each u ∈ V(G) ∖ D, u is adjacent to some vertex v ∈ D. The domination number, γ(G) of G, is the minimum cardinality of a dominating set of G. For an even integer n ≥ 2 and 1 ≤ Δ ≤ ⌊log2n⌋, a Knödel graph WΔ, n is a Δ-regular bipartite graph of even order n, with vertices (i, j), for i = 1, 2 and 0 ≤ j ≤ n/2 − 1, where for every j, 0 ≤ j ≤ n/2 − 1, there is an edge between vertex (1, j) and every vertex (2, (j+2k − 1) mod (n/2)), for k = 0, 1, ⋯, Δ − 1. In this paper, we determine the domination number in 4-regular Knödel graphs W4,n.
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Stepanov-like pseudo almost periodic functions on time scales and applications to dynamic equations with delay

Tang, Chao-Hong; Li, Hong-Xu

2018 Open Mathematics

doi: 10.1515/math-2018-0073

AbstractIn this paper, we introduce the concept of Sp-pseudo almost periodicity on time scales and present some basic properties of it, including the translation invariance, uniqueness of decomposition, completeness and composition theorem. Moreover, we prove the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almost periodicity. As an application of the abstract results, we present some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay.
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Algebras of right ample semigroups

Guo, Junying; Guo, Xiaojiang

2018 Open Mathematics

doi: 10.1515/math-2018-0075

AbstractStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.
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Random attractors for stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domains

Jia, Xiaoyao; Ding, Xiaoquan; Gao, Juanjuan

2018 Open Mathematics

doi: 10.1515/math-2018-0076

AbstractIn this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝn (n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion equations with random parameter by Ornstein-Uhlenbeck process. Next, we show the original equations generate the random dynamical systems, and prove the existence of random attractors by conjugation relation between two random dynamical systems. In this process, we use the cut-off technique to obtain the pullback asymptotic compactness.
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Nontrivial periodic solutions to delay difference equations via Morse theory

Long, Yuhua; Shi, Haiping; Deng, Xiaoqing

2018 Open Mathematics

doi: 10.1515/math-2018-0077

AbstractIn this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.
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A note on the three-way generalization of the Jordan canonical form

Cui, Lu-Bin; Li, Ming-Hui

2018 Open Mathematics

doi: 10.1515/math-2018-0078

AbstractThe limit point 𝓧 of an approximating rank-R sequence of a tensor Ƶ can be obtained by fitting a decomposition (S, T, U) ⋅ 𝓖 to Ƶ. The decomposition of the limit point 𝓧 = (S, T, U) ⋅ 𝓖 with 𝓖 = blockdiag(𝓖1, … , 𝓖m) can be seen as a three order generalization of the real Jordan canonical form. The main aim of this paper is to study under what conditions we can turn 𝓖j into canonical form if some of the upper triangular entries of the last three slices of 𝓖j are zeros. In addition, we show how to turn 𝓖j into canonical form under these conditions.
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On some varieties of ai-semirings satisfying xp+1 ≈ x

Wang, Aifa; Shao, Yong

2018 Open Mathematics

doi: 10.1515/math-2018-0079

AbstractThe aim of this paper is to study the lattice of subvarieties of the ai-semiring variety defined by the additional identitiesxp+1≈xandzxyz≈(zxzyz)pzyxz(zxzyz)p,$$\begin{array}{}\displaystyle x^{p+1}\approx x\,\,\mbox{and}\,\,zxyz\approx(zxzyz)^{p}zyxz(zxzyz)^{p},\end{array} $$where p is a prime. It is shown that this lattice is a distributive lattice of order 179. Also, each member of this lattice is finitely based and finitely generated.
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Abstract-valued Orlicz spaces of range-varying type

Zhang, Qinghua

2018 Open Mathematics

doi: 10.1515/math-2018-0080

AbstractThis paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and L+ϱθ(⋅)$\begin{array}{}L_{+}^{\varrho_{\theta(\cdot)}}\end{array} $(I, Xθ(⋅)), and discuss their geometrical properties as well as the representation of L+ϱθ(⋅)$\begin{array}{}L_{+}^{\varrho_{\theta(\cdot)}}\end{array} $(I, Xθ(⋅))*. We also investigate some functionals and operators on Lϱθ(⋅)(I, Xθ(⋅)), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W1, ϱθ(⋅)(I, Xθ(⋅)) and Wper1,ϱθ(⋅)$\begin{array}{}W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}}\end{array} $(I, Xθ(⋅)), and the intersection space Wper1,ϱθ(⋅)$\begin{array}{}W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}}\end{array} $(I, Xθ(⋅)) ∩ Lφϑ(⋅)(I, Vϑ(⋅)), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account.
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On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums

