Caspian Journal of Mathematical Sciences
Volume:4 Issue: 2, Summer Autumn 2015

In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.

In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The applicability of the main result is demonstrated by means of an example as a model of neural nets.

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

In the following text we prove that in a generalized shift dynamical system (X Γ , σϕ) for discrete X with at least two elements, arbitrary nonempty Γ and bijection ϕ : Γ → Γ, the following statements are equivalent: • (X Γ , σϕ) is pointwise recurrent; • (X Γ , σϕ) is pointwise almost periodic; • (X Γ , σϕ) is pointwise regularly almost periodic; • (X Γ , σϕ) is compactly almost periodic; • Per(ϕ) = Γ (ϕ : Γ → Γ is pointwise periodic). Keywords: Almost periodic, Compactly almost periodic, Compactly recurrent, Dynamical system, Generalized shift, Periodic, Pointwise almost periodic, Pointwise periodic, Pointwise regularly almost periodic, Pointwise recurrent, Recurrent. 2000 Mathematics subject classification: 37B05, 54H20

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs).SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations.Then a recurrent neural network model is proposed to compute related primal and dual solutions simultaneously.Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations.We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. Based on this formulation, a solitary solution can be easily obtained using the Ritz method. The Kudryashov method is used to construct exact solutions of the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system.Moreover, it is observed that the suggested techniques are compatible with the physical nature of such problems.

In this paper, Lie group and Lie algebra structures of unit complex 3-sphere S 3 C are studied. In order to do this, adjoint representation of unit biquaternions (complexified quaternions) is obtained. Also, a correspondence between the elements of S 3 C and the special bicomplex unitary matrices SU C2 (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers C 2 2. The relation SO(R 3 ) ∼= S 3 /{±1} = RP 3 among the special orthogonal group SO(R 3 ), the quotient group of unit real quaternions S 3 /{±1} and the projective space RP 3 is known as the Euclidean-projective space [1]. This relation is generalized to the Complex-projective space and is obtained as SO(C 3 ) ∼= S 3 C/{±1} = CP 3 .

In this paper, we examine a discrete-time plant-herbivore model. We investigate stability of model  xt+1 = xte r[1−xt]−ayt , yt+1 = xte r[1−xt] [1 − e −ayt ]. Phase portraits are drawn for different ranges of parameters. We use the Liapunov-Schmidt reduction for attain a simpler and smaller system. Transition route to chaos dynamics is established via period-doubling bifurcations. Conditions of occurrence the perioddoubling, Neimark-Sacker and saddle-node bifurcations are analysed. We study stable and unstable manifolds for this system in equilibrium points. Without the herbivore, the plant population follows the dynamics of the Ricker model.

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. Some examples are presented to support the results proved herein. Our results generalized and extend various comparable results in the existing literature.                                            Also,     Also, Hardy- Rogers G-contractions have been introduced and some xed point theorems have been proved.

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphisms of the group, respectively. If G is nilpotent or solvable with respect to the all its automorphisms, then is referred as it absolute nilpotent or solvable group.Subsequently, N(G) and S(G) are obtained for certain groups. This work is a study of the nilpotency and solvability of the group G from the point of view of the automorphism which the nilpotent and solvable groups have been divided to smaller classes of the nilpotency and the solvability with respect to its automorphisms.