Asian-European Journal of Mathematics

This paper presents a fractional-order nonlinear system of delay integro-differential equations which is used to model biological species living together. A numerical scheme based on the Chelyshkov polynomials is implemented to solve this fractional order system of integro-differential equations. The main advantages of the presented method is that it reduces under consideration problem to a system of nonlinear algebraic equations. Some test problems are considered to confirm validity and accuracy of the presented method. Moreover, the obtained numerical results are compared with those existing in the literature.

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes ${(2n,M,d,(m,0))}_q$ based on totally isotropic subspaces in symplectic space ${𝔽}_q^{2n}$ and on the subspace codes ${(2n+l,M,d,(m,0))}_q$ based on totally isotropic subspace in extended symplectic space ${𝔽}_q^{(2n+l)}$.

Existing study gives ordering policy for non-instantaneous deteriorating items having three-variable Weibull distribution deterioration rate. Demand rate varies in different time interval. Before deterioration starts, demand is constant and after that it decreases exponentially with respect to time. The study considers total cost function as objective function including salvage value. Shortages are not allowed to stay in time-based competition. Results are proved theoretically and numerically. Sensitivity analysis is performed with respect to salvage value, scale parameter, shape parameter and location parameter including in deterioration rate function to show the liability of the model.

In this paper, a new approach and methodology is developed by incorporating differential quadrature technique with Bernstein polynomials. In differential quadrature method, approximations are done in a way that the derivatives of the function are replaced by a linear sum of functional values at the grid points of the given domain. In Bernstein differential quadrature method (BDQM), Bernstein polynomials are employed for spatial discretization so that a system of ordinary differential equations (ODE’s) is obtained which is solved by SSPRK-43 method. The stability of the method is also studied. The accuracy of the present method is checked by performing numerical experiments on two-dimensional coupled Burgers’ and Brusselator systems and fourth-order extended Fisher Kolmogorov (EFK) equation. Implementation of the method is very easy, efficient and capable of reducing the size of computational efforts.

We introduce the dual notions of $S(N)$-weakly prime submodules, that is, $S(0)$-weakly second submodules in a commutative ring with identity. We investigate the properties of $S(0)$-weakly second submodules and obtain some related useful characterizations of this dualization. Moreover, we also prove some properties of $S(0)$-weakly second submodules related to multiplication and comultiplication modules.

In this paper, we introduce and discuss a concept of co-quasiordered residuated relational systems. The setting of this research is Bishop’s constructive mathematics — a mathematics based on the Intuitionisic logic and particular principle-philosophical orientation of this attitude. Moreover, we introduce the concept of co-filters in such relational system. Additionally, some of the fundamentals properties of these substructures we have been shown.

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type $(2,0)$. We say that a graph $G$ satisfies a term equation $s\approx t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s\approx t$. The set of all term equations $s\approx t$, which the graph $G$ satisfies, is denoted by $\mathrm{\text{Id}}(\{G\})$. The class of all graph algebras satisfy all term equations in $\mathrm{\text{Id}}(\{G\})$ is called the graph variety generated by $G$ denoted by ${{𝒱}}_g(\{G\})$. A term is called a linear term if each variable which occurs in the term, occurs only once. A term equation $s\approx t$ is called a linear term equation if $s$ and $t$ are linear terms. This paper is devoted to a thorough investigation of graph varieties defined by linear term equations. In particular, we give a complete description of rooted graphs generating a graph variety described by linear term equations.

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

In the present paper, we consider general helix with spacelike slope axis for all possible types of curves in Minkowski $3$-space. We give the conditions under which the curves in Minkowski $3$-space have spacelike slope axis. In addition, we find the parametric equations of the curves. Also, we give the related examples and their graphics.

In this paper, we introduce a new four-step iterative process and name it as RK-iterative process and prove some $\mathrm{\Delta }$-convergence and strong convergence results using this process for generalized nonexpansive mappings in CAT(0) spaces. Our results generalize the corresponding results of many authors in different directions.

