$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 16 Issue 1

January 2018

Issue of Open Mathematics

Submit manuscript

Contents
Journal Overview

In (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.

It is shown that the strongly noncanonical fourth order operator Ly=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 as Ly=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 equations r3(t)r2(t)r1(t)y′(t)′′′+p(t)y(τ (t))=0.$$\begin{array}{} \displaystyle \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0. \end{array}$$

Random 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.

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes original and relevant works on topics across the full span of mathematics. The journal's primary goal is to maintain the high quality of its published content and to provide free, instant, and continued access to all content worldwide.

AIMS AND SCOPE
Open Mathematics aims to promote knowledge directly relevant to all fields of mathematics. Subject areas suitable for publication include, but are not limited to, the following:

Algebra, Algebraic Geometry, Category Theory, Complex Analysis, Control Theory and Optimization, Differential Equations, Differential Geometry, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Functional Analysis, Geometry, Mathematical Logic and Foundations, Mathematical Physics, Number Theory, Numerical Analysis, Operator Theory, Probability Theory and Statistics, Real Analysis, and Topology.

The journal accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.

Volume 16 Issue 1

Issue of Open Mathematics

Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras

Abstract

On a viscous two-fluid channel flow including evaporation

Abstract

Generation of pseudo-random numbers with the use of inverse chaotic transformation

Abstract

Singular Cauchy problem for the general Euler-Poisson-Darboux equation

General Euler-Poisson-Darboux equation

Abstract

Ternary and n-ary f-distributive structures

Abstract

On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics

Abstract

Evaluation of integrals with hypergeometric and logarithmic functions

Abstract

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Abstract

Oscillation of first order linear differential equations with several non-monotone delays

Abstract

Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Abstract

The log-concavity of the q-derangement numbers of type B

Abstract

Generalized state maps and states on pseudo equality algebras

Abstract

Monotone subsequence via ultrapower

Abstract

Note on group irregularity strength of disconnected graphs

Abstract

On the security of the Courtois-Finiasz-Sendrier signature

Abstract

A further study on ordered regular equivalence relations in ordered semihypergroups

Abstract

On the structure vector field of a real hypersurface in complex quadric

Abstract

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

Abstract

Lie n superderivations and generalized Lie n superderivations of superalgebras

Abstract

Time parallelization scheme with an adaptive time step size for solving stiff initial value problems

Abstract

Stability problems and numerical integration on the Lie group SO(3) × R3 × R3

Abstract

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

Abstract

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

Abstract

A greedy algorithm for interval greedoids

Abstract

On nonlinear evolution equation of second order in Banach spaces

Abstract

A primal-dual approach of weak vector equilibrium problems

Abstract

On new strong versions of Browder type theorems

Abstract

A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Abstract

Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖i| ≤ 7)

Abstract

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

Abstract

Introduction to disoriented knot theory

Abstract

Restricted triangulation on circulant graphs

Abstract

Boundedness control sets for linear systems on Lie groups

Abstract

Chen’s inequalities for submanifolds in (κ, μ)-contact space form with a semi-symmetric metric connection

Abstract

Disjointed sum of products by a novel technique of orthogonalizing ORing

Abstract

A parametric linearizing approach for quadratically inequality constrained quadratic programs

Abstract

Generalizations of Steffensen’s inequality via the extension of Montgomery identity

Abstract

Vector fields satisfying the barycenter property

Abstract

On the freeness of hypersurface arrangements consisting of hyperplanes and spheres

Stability problems and numerical integration on the Lie group SO(3) × R³ × R³

On algebraic characterization of SSC of the Jahangir’s graph 𝓙_n,m

Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖_i| ≤ 7)

Constacyclic codes over 𝔽_p^m[u₁, u₂,⋯,u_k]/〈 u_i² = u_i, u_iu_j = u_ju_i〉

On the boundedness of square function generated by the Bessel differential operator in weighted Lebesque L_p,α spaces