Shen, Shimeng

2018 Open Mathematics

doi: 10.1515/math-2018-0081

AbstractThe main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation mod p, an odd prime.
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Arithmetic of generalized Dedekind sums and their modularity

Choi, Dohoon; Jun, Byungheup; Lee, Jungyun; Lim, Subong

2018 Open Mathematics

doi: 10.1515/math-2018-0082

AbstractDedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.
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Multipreconditioned GMRES for simulating stochastic automata networks

Wen, Chun; Huang, Ting-Zhu; Gu, Xian-Ming; Shen, Zhao-Li; Zhang, Hong-Fan; Liu, Chen

2018 Open Mathematics

doi: 10.1515/math-2018-0083

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.
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Regularization and error estimates for an inverse heat problem under the conformable derivative

Vu, Ho; O’Regan, Donal; Hoa, Ngo Van

2018 Open Mathematics

doi: 10.1515/math-2018-0084

AbstractIn this paper we study an inverse time problem for the nonhomogeneous heat equation under the conformable derivative which is a severely ill-posed problem. Using the quasi-boundary value method with two regularization parameters (one related to the error in a measurement process and the other is related to the regularity of the solution) we regularize this problem and obtain a Hölder-type estimation error for the whole time interval. Numerical results are presented to illustrate the accuracy and efficiency of the method.
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Transitivity of the εm-relation on (m-idempotent) hyperrings

Norouzi, Morteza; Cristea, Irina

2018 Open Mathematics

doi: 10.1515/math-2018-0085

AbstractOn a general hyperring, there is a fundamental relation, denoted γ*, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm on general hyperrings, proving that its transitive closure εm∗$\begin{array}{}\displaystyle\varepsilon^{*}_{m}\end{array}$ is a strongly regular equivalence relation smaller than the γ*-relation on some classes of hyperrings, such that the associated quotient structure modulo εm∗$\begin{array}{}\displaystyle\varepsilon^{*}_{m}\end{array}$ is an ordinary ring. Thus, on such hyperrings, εm∗$\begin{array}{}\displaystyle\varepsilon^{*}_{m}\end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm-relation on hyperrings and m-idempotent hyperrings.
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Learning Bayesian networks based on bi-velocity discrete particle swarm optimization with mutation operator

Wang, Jingyun; Liu, Sanyang

2018 Open Mathematics

doi: 10.1515/math-2018-0086

AbstractThe problem of structures learning in Bayesian networks is to discover a directed acyclic graph that in some sense is the best representation of the given database. Score-based learning algorithm is one of the important structure learning methods used to construct the Bayesian networks. These algorithms are implemented by using some heuristic search strategies to maximize the score of each candidate Bayesian network. In this paper, a bi-velocity discrete particle swarm optimization with mutation operator algorithm is proposed to learn Bayesian networks. The mutation strategy in proposed algorithm can efficiently prevent premature convergence and enhance the exploration capability of the population. We test the proposed algorithm on databases sampled from three well-known benchmark networks, and compare with other algorithms. The experimental results demonstrate the superiority of the proposed algorithm in learning Bayesian networks.
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Simultaneous prediction in the generalized linear model

Bai, Chao; Li, Haiqi

2018 Open Mathematics

doi: 10.1515/math-2018-0087

AbstractThis paper studies the prediction based on a composite target function that allows to simultaneously predict the actual and the mean values of the unobserved regressand in the generalized linear model. The best linear unbiased prediction (BLUP) of the target function is derived. Studies show that our BLUP has better properties than some other predictions. Simulations confirm its better finite sample performance.
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Two asymptotic expansions for gamma function developed by Windschitl’s formula

