On a viscous two-fluid channel flow including evaporationSocolowsky, 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.

Generation of pseudo-random numbers with the use of inverse chaotic transformationLawnik, 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.

Evaluation of integrals with hypergeometric and logarithmic functionsSofo, 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.

Oscillation of first order linear differential equations with several non-monotone delaysAttia, 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.

Generalized state maps and states on pseudo equality algebrasCheng, 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.

A further study on ordered regular equivalence relations in ordered semihypergroupsTang, 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.

Rank relations between a {0, 1}-matrix and its complementMa, 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.

Time parallelization scheme with an adaptive time step size for solving stiff initial value problemsBu, 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.

On some fixed point results for (s, p, α)-contractive mappings in b-metric-like spaces and applications to integral equationsZoto, 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.

On algebraic characterization of SSC of the Jahangir’s graph 𝓙n,mRaza, 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.

A primal-dual approach of weak vector equilibrium problemsLászló, 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.

On new strong versions of Browder type theoremsSanabria, 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).

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.

Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponentsYang, 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.

Introduction to disoriented knot theoryAltıntaş, 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.

Restricted triangulation on circulant graphsAli, 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.

Disjointed sum of products by a novel technique of orthogonalizing ORingCan, 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.

A parametric linearizing approach for quadratically inequality constrained quadratic programsJiao, 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.

Vector fields satisfying the barycenter propertyLee, 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].

Recursive interpolating sequencesTugores, 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.

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.

On 𝓠-regular semigroupsFeng, 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.

One kind power mean of the hybrid Gauss sumsLan, 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.

A reduced space branch and bound algorithm for a class of sum of ratios problemsZhao, 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.

A relaxed block splitting preconditioner for complex symmetric indefinite linear systemsHuang, 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.

A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environmentYin, 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.

Dynamic behavior analysis of a prey-predator model with ratio-dependent Monod-Haldane functional responseFeng, 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.

The points and diameters of quantalesLiang, 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.

Linearity in decimation-based generators: an improved cryptanalysis on the shrinking generatorCardell, 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.

On dynamic network security: A random decentering algorithm on graphsTrobajo, 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.

Directed colimits of some flatness properties and purity of epimorphisms in S-posetsLiang, 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.

Super (a, d)-H-antimagic labeling of subdivided graphsTaimur, 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.

On generalized P-reducible Finsler manifoldsZamanzadeh, 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.

On Banach and Kuratowski Theorem, K-Lusin sets and strong sequencesJureczko, 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.

On the boundedness of square function generated by the Bessel differential operator in weighted Lebesque Lp,α spacesBayrakci, 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.

On the different kinds of separability of the space of Borel functionsOsipov, 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.

Functional analysis method for the M/G/1 queueing model with single working vacationKasim, 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.

Domination in 4-regular Knödel graphsMojdeh, 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.

Algebras of right ample semigroupsGuo, 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.

A note on the three-way generalization of the Jordan canonical formCui, 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.

On some varieties of ai-semirings satisfying xp+1 ≈ xWang, 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.

Abstract-valued Orlicz spaces of range-varying typeZhang, 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.

Multipreconditioned GMRES for simulating stochastic automata networksWen, 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.

Transitivity of the εm-relation on (m-idempotent) hyperringsNorouzi, 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.

Learning Bayesian networks based on bi-velocity discrete particle swarm optimization with mutation operatorWang, 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.

Two asymptotic expansions for gamma function developed by Windschitl’s formulaYang, 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=2πxxexxsinh1xx/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.

State maps on semihoopsFu, 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.

𝓜𝓝-convergence and lim-inf𝓜-convergence in partially ordered setsSun, 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.

New topology in residuated latticesHoldon, 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.

Nonlinear elastic beam problems with the parameter near resonanceXu, 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.

Weak group inverseWang, 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.

Translatability and translatable semigroupsDudek, 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.

Sharp bounds for partition dimension of generalized Möbius laddersHussain, 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.

An effective algorithm for globally solving quadratic programs using parametric linearization techniqueTang, 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.

Bounds of Strong EMT Strength for certain Subdivision of Star and BistarKanwal, 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.

Dunkl analogue of Szász-mirakjan operators of blending typeDeshwal, 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.

Analyzing a generalized pest-natural enemy model with nonlinear impulsive controlLi, 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.

Spectrum of free-form Sudoku graphsAbudayah, 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.

Pretty good state transfer on 1-sum of star graphsHou, 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.

On a conjecture about generalized Q-recurrenceAlkan, 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.

Univariate approximating schemes and their non-tensor product generalizationMustafa, 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.

Homoclinic and heteroclinic solutions to a hepatitis C evolution modelTelksnys, 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.

Regularity of one-sided multilinear fractional maximal functionsLiu, 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.

Galois connections between sets of paths and closure operators in simple graphsŠlapal, 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.

KGSA: A Gravitational Search Algorithm for Multimodal Optimization based on K-Means Niching Technique and a Novel Elitism StrategyGolzari, 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.

An integral that counts the zeros of a functionHungerbühler, 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.

On rough sets induced by fuzzy relations approach in semigroupsPrasertpong, 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.

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 simulationCalatayud, 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.

The fourth order strongly noncanonical operatorsBaculikova, 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.$$\begin{array}{}\displaystyle\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0.\end{array}$$