Open Mathematics Volume 16 Issue 1

Journal Article

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.

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Journal Article

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...

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Journal Article

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,...

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Journal Article

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.

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Journal Article

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...

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Journal Article

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 =...

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Journal Article

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...

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Journal Article

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.

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Journal Article

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+),...

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Journal Article

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...

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Open Mathematics Volume 16 Issue 1

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