Yang, Zhen-Hang; Tian, Jing-Feng

2018 Open Mathematics

doi: 10.1515/math-2018-0088

AbstractIn this paper we develop Windschitl’s approximation formula for the gamma function by giving two asymptotic expansions using a little known power series. In particular, for n ∈ ℕ with n ≥ 4, we haveΓx+1=2πxxexxsinh⁡1xx/2exp∑k=3n−1anx2n−1+Rnx$$\begin{array}{}\displaystyle{\it \Gamma} \left( x+1\right) =\sqrt{2\pi x}\left( \tfrac{x}{e}\right) ^{x}\left(x\sinh \tfrac{1}{x}\right) ^{x/2}\exp \left( \sum_{k=3}^{n-1}{\frac{a_{n}}{x^{2n-1}}}+R_{n}\left( x\right) \right)\end{array}$$withRnx≤B2n2n2n−11x2n−1$$\begin{array}{}\displaystyle\left\vert R_{n}\left( x\right) \right\vert \leq \frac{\left\vert B_{2n}\right\vert }{2n\left( 2n-1\right)}\frac{1}{x^{2n-1}}\end{array}$$for all x > 0, where an has a closed-form expression, B2n is the Bernoulli number. Moreover, we present some approximation formulas for the gamma function related to Windschitl’s approximation, which have higher accuracy.
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State maps on semihoops

Fu, Yu Long; Xin, Xiao Long; Wang, Jun Tao

2018 Open Mathematics

doi: 10.1515/math-2018-0089

AbstractIn this paper, we introduce the notion of state maps from a semihoop H1 to another semihoop H2, which is a generalization of internal states (or state operators) on a semihoop H. Also we give a type of special state maps from a semihoop H1 to H1, which is called internal state maps (or IS-maps). Then we give some examples and basic properties of (internal) state maps on semihoops. Moreover, we discuss the relations between state maps and internal states on other algebras. Then we introduce several kinds of filters by state maps on semihoops, called SM-filters, state filters and dual state filters, respectively, and discuss the relations among them. Furthermore we introduce and study the notion of prime SM-filters on semihoops. Finally, using SM-filter, we characterize two kinds of state semihoops.
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𝓜𝓝-convergence and lim-inf𝓜-convergence in partially ordered sets

Sun, Tao; Li, Qingguo; Fan, Nianbai

2018 Open Mathematics

doi: 10.1515/math-2018-0090

AbstractIn this paper, we first introduce the notion of 𝓜𝓝-convergence in posets as an unified form of O-convergence and O2-convergence. Then, by studying the fundamental properties of 𝓜𝓝-topology which is determined by 𝓜𝓝-convergence according to the standard topological approach, an equivalent characterization to the 𝓜𝓝-convergence being topological is established. Finally, the lim-inf𝓜-convergence in posets is further investigated, and a sufficient and necessary condition for lim-inf𝓜-convergence to be topological is obtained.
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Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation

Wei, Leilei; Mu, Yundong

2018 Open Mathematics

doi: 10.1515/math-2018-0091

AbstractIn this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes carefully we prove stability and give an error estimate. Finally some numerical examples are computed to show the convergence order and excellent numerical performance of proposed method.
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New topology in residuated lattices

Holdon, L.C.

2018 Open Mathematics

doi: 10.1515/math-2018-0092

AbstractIn this paper, by using the notion of upsets in residuated lattices and defining the operator Da(X), for an upset X of a residuated lattice L we construct a new topology denoted by τa and (L, τa) becomes a topological space. We obtain some of the topological aspects of these structures such as connectivity and compactness. We study the properties of upsets in residuated lattices and we establish the relationship between them and filters. O. Zahiri and R. A. Borzooei studied upsets in the case of BL-algebras, their results become particular cases of our theory, many of them work in residuated lattices and for that we offer complete proofs. Moreover, we investigate some properties of the quotient topology on residuated lattices and some classes of semitopological residuated lattices. We give the relationship between two types of quotient topologies τa/F and τa−$\begin{array}{}\displaystyle\mathop {{\tau _a}}\limits^ -\end{array}$. Finally, we study the uniform topology τΛ¯$\begin{array}{}\displaystyle{\tau _{\bar \Lambda }}\end{array}$ and we obtain some conditions under which (L/J,τΛ¯)$\begin{array}{}\displaystyle(L/J,{\tau _{\bar \Lambda }})\end{array}$ is a Hausdorff space, a discrete space or a regular space ralative to the uniform topology. We discuss briefly the applications of our results on classes of residuated lattices such as divisible residuated lattices, MV-algebras and involutive residuated lattices and we find that any of this subclasses of residuated lattices with respect to these topologies form semitopological algebras.
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Optimality and duality in set-valued optimization utilizing limit sets

Kong, Xiangyu; Zhang, Yinfeng; Yu, GuoLin

2018 Open Mathematics

doi: 10.1515/math-2018-0095

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.
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An improved Schwarz Lemma at the boundary

Mercer, Peter R.

