Asian-European Journal of Mathematics

An ordered semiring $(S,+,\cdot ,\le )$ is called ordered $k$-regular if for every element $a$ of $S$ there exist $x,y,s,t\in S$ with $x\le asa,y\le ata$ such that $a+x\le y$. An ordered ideal $A$ of $S$ is called an ordered $k$-ideal, if $x\in S$ and $x+a=b$ for some $a,b\in A$ then $x\in A$. In this work, we characterize ordered $k$-regular semirings using their ordered $k$-ideals. Moreover, characterizations of left(right) ordered $k$-regular semirings and left(right) ordered $k$-weakly regular semirings are investigated.

In this paper, we introduce a generalization of Condition $(P)$, called Condition $(GP)$, and will characterize monoids by this condition of their right (Rees factor) acts. Furthermore, we will show that Conditions $(GP)$ and $(E)$ are interpolation type conditions for strong flatness.

Let ${𝒜}$ and ${ℬ}$ be two unital $C^{\ast }$-algebras with unit $I$. It is shown that the mapping $\varphi :{{𝒜}}_s\to {{ℬ}}_s$ which preserves arithmetic mean and Jordan triple product is a difference of two Jordan homomorphisms provided that $0\in \mathrm{\text{Ran}}\varphi$. The structure of $\varphi$ is more refined when $\varphi (I)\ge 0$ or $\varphi (I)\le 0$. Furthermore, if ${𝒜}$ is a $C^{\ast }$-algebra of real rank zero and $\varphi :{𝒜}\to {ℬ}$ is additive and preserves absolute value of product, then $\varphi ={\varphi }_1\oplus {\varphi }_2$ such that ${\varphi }_1$ (respectively, ${\varphi }_2$) is a complex linear (respectively, antilinear) ∗-homomorphism.

Let $R$ be a ring, $(S,\le )$ a strictly totally ordered monoid which is also artinian and $\omega :S\to \mathrm{\text{Aut}}(R)$ a monoid homomorphism. Given a right $R$-module $M$, denote by ${[M^{S,\le }]}_{[[R^{S,\le },\omega ]]}$ the generalized inverse polynomial module over the skew generalized power series ring $[[R^{S,\le },\omega ]]$. It is shown in this paper that if $M_R$ is a completely $\omega$-compatible module and $I$ an attached prime ideal of $M_R$, then $[[I^{S,\le },\omega ]]$ is an attached prime ideal of ${[M^{S,\le }]}_{[[R^{S,\le },\omega ]]}$, and that if ${[M^{S,\le }]}_R$ is a completely $\omega$-compatible Bass module, then every attached prime ideal of ${[M^{S,\le }]}_{[[R^{S,\le },\omega ]]}$ can be written as the form of $[[I^{S,\le },\omega ]]$ where $I$ is an attached prime ideal of $M_R$.

Let $G$ be a finite group, whose order has $n$ prime divisors. In this paper, we prove that if $G$ has a $p$-complement for $n-1$ prime divisors $p$ of $\left|G\right|$ and $G$ has no section isomorphic to $L_2(7)$. Then $G$ is solvable, which generalizes a theorem of Hall.

This paper is concerned with the global synchronization problems for coupled neural networks (NNs) with hybrid coupling and interval time-varying delays. An appropriate Lyapunov–Krasovskii functional (LKF) and Kronecker product properties are used to form some new delay-dependent synchronization conditions in terms of linear matrix inequalities. A matrix-based quadratic convex approach introduce for sufficient conditions to ensure global synchronization where the time-varying delay is continuous uniformly bounded and its time-derivative bounded by upper and lower bounds. Simulation results are given to show the effectiveness and benefits of the proposed methods.

In this paper, we applied the adaptive grid Haar wavelet collocation method (AGHWCM) for the numerical solution of parabolic partial differential equations (PDEs). The approach of AGHWCM for the numerical solution of parabolic PDEs is mentioned, the obtained numerical results, error analysis are presented in figures and tables. This shows that, the AGHWCM gives better accuracy than the HWCM and FDM. Some of the test problems are taken for demonstrating the validity and applicability of the AGHWCM.

In this paper, we study certain properties involving the generalized Srivastava–Attiya operator. A set of subordination results are obtained and some special cases connected with the Hurwitz–Lerch zeta function and their relevances with known results are also pointed out.

The main aim of this study is to obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical Durrmeyer type modified Baskakov operators.

In this paper, the modified Burgers’ equation is considered. These kinds of problems come from the field of sonic boom and explosions theories. At big Reynolds’ number there is a boundary layer in the right side of the domain. From numerical point of view, the major difficulty in dealing with this type of problem is that the smooth initial data can give rise to solution varying regions i.e. boundary layer regions. To tackle this situation, we propose a numerical method on nonuniform mesh of Shishkin type, which works well at high as well as low Reynolds number. The proposed method comprises of Euler implicit scheme and hybrid scheme in time and space direction, respectively. First, we discretize the continuous problem in temporal direction by Euler implicit method, which yields a set of ode’s at each time level. The resulting set of differential equations are approximated by a hybrid scheme on Shishkin mesh i.e. upwind in regular region (nonboundary layer region) and central difference in boundary layer regions. The convergence of proposed method has been shown parameter uniform. Some numerical experiments have been carried out to corroborate the theoretical results.