Iota energy of signed digraphs is defined as sum of absolute values of imaginary parts of its eigenvalues. Extremal energy and iota energy of unicyclic signed digraphs is known. In this paper, we address the problem of finding signed digraphs with extremal iota energy among vertex-disjoint bicyclic signed digraphs of fixed order.

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der $R$ of derivations in a commutative differentially prime rings $R$. We study Lie rings Der $R$ in the non-commutative case and prove that if $R$ is a $2$-torsion-free $D$-semiprime ring, then $D$ is a semiprime Lie ring or $R$ is a commutative ring.

In this paper, we introduce the concepts of a $\mathrm{\Gamma }$-prime (respectively semiprime) ideals of the $\mathrm{\Gamma }$-semigroup on ${𝒪}-{{𝒪}}^{´}$, where $({𝒪},{ℱ},{\sim }_{B_r},N_r)$ and $({{𝒪}}^{´},{ℱ},{\sim }_{B_r},N_r)$ are two different weak near approximation spaces. Several characterizations of them are furnished.

Let $G$ be a non-abelian finite group and $Z(G)$ be the center of $G$. The non-commuting graph, $\nabla (G)$, associated to $G$ is the graph whose vertex set is $G\backslash Z(G)$ and two distinct vertices $x,y$ are adjacent if and only if $xy\ne yx$. We conjecture that if $G$ is an almost simple group and $H$ is a non-abelian finite group such that $\nabla (G)\cong \nabla (H)$, then $\left|G\right|=\left|H\right|$. Among other results, we prove that if $G$ is a certain almost simple group and $H$ is a non-abelian group with isomorphic non-commuting graphs, then $G\cong H$.

A closure endomorphism of a Hilbert algebra $A$ is a mapping that is simultaneously an endomorphism of and a closure operator on $A$. It is known that the set $CE$ of all closure endomorphisms of $A$ is a distributive lattice where the meet of two elements is defined pointwise and their join is given by their composition. This lattice is shown in the paper to be isomorphic to the lattice of certain filters of $A$, anti-isomorphic to the lattice of certain closure retracts of $A$, and compactly generated. The set of compact elements of $CE$ coincides with the adjoint semilattice of $A$; conditions under which two Hilbert algebras have isomorphic adjoint semilattices (equivalently, minimal Brouwerian extensions) are discussed. Several consequences are drawn also for implication algebras.

In this paper, we study skew cyclic and skew constacyclic codes over the ring ${𝔽}_p+u_1{𝔽}_p+\cdots +u_{2m}{𝔽}_p$, where $u_i^2=u_i$ and $u_i{u}_j=0$, for $i,j=1,\dots ,2m$ and $i\ne j$. We have introduced some new Gray maps and determined the relation between codes using the ${𝔽}_p$-Gray images of skew constacyclic codes.

Let $A$ and $B$ be two bounded linear operators on a Banach space $X$ and $k$ be a positive integer such that $A^k{B}^k{A}^k=A^{k+1}$ and $B^k{A}^k{B}^k=B^{k+1}$, then $A$, $B$, $A^k{B}^k$ and $B^k{A}^k$ have some common spectral properties. Drazin invertibility and polaroidness of these operators are also discussed. Cline’s formula for Drazin inverse in a ring with identity is also studied under the assumption that $a^k{b}^k{a}^k=a^{k+1}$ for some positive integer $k$.

Generalized cyclotomic numbers of order $e\ge 1$ with respect to an odd prime power are obtained. Hence, explicit expressions for primitive idempotents in the ring $Z_4[x]/(x^{p^n}-1)$ are obtained in two cases, when the multiplicative order of 2 modulo $p^n$ is $\varphi (p^n)/2$ and $\varphi (p^n)/4$, where $p$ is an odd prime. Orthogonality and self-duality of some $Z_4$ cyclic codes are also discussed. Further, a method for obtaining cyclic self-dual/isodual codes of length $p^n$ over $Z_4$ is given.