2018 Open Mathematics

doi: 10.1515/math-2018-0096

AbstractWe obtain an new boundary Schwarz inequality, for analytic functions mapping the unit disk to itself. The result contains and improves a number of known estimates.
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Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit

Fan, Xiaoting; Wang, Shu; Xu, Wen-Qing; Liu, Mingshuo

2018 Open Mathematics

doi: 10.1515/math-2018-0094

AbstractThe main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O(ε32)$O(\varepsilon^{\frac{3}{2}})$ and O(ε2).
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Toeplitz matrices whose elements are coefficients of Bazilevič functions

Radhika, Varadharajan; Jahangiri, Jay M.; Sivasubramanian, Srikandan; Murugusundaramoorthy, Gangadharan

2018 Open Mathematics

doi: 10.1515/math-2018-0093

AbstractWe consider the Toeplitz matrices whose elements are the coefficients of Bazilevič functions and obtain upper bounds for the first four determinants of these Toeplitz matrices. The results presented here are new and noble and the only prior compatible results are the recent publications by Thomas and Halim [1] for the classes of starlike and close-to-convex functions and Radhika et al. [2] for the class of functions with bounded boundary rotation.
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Epi-mild normality

Kalantan, Lutfi; Alshammari, Ibtesam

2018 Open Mathematics

doi: 10.1515/math-2018-0099

AbstractA space (X, τ) is called epi-mildly normal if there exists a coarser topology τ′ on X such that (X, τ′) is Hausdorff (T2) mildly normal. We investigate this property and present some examples to illustrate the relationships between epi-mild normality and other weaker kinds of normality.
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Nonlinear elastic beam problems with the parameter near resonance

Xu, Man; Ma, Ruyun

2018 Open Mathematics

doi: 10.1515/math-2018-0097

AbstractIn this paper, we consider the nonlinear fourth order boundary value problem of the formu(4)(x)−λu(x)=f(x,u(x))−h(x),x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,$$ \begin{array}\text \left\{ \begin{aligned}&u^{(4)}(x)-\lambda u(x)=f(x, u(x))-h(x), \ \ x\in (0,1),\\&u(0)=u(1)=u'(0)=u'(1)=0,\\\end{aligned}\right.\end{array} $$which models a statically elastic beam with both end-points cantilevered or fixed. We show the existence of at least one or two solutions depending on the sign of λ−λ1, where λ1 is the first eigenvalue of the corresponding linear eigenvalue problem and λ is a parameter. The proof of the main result is based upon the method of lower and upper solutions and global bifurcation techniques.
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Orlicz difference bodies

Shi, Wei; Wang, Weidong; Ma, Tongyi

2018 Open Mathematics

doi: 10.1515/math-2018-0098

AbstractIn this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars.
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The Picard group of Brauer-Severi varieties

Badr, Eslam; Bars, Francesc; García, Elisa Lorenzo

2018 Open Mathematics

doi: 10.1515/math-2018-0101

AbstractIn this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces. To produce these generators we use the theory of twists of smooth plane curves.
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Galoisian and qualitative approaches to linear Polyanin-Zaitsev vector fields

Acosta-Humánez, Primitivo B.; Reyes-Linero, Alberto; Rodriguez-Contreras, Jorge

2018 Open Mathematics

doi: 10.1515/math-2018-0102

AbstractIn this paper we study a particular parametric family of differential equations, the so-called Linear Polyanin-Zaitsev Vector Field, which has been introduced in a general case in [1] as a correction of a family presented in [2]. Linear Polyanin-Zaitsev Vector Field is transformed into a Liénard equation and, in particular, we obtain the Van Der Pol equation. We present some algebraic and qualitative results to illustrate some interactions between algebra and the qualitative theory of differential equations in this parametric family.
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Weak group inverse

Wang, Hongxing; Chen, Jianlong

2018 Open Mathematics

doi: 10.1515/math-2018-0100

AbstractIn this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses.
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Infinite growth of solutions of second order complex differential equation