In the paper, we shall prove the results on the existence of fixed points of mapping defined on generalized metric space satisfying a nonlinear contraction condition, which is a generalization of Diaz and Margolis theorem (see [A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968) 305–309]). We also present local fixed point theorems both in generalized and ordinary metric spaces. Our results are generalizations of Banach fixed point theorem and many other results.

In this paper, we consider an inverse source problem for a time-fractional equation with variable coefficients in a general bounded domain. The fractional derivative in the problem is in the Caputo sense. Transforming time-fractional inverse problems into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation using Mathematica7 and we have the coefficients of polynomial expansion. We extensively discuss the convergence of the method. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Let $R$ be a $2$-torsion free prime ring, and $U$ a square closed Lie ideal of $R.$ Further let $G,$ and $F$ be generalized derivations associated with derivations $g$ and $d$, respectively on $R.$ If one of the following conditions holds: (i) $G(uv)+d(u)F(v)+uv\in Z(R),$ (ii) $G(uv)+d(u)F(v)+vu\in Z(R),$ (iii) $G(uv)+d(u)F(v)+uv\in Z(R),$ (iv) $G(vu)+F(u)F(v)+uv\in Z(R),$ (v) $G(uv)+d(v)F(u)+uv\in Z(R),$ for all $u,v\in U,$ then it is proved that either $g=d=0$ or $U\subseteq R.$

In a graph $G=(V,E)$, a non-empty set $S\subseteq V(G)$ is said to be an open packing set if no two vertices of $S$ have a common neighbor in $G.$ Let $v\in V$ and let $OS(v)$ denote the maximum cardinality of an open packing set in $G$ which contains $v$. Then $OS(G)=min\{OS(v):v\in V\}$ is called the open packing saturation number of $G$. In this paper, we initiate a study on this parameter.

Let $R$ be a ring, $(S,\le )$ a strictly ordered monoid, and $\omega :S\to \mathrm{\text{End}}(R)$ a monoid homomorphism. The skew generalized power series ring $R[[S,\omega ]]$ is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent series rings. In this paper, we introduce and study the $(S,\omega )$-nil-Armendariz condition on $R$, a generalization of the standard nil-Armendariz condition from polynomials to skew generalized power series. We resolve the structure of $(S,\omega )$-nil-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be $(S,\omega )$-nil-Armendariz. The $(S,\omega )$-nil-Armendariz condition is connected to the question of whether or not a skew generalized power series ring $R[[S,\omega ]]$ over a nil ring $R$ is nil, which is related to a question of Amitsur [Algebras over infinite fields, Proc. Amer. Math. Soc. 7 (1956) 35–48]. As particular cases of our general results we obtain several new theorems on the nil-Armendariz condition. Our results extend and unify many existing results.

In the present paper, we investigate totally real submanifolds in generalized complex space form. We study the $f$-structure in the normal bundle of a totally real submanifold and derive some integral formulas computing the Laplacian of the square of the second fundamental form and using these formulas, we prove a pinching theorem. In fact, the purpose of this note is to generalize results proved in B. Y. Chen and K. Ogiue, On totally real manifolds, Trans. Amer. Math. Soc. 193 (1974) 257–266, S. S. Chern, M. Do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Fields (Springer-Verlag, 1970), pp. 57–75 to the case, when the ambient manifold is generalized complex space form.

In this paper, the concept of normally conjugative relations on sets is introduced. A characterizations of this relations is obtained. In addition, particulary, we show when the anti-order relation $\nleqq$ is normally conjugative. Besides, the concept of finitely normal conjugative relations is introduced and analyzed.

In this paper, we consider the category Dcpo-S of $S$-dcpos and $S$-dcpo maps between them. This category is enriched over the symmetric monoidal closed category Dcpo. So, we are going to find weighted limits in this category. In fact, we show that the category of $S$-dcpos has weighted limits. Finally, we give a concrete construction of some kinds of weighted limits in this category.

Let $f$ be a symplectic diffeomorphism on a closed $C^{\infty }$$2n$-dimensional Riemannian manifold $M$. In this paper, we show that $f$ is Anosov if any of the following statements holds: $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the limit shadowing property or $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the limit weak shadowing property or $f$ belongs to the $C^1$-interior of the set of symplectic diffeomorphisms satisfying the s-limit shadowing property.

In this paper, we show some relations between traveling fronts of curvature flow and constant $\phi$-curvature curves. In the plane with density $e^{\phi }$ satisfying $\mathrm{\Delta }\phi =0$, we prove a Fenchel’s type theorem for the class of simple, closed, convex curves. We also prove that among all curves joining two given points, a curve minimizes weighted arc-length if and only if its $\phi$-curvature is 0. Another proof is also presented for the fact “the plane with density $e^x$ contains no isoperimetric region”.

We present a unified local convergence analysis for deformed Euler–Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The convergence ball and error estimates are given for these methods under hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the second Fréchet derivative. Numerical examples are also provided in this study.

We establish a calculus of boundary value problems (BVPs) on a manifold $N$ with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.