Automorphism subgroups for designs with $$\lambda =1$$ λ = 1

Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order,  if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there...     

The existence of cyclic (v, 4, 1)-designs

Designs, Codes and Cryptography - Even though Peltesohn proved that a cyclic (v, 3, 1)-design exists if and only if $$v\equiv 1,3\pmod {6}$$ as early as 1939, the problem of...     

Tag-based ABE in prime-order groups via pair encoding

Designs, Codes and Cryptography - Predicate/pair encodings are simple frameworks for designing attribute-based encryption ( $$\textsf {ABE}$$ ) for complex predicates, with pair encodings...     

Hamming weight distributions of multi-twisted codes over finite fields

Designs, Codes and Cryptography - Let $${\mathbb {F}}_q$$ denote the finite field of order q,  and let $$n = m_1+m_2+\cdots +m_\ell ,$$ where $$m_1,m_2,\ldots ,m_\ell $$ are arbitrary...     

Isomorphism of maximum length circuit codes

Designs, Codes and Cryptography - Douglas (J Comb Theory 6(4):323–339, 1969) proved that for odd spread k and dimension $$d={\frac{1}{2}(3k+3)}$$ all maximum length (d, k) circuit...     

Double Hopf bifurcation and chaos in Liu system with delayed feedback

In this paper, we consider the stability of equilibria, Hopf and double Hopf bifurcation in Liu system with delay feedback. Firstly, we identify the critical values for stability switches and Hopf bifurcationusing the method of bifurcation analysis. When we choose appropriate feedback strength and delay, two symmetrical nontrivial equilibria of Liusystem can be controlled to be stable at the same time, and the stable bifurcating periodic solutions occur in the neighborhood of the two equilibria at the same time. Secondly, by applying the normal form method and center manifold theory,the normal form near the double Hopf bifurcation, as well as classifications of local dynamics are analyzed. Furthermore, we give the bifurcation diagram to illustrate numerically that a family of stable periodic solutions bifurcated from Hopf bifurcation occur in a large region of delay and the Liu system with delay can appear the phenomenon of ``chaos switchover''.     

Bifurcation of limit cycles and isochronous center at infinity for a class of differential systems

In this paper, we study a seventh degree polynomial differential system with full linear terms and cubic terms. The conditions of infinity to be a center and to be a fine focus of the highestorder are given and it is proved that this system has eight limit cycles in the neighborhood of infinity. Moreover, the conditions of infinity to be an isochronous center for a rational system associated the seventh degree polynomial differential system are obtained.     

Cauchy problem for the Zakharov System Arising from Ion-Acoustic Modes with low regularity data

We prove local well-posedness results for the Zakharov System Arising from Ion-Acoustic Modes in two spacial dimension with large initial data in low regularity Sobolev space \(   (\dot{H}^1 \bigcup H^{\frac{1}{2}})\times L^2 \times H^{-1}  \).  Using ”derivative sharing”, the local well-posedness results in \( (\dot{H}^1 \bigcup H^{\frac{1}{2}-\delta})\times H^{\delta} \times H^{-1+\delta}\)  are also obtained, for any  0 \(\leq \delta \leq 1/2 \).     

On uniqueness and analyticity in thermoviscoelastic solids with voids

In this paper we consider the most general system proposed to describe the thermoviscoelasticity with voids. We study two qualitative properties of the solutions of this theory. First, we obtain a uniqueness result when we do not assume any sign to the internal energy. Second we extend some previous results and prove the analyticity of the solutions. The impossibility of localization in time of the solutions is a consequence. Last result we present corresponds to the analyticity of solutions in case that the dissipation is not very strong, but with suitable coupling terms.     

Locally Finite Groups with Prescribed Structure of Finite Subgroups

Siberian Mathematical Journal - Let  $ {\mathfrak{M}} $ be a set of finite groups. Given a group  $ G $ , denote the set of all subgroups of  $ G $...     

On the integrability of the differential systems in dimension two and of the polynomial differential systems in arbitrary dimension

This is a survey on recent results providing sufficient conditions for the existence of a first integral, first for vector fields defined on real surfaces, and second for polynomial vector fields in \(R^n\) or \(C^n\) with \(n\geq 2\). We also provide an open question and some applications based on the existence of such first integrals.               