Zhang, Guowei

2018 Open Mathematics

doi: 10.1515/math-2018-0103

AbstractIn this paper we study the growth of solutions of second order differential equation f′′ + A(z)f′ + B(z)f = 0. Under certain hypotheses, the non-trivial solution of this equation is of infinite order.
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Semi-Hurewicz-Type properties in ditopological texture spaces

Ullah, Hafiz; Khan, Moiz ud Din

2018 Open Mathematics

doi: 10.1515/math-2018-0104

AbstractIn this paper we will define and discuss semi-Hurewicz type covering properties in ditopological texture spaces. We consider the behaviour of semi-Hurewicz and co-semi-Hurewicz selection properties under direlation and difunction between ditopological texture spaces.
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Chaos and bifurcation in the controlled chaotic system

Liu, Yongjian; Huang, Xiezhen; Zheng, Jincun

2018 Open Mathematics

doi: 10.1515/math-2018-0105

AbstractIn this paper, chaos and bifurcation are explored for the controlled chaotic system, which is put forward based on the hybrid strategy in an unusual chaotic system. Behavior of the controlled system with variable parameter is researched in detain. Moreover, the normal form theory is used to analyze the direction and stability of bifurcating periodic solution.
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Translatability and translatable semigroups

Dudek, Wieslaw A.; Monzo, Robert A. R.

2018 Open Mathematics

doi: 10.1515/math-2018-0106

AbstractThe concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved. Necessary and sufficient conditions are found for a left cancellative k-translatable groupoid to be a semigroup. Any such semigroup is proved to be left unitary and a union disjoint copies of cyclic groups of the same order. Methods of constructing k-translatable semigroups that are not left cancellative are given.
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Sharp bounds for partition dimension of generalized Möbius ladders

Hussain, Zafar; Khan, Junaid Alam; Munir, Mobeen; Saleem, Muhammad Shoaib; Iqbal, Zaffar

2018 Open Mathematics

doi: 10.1515/math-2018-0109

AbstractThe concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing. It is hard to compute exact values of partition dimension for a graphic metric space, (G, dG) and networks. In this article, we give the sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, Mm, n, for all n≥3 and m≥2.
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Uniqueness theorems for L-functions in the extended Selberg class

Hao, Wen-Jie; Chen, Jun-Fan

2018 Open Mathematics

doi: 10.1515/math-2018-0107

AbstractIn this paper, we obtain uniqueness theorems of L-functions from the extended Selberg class, which generalize and complement some recent results due to Li, Wu-Hu, and Yuan-Li-Yi.
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An effective algorithm for globally solving quadratic programs using parametric linearization technique

Tang, Shuai; Chen, Yuzhen; Guo, Yunrui

2018 Open Mathematics

doi: 10.1515/math-2018-0108

AbstractIn this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc. By utilizing new parametric linearization technique, we can derive the parametric linear programming relaxation problem of the quadratic programs with quadratic constraints. To improve the computational speed of the proposed algorithm, some interval reduction operations are used to compress the investigated interval. By subsequently partitioning the initial box and solving a sequence of parametric linear programming relaxation problems the proposed algorithm is convergent to the global optimal solution of the initial problem. Finally, compared with some known algorithms, numerical experimental results demonstrate that the proposed algorithm has higher computational efficiency.
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Bounds of Strong EMT Strength for certain Subdivision of Star and Bistar

Kanwal, Salma; Riasat, Ayesha; Imtiaz, Mariam; Iftikhar, Zurdat; Javed, Sana; Ashraf, Rehana

2018 Open Mathematics

doi: 10.1515/math-2018-0111

AbstractA super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) onto {1, 2,…,|V (℘)∪E(℘) |} such that ∃ a constant “a” satisfying ϒ(υ) + ϒ(υν) + ϒ(ν) = a, for each edge υν ∈E(℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified as μs(℘)$\mu_{s}(\wp)$ is the least non-negative integer n so that ℘∪nK1 has a SEMT labeling or +∞ if such n does not exist. In this paper, we will formulate the results on SEMT labeling and deficiency of fork, H -tree and disjoint union of fork with star, bistar and path. Moreover, we will evaluate the SEMT strength for trees.
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On categorical aspects of S -quantales

Zhang, Xia; Zhou, Yunyan

2018 Open Mathematics

doi: 10.1515/math-2018-0110

AbstractS-quantales are characterized as injective objects in the category of S-posets with respect to certain class of homomorphisms that are order-preserving mappings. This paper is devoted to exhibitions of categorical structures on S-quantales.
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On the algebraicity of coefficients of half-integral weight mock modular forms

