Asian-European Journal of Mathematics

We consider a nonhomogeneous Schrödinger–Poisson system in the whole physical space involving nonlinear potential of critical growth, and we prove existence of two waves with energy sign-changing by using the Mountain-Pass theorem.

Known and new results on identities of an $n$-ary group are studied in this paper.

In this paper, we introduce and investigate some inclusion theorems, convolution theorems and class preserving transforms for subclasses of the meromorphic multivalent function associated with the El-Ashwah operator. Some interesting corollaries and consequences of the main results are pointed out.

In an earlier paper, we studied the Hilbert quasi-polynomial functions of finitely generated bigraded modules in the general framework when the base ring is bigraded and generated by finitely many homogeneous elements of arbitrary degrees. In this paper, we introduce the concept of $(f,g)$-good bifiltration $\mathrm{\Phi }$ on a finitely generated $A$-module $M$, where $f$ and $g$ are specified noetherian filtrations on the noetherian ring $A$. The bigraded modules associated with such bifiltrations are shown to be finitely generated under reasonable hypotheses. Their Hilbert functions are studied. The Hilbert–Samuel function of $M$ with respect to the $(f,g)$-good bifiltration $\mathrm{\Phi }$ of $M$ is one of them. It is proved, among others, that this function is a quasi-polynomial function in two variables and that if $A$ is a noetherian local ring and if the filtrations $f$ and $g$ are primary filtrations, then its degree equals the Krull dimension of $M$.

In this paper, two methods based on CAS wavelets and Legendre polynomials are applied to approximate the solutions of a kind of fractional Volterra integral equations called weakly singular integral equations. The methods are compared presenting some examples.

We generalize the notion of large submodules by introducing what we call a quasi-large submodule. Here, we examine two notions closely related to quasi-large submodules; namely, the notions of $HT$-modules and that of essentially finitely indecomposable modules. The basic properties of these concepts and their interrelationships are explored, and are further related to the notions of closed modules.

We present a local convergence analysis for some families of fourth and sixth-order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies [V. Candela and A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing 45 (1990) 355–367; C. Chun, P. Stanica and B. Neta, Third order family of methods in Banach spaces, Comput. Math. Appl. 61 (2011) 1665–1675; J. M. Gutiérrez and M. A. Hernández, Recurrence relations for the super-Halley method, Comput. Math. Appl. 36 (1998) 1–8; M. A. Hernández and M. A. Salanova, Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method, J. Comput. Appl. Math. 126 (2000) 131–143; M. A. Hernández, Chebyshev’s approximation algorithms and applications, Comput. Math. Appl. 41 (2001) 433–455; M. A. Hernández, Second-derivative-free variant of the Chebyshev method for nonlinear equations, J. Optim. Theory Appl. 104(3) (2000) 501–515; J. L. Hueso, E. Martinez and C. Teruel, Convergence, efficiency and dynamics of new fourth and sixth-order families of iterative methods for nonlinear systems, J. Comput. Appl. Math. 275 (2015) 412–420; Á. A. Magre nán, Estudio de la dinámica del método de Newton amortiguado, Ph.D. thesis, Servicio de Publicaciones, Universidad de La Rioja (2013), http://dialnet.unirioja.es/servlet/tesis?codigo=38821; J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970); M. S. Petkovic, B. Neta, L. Petkovic and J. Džunič, Multi-Point Methods for Solving Nonlinear Equations (Elsevier, 2013); J. F. Traub, Iterative Methods for the Solution of Equations, Automatic Computation (Prentice-Hall, Englewood Cliffs, NJ, 1964); X. Wang and J. Kou, Semilocal convergence and $R$-order for modified Chebyshev–Halley methods, Numer. Algorithms 64(1) (2013) 105–126] have used hypotheses on the fourth Fréchet derivative of the operator involved. We use hypotheses only on the first Fréchet derivative in our local convergence analysis. This way, the applicability of these methods is extended. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples illustrating the theoretical results are also presented in this study.

In this paper a method to construct a global sheaf space over a topological space for an arbitrary set using tolerance relations is proposed. It is observed that in general, the sheaf constructed by this method is different from the sheaf constructed by the method discussed in [U. M. Swamy, Representation of Universal algebra by sheaves, Proc. Amer. Math. Soc. 45 (1974) 55–58]. A necessary and sufficient condition for embedding a non-empty set into the set of all global sections of a sheaf over given topological space is established, and further an application over graphs is studied.