Essentially Invertible Measurable Operators Affiliated to a Semifinite von Neumann Algebra and Commutators

Siberian Mathematical Journal - Suppose that a von Neumann operator algebra  $ {\mathcal{M}} $ acts on a Hilbert space  $ {\mathcal{H}} $ and $ \tau $...     

Numerical solution of fuzzy Camassa-Holm equation by using Homotopy analysis methods

In this paper, a fuzzy Camassa-Holm equation is solved by using the  homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed method are proved.     

Resonances of the SD oscillator due to the discontinuous phase

Resonant phenomenon of a harmonically excited system with multiple well dynamics plays a very important role in nonlinear dynamics research. In this paper, we investigate resonant behaviors of a discontinuous forced SD system with snap-through buckling and double-well dynamics. Firstly, a discontinuous time dependent Hamiltonian is derived from the discontinuous stage of SD oscillator providing a Du±ng type nonlinearity with snap-through buckling and double-well dynamics. This system comprises two subsystems connected at x = 0, where the system is discontinuous. We construct a series of generating functions and canonical transformations to get the canonical form of the system to reveal the complicated resonant behavior of the system. Furthermore, we introduce a composed winding number to explorer the complicated resonant phenomena of the system.This formulation for resonant phenomena given in this paper generalizes the formulation of n!0 = m! in regular perturbation theory, where n and m are relative prime integers,!0 and ! are the natural frequency and external frequencies respectively. Understanding the resonant behaviors of the SD oscillator at discontinuous stage enables us to further reveal the vibrational energy transition mechanism of the smooth and discontinuous nonlinear dynamic system.     

Intersections of Three Nilpotent Subgroups in a Finite Group

Siberian Mathematical Journal - We complete the proof of the theorem that any nilpotent subgroups  $ A $ , $ B $ , and  $ C $ of a finite group  $ G $ satisfy...     

Nonlinear boundary conditions derived by singular pertubation in age structured population dynamics model

In this article, we derive Ricker’s [22, 23] type nonlinear boundary condition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the convergence uniformly of the singularly perturbed system with respect to the initial distribution in bounded sets.     

Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach

In this paper, we study the traveling wave solutions of the Kaup-Kupershmidt (KK) equation through using the dynamical system approach, which is an integrable fifth-order wave equation. Based on Cosgrove's work [3] and the phase analysis method of dynamical systems, infinitely many soliton solutions are presented in an explicit form. To guarantee the existence of soliton solutions, we discuss the parameters range as well as geometrical explanation of soliton solutions.     

On the existence of bubble-type solutions of nonlinear singular problems

Considered in this paper is a class of singular boundary value problem, arising in hydrodynamics and nonlinear field theory, when centrally bubble-type solutions are sought: \((p(t)u0)0 = c(t)p(t)f(u); u0(0) = 0; u(+1) = L > 0\) in the half-line \([0;+1)\), where \(p(0) = 0\). We are interested in strictly increasing solutions of this problem in \([0;1)\) having just one zero in \((0;+1) \)and finite limit at zero, which has great importance in applications or pure and applied mathematics. Su±cient conditions of the existence of such solutions are obtained by applying the critical point theory and by using shooting argument [9,10] to better analysis the properties of certain solutions associated with the singular di®erential equation. To the authors' knowledge, for the first time, the above problem is dealt with when f satis¯es non-Lipschitz condition. Recent results in the literature are generalized and signi¯cantly improved.     

On the Diophantine equation $$x^2+3^a41^b=y^n $$ x 2 + 3 a 41 b = y n

Periodica Mathematica Hungarica - In this paper we find all positive integer solutions (x, y, n, a, b) of the equation in the title for non negative integers a...     

On the Right-Symmetric Algebras with a Unital Matrix Subalgebra

Siberian Mathematical Journal - Under study are the right-symmetric algebras over a field  $ F $ which possess a “unital” matrix subalgebra  $...