Choi, SoYoung; Kim, Chang Heon

2018 Open Mathematics

doi: 10.1515/math-2018-0112

AbstractExtending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.
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Dunkl analogue of Szász-mirakjan operators of blending type

Deshwal, Sheetal; Agrawal, P.N.; Araci, Serkan

2018 Open Mathematics

doi: 10.1515/math-2018-0116

AbstractIn the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of convergence in terms of the modulus of continuity, second order modulus of continuity via Steklov-mean, the degree of approximation for Lipschitz class of functions and the weighted space. Furthermore, we obtain the rate of convergence of the considered operators with the aid of the unified Ditzian-Totik modulus of smoothness and for functions having derivatives of bounded variation.
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Majorization, “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law

Latif, Naveed; Pečarić, Đilda; Pečarić, Josip

2018 Open Mathematics

doi: 10.1515/math-2018-0113

AbstractIn this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, “useful” Csiszár functional and “useful” Zipf-Mandelbrot law. By considering “useful” Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given.
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Global stability of a distributed delayed viral model with general incidence rate

Ávila-Vales, Eric; Canul-Pech, Abraham; Rivero-Esquivel, Erika

2018 Open Mathematics

doi: 10.1515/math-2018-0117

AbstractIn this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.
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Analyzing a generalized pest-natural enemy model with nonlinear impulsive control

Li, Changtong; Tang, Sanyi

2018 Open Mathematics

doi: 10.1515/math-2018-0114

AbstractDue to resource limitation, nonlinear impulsive control tactics related to integrated pest management have been proposed in a generalized pest-natural enemy model, which allows us to address the effects of nonlinear pulse control on the dynamics and successful pest control. The threshold conditions for the existence and global stability of pest-free periodic solution are provided by Floquet theorem and analytic methods. The existence of a nontrivial periodic solution is confirmed by showing the existence of nontrivial fixed point of the stroboscopic mapping determined by time snapshot, which equals to the common impulsive period. In order to address the applications of generalized results and to reveal how the nonlinear impulses affect the successful pest control, as an example the model with Holling II functional response function is investigated carefully. The main results reveal that the pest free periodic solution and a stable interior positive periodic solution can coexist for a wide range of parameters, which indicates that the local stability does not imply the global stability of the pest free periodic solution when nonlinear impulsive control is considered, and consequently the resource limitation (i.e. nonlinear control) may result in difficulties for successful pest control.
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Boundary value problems of a discrete generalized beam equation via variational methods

Liu, Xia; Zhou, Tao; Shi, Haiping

2018 Open Mathematics

doi: 10.1515/math-2018-0121

AbstractThe authors explore the boundary value problems of a discrete generalized beam equation. Using the critical point theory, some sufficient conditions for the existence of the solutions are obtained. Several consequences of the main results are also presented. Examples are given to illustrate the theorems.
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Common fixed point theorem of six self-mappings in Menger spaces using (CLRST) property

Liu, Xiao-lan; Zhou, Mi; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Damjanović, Boško

2018 Open Mathematics

doi: 10.1515/math-2018-0120

AbstractIn this paper, we study the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by (CLRST)) of two pairs. Our results improve, extend, complement and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.
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Periodic and subharmonic solutions for a 2nth-order p-Laplacian difference equation containing both advances and retardations

Mei, Peng; Zhou, Zhan

2018 Open Mathematics

doi: 10.1515/math-2018-0123

AbstractWe consider a 2nth-order nonlinear difference equation containing both many advances and retardations with p-Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.
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Spectrum of free-form Sudoku graphs

Abudayah, Mohammad; Alomari, Omar; Sander, Torsten

2018 Open Mathematics

doi: 10.1515/math-2018-0125

AbstractA free-form Sudoku puzzle is a square arrangement of m ×m cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers 1, . . , m in the cells such that the numbers in every row, column and block are distinct. Represent each cell by a vertex and add edges between two vertices exactly when the corresponding cells, according to the rules, must contain different numbers. This yields the associated free-form Sudoku graph. This article studies the eigenvalues of free-form Sudoku graphs, most notably integrality. Further, we analyze the evolution of eigenvalues and eigenspaces of such graphs when the associated puzzle is subjected to a ‘blow up’ operation, which scales the cell grid including its block partition.
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Regularity of fuzzy convergence spaces