There is a large body of evidence showing that the existence of a suitably-constrained derivation on a 3-prime near-ring forces the near-ring to be a commutative ring. The purpose of this paper is to study generalized semiderivations which satisfy certain identities on 3-prime near-ring and generalize some results due to [H. E. Bell and G. Mason, On derivations in near-rings, North-Holland Math. Stud. 137 (1987) 31–35; H. E. Bell, On prime near-rings with generalized derivation, Int. J. Math. Math. Sci. 2008 (2008), Article ID: 490316, 5pp; A. Boua and L. Oukhtite, Some conditions under which near-rings are rings, Southeast Asian Bull. Math. 37 (2013) 325–331]. Moreover, an example is given to prove that the necessity of the 3-primeness hypothesis imposed on the various theorems cannot be marginalized.

In this paper, we study solvable groups in which $r_n(F)$ is at most 2. In particular, we investigated groups of odd order and $A_4$-free groups with this property. Exact estimations of the derived length and nilpotent length of such groups are obtained.

Let $H_d[x_1,\dots ,x_m]$ be the complex vector space of homogeneous polynomials of degree $d$ with the independent variables $x_1,\dots ,x_m$. Let $V$ be the complex vector space of homogeneous linear polynomials in the variables $x_1,\dots ,x_m$. For any linear operator $T$ acting on $V$, there is a (unique) induced operator $P(T)$ acting on $H_d[x_1,\dots ,x_m]$ satisfying

An improved version of infeasible interior-point algorithm for $P_{*}(\kappa )$ horizontal linear complementarity problem over symmetric cones is presented. In the earlier version (optimization, doi: 10.1080/02331934.2015.1062011) each iteration of the algorithm consisted of one so-called feasibility step and some centering steps. The main advantage of the modified version is that it uses only one feasibility step in each iteration and the centering steps not to be required. Furthermore, giving a complexity analysis of the algorithm, we derive the currently best-known iteration bound for infeasible interior-point methods.

In this paper, associated with convolutions, linear operators ${𝒟}([\alpha ])$ and ${ℐ}([\alpha ])$ are defined with the requirement of certain recurring relations. Some results based on analytic functions involving these operators are derived. Taking some specific forms of such operators, results involving the Dziok–Srivastava operator, the Jung–Kim–Srivastava integral operator, the Srivastava–Attiya linear operator and others, are also mentioned.

Let $A$ be a family of connected graphs. A spanning subgraph $H$ of $G$ is called an $A$-factor (component factor) of $G$ if each component of $H$ is in $A$. In this paper, we study the component factors of the Cartesian product of graphs. Here, we take $A=\{K_{1,n},C_4\}$ and show that every connected graph $G\cong H_1\square H_2$ has a $\{K_{1,n},C_4\}$-factor where $1\le n\le t$ and $t$ is the maximum degree of an induced subgraph $K_{1,t}$ in $H_1$ or $H_2$. Also, we characterize graphs $G\cong H_1\square H_2$ having a $C_4$-factor.

In this paper, we introduce some interesting inequalities regarding the argument of certain p-valent functions. The subclass under investigation is defined by using certain new integral operator. Moreover, special cases and connections of the results presented here with those obtained in earlier works are pointed out.

In this paper, we prove some common fixed point theorems by using the generalized distance in a cone metric space. The results of this paper extend well-known results in the literature.

A right $R$-module $M$ is called to satisfy condition $({𝒞})$ if, for every $s\in S={\mathrm{\text{End}}}_R(M)$ and $s\ne 0$, there exists $n\in \mathbb{N}$ such that $s^n\ne 0$ and if $\mathrm{\text{Ker}}(s^n)$ is a direct summand of $M$, then $\mathrm{\text{IM}}(s^n)$ is a direct summand of $M$. In this paper, we give some properties of rings and modules to satisfy condition $({𝒞})$. Moreover, their connections with von Neumann regular rings, Hereditary rings, Noetherian rings and (semi)artinian rings are addressed.

In this paper, the $C$-radius stability of a matrix polynomial $P(\lambda )$ relative to a domain $\mathrm{\Omega }$ of the complex plane and its relation with the $C$-numerical range of $P(\lambda )$ are