Li, Lingqiang; Jin, Qiu; Yao, Bingxue

2018 Open Mathematics

doi: 10.1515/math-2018-0118

Abstract(Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we discuss a regularity of ⊤-convergence spaces.
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The well-posedness of solution to a compressible non-Newtonian fluid with self-gravitational potential

Song, Yukun; Chen, Shuai; Liu, Fengming

2018 Open Mathematics

doi: 10.1515/math-2018-0122

AbstractWe study the initial boundary value problem of a compressible non-Newtonian fluid. The system describes the motion of the compressible viscous isentropic gas flow driven by the non-Newtonian self-gravitational force. The existence of strong solutions are derived in one dimensional bounded intervals by constructing a semi-discrete Galerkin scheme. Moreover, the uniqueness of solutions are also investigated. The main point of the study is that the viscosity term and potential term are fully nonlinear, and the initial vacuum is allowed.
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On further refinements for Young inequalities

Furuichi, Shigeru; Moradi, Hamid Reza

2018 Open Mathematics

doi: 10.1515/math-2018-0115

AbstractIn this paper sharp results on operator Young’s inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young’s inequality. Secondly, we give an additive result, which improves a well-known inequality due to Tominaga. We also provide some estimates for the difference A1/2(A−1/2BA−1/2)vA1/2-{(1-v)A + vB} for v∉[ 0,1].
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Pretty good state transfer on 1-sum of star graphs

Hou, Hailong; Gu, Rui; Tong, Mengdi

2018 Open Mathematics

doi: 10.1515/math-2018-0119

AbstractLet A be the adjacency matrix of a graph G and suppose U(t) = exp(itA). We say that we have perfect state transfer in G from the vertex u to the vertex v at time t if there is a scalar γ of unit modulus such that U(t)eu = γ ev. It is known that perfect state transfer is rare. So C.Godsil gave a relaxation of this definition: we say that we have pretty good state transfer from u to v if there exists a complex number γ of unit modulus and, for each positive real ϵ there is a time t such that ‖U(t)eu–γ ev‖ < ϵ. In this paper, the quantum state transfer on 1-sum of star graphs Fk,l is explored. We show that there is no perfect state transfer on Fk,l, but there is pretty good state transfer on Fk,l if and only if k = l.
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On a conjecture about generalized Q-recurrence

Alkan, Altug

2018 Open Mathematics

doi: 10.1515/math-2018-0124

AbstractChaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested recurrences. In this study, a recent generalization of Hofstadter’s famous Q-sequence is studied beyond the known methods of generational approaches in order to propose a generalized conjecture regarding the existence of infinitely many different solutions for all corresponding recurrences of this generalization.
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Univariate approximating schemes and their non-tensor product generalization

Mustafa, Ghulam; Bashir, Robina

2018 Open Mathematics

doi: 10.1515/math-2018-0126

AbstractThis article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.
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Multi-term fractional differential equations with nonlocal boundary conditions

Ahmad, Bashir; Alghamdi, Najla; Alsaedi, Ahmed; Ntouyas, Sotiris K.

2018 Open Mathematics

doi: 10.1515/math-2018-0127

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.
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Homoclinic and heteroclinic solutions to a hepatitis C evolution model

Telksnys, Tadas; Navickas, Zenonas; Marcinkevicius, Romas; Cao, Maosen; Ragulskis, Minvydas

2018 Open Mathematics

doi: 10.1515/math-2018-0130

AbstractHomoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.
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Regularity of one-sided multilinear fractional maximal functions

Liu, Feng; Xu, Lei

2018 Open Mathematics

doi: 10.1515/math-2018-0129

AbstractIn this paper we introduce and investigate the regularity properties of one-sided multilinear fractional maximal operators, both in continuous case and in discrete case. In the continuous setting, we prove that the one-sided multilinear fractional maximal operatorsMβ+andMβ−$\mathfrak{M}_\beta^{+}\; \text{and}\, \mathfrak{M}_\beta^{-}$map W1,p1 (ℝ)×· · ·×W1,pm (ℝ) into W1,q(ℝ) with 1 < p1, … , pm < ∞, 1 ≤ q < ∞ and 1/q=∑i=1m1/pi−β$1/q= \sum_{i=1}^m1/p_i-\beta$, boundedly and continuously. In the discrete setting, we show that the discrete one-sided multilinear fractional maximal operators are bounded and continuous from ℓ1(ℤ)×· · ·×ℓ1(ℤ) to BV(ℤ). Here BV(ℤ) denotes the set of functions of bounded variation defined on ℤ. Our main results represent significant and natural extensions of what was known previously.
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Galois connections between sets of paths and closure operators in simple graphs

Šlapal, Josef

2018 Open Mathematics

doi: 10.1515/math-2018-0128

AbstractFor every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph. We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.
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KGSA: A Gravitational Search Algorithm for Multimodal Optimization based on K-Means Niching Technique and a Novel Elitism Strategy

Golzari, Shahram; Zardehsavar, Mohammad Nourmohammadi; Mousavi, Amin; Saybani, Mahmoud Reza; Khalili, Abdullah; Shamshirband, Shahaboddin

2018 Open Mathematics

doi: 10.1515/math-2018-0132

AbstractGravitational Search Algorithm (GSA) is a metaheuristic for solving unimodal problems. In this paper, a K-means based GSA (KGSA) for multimodal optimization is proposed. This algorithm incorporates K-means and a new elitism strategy called “loop in loop” into the GSA. First in KGSA, the members of the initial population are clustered by K-means. Afterwards, new population is created and divided in different niches (or clusters) to expand the search space. The “loop in loop” technique guides the members of each niche to the optimum direction according to their clusters. This means that lighter members move faster towards the optimum direction of each cluster than the heavier members. For evaluations, KGSA is benchmarked on well-known functions and is compared with some of the state-of-the-art algorithms. Experiments show that KGSA provides better results than the other algorithms in finding local and global optima of constrained and unconstrained multimodal functions.
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θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

Yang, Yanqi; Tao, Shuangping

2018 Open Mathematics

doi: 10.1515/math-2018-0133

AbstractThe aim of this paper is to deal with the boundedness of the θ-type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p(⋅), q(⋅). It is proved that the θ-type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents K˙p(⋅)α,q(⋅)(Rn).$\begin{array}{}\displaystyle\dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}).\end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.
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An integral that counts the zeros of a function

Hungerbühler, Norbert; Wasem, Micha

2018 Open Mathematics

doi: 10.1515/math-2018-0131

AbstractGiven a real function f on an interval [a, b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f, f′ and f″. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of f by evaluating finitely many values of f, f′ and f″. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.
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On rough sets induced by fuzzy relations approach in semigroups

Prasertpong, Rukchart; Siripitukdet, Manoj

2018 Open Mathematics

doi: 10.1515/math-2018-0136

AbstractIn this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.
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Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation

Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc

2018 Open Mathematics

doi: 10.1515/math-2018-0134

AbstractThis paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential equations, via adaptive generalized Polynomial Chaos (gPC) and the stochastic Galerkin projection technique. Unlike the random Fröbenius method, which can only deal with particular random linear differential equations and needs the random inputs (coefficients and forcing term) to be analytic, adaptive gPC allows approximating the expectation and covariance of the solution stochastic process to general random second-order linear differential equations. The random inputs are allowed to functionally depend on random variables that may be independent or dependent, both absolutely continuous or discrete with infinitely many point masses. These hypotheses include a wide variety of particular differential equations, which might not be solvable via the random Fröbenius method, in which the random input coefficients may be expressed via a Karhunen-Loève expansion.
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The fourth order strongly noncanonical operators

Baculikova, Blanka; Dzurina, Jozef

2018 Open Mathematics

doi: 10.1515/math-2018-0135

AbstractIt is shown that the strongly noncanonical fourth order operatorLy=r3(t)r2(t)r1(t)y′(t)′′′$$\begin{array}{}\displaystyle\mathcal{L}\,y=\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'\end{array}$$can be written in essentially unique canonical form asLy=q4(t)q3(t)q2(t)q1(t)q0(t)y(t)′′′′.$$\begin{array}{}\displaystyle\mathcal{L}\,y = q_4(t)\left(q_3(t)\left(q_2(t)\left(q_1(t)\left(q_0(t)y(t)\right)'\right)'\right)'\right)'.\end{array}$$The canonical representation essentially simplifies examination of the fourth order strongly noncanonical equationsr3(t)r2(t)r1(t)y′(t)′′′+p(t)y(τ(t))=0.$$\begin{array}{}\displaystyle\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0.\end{array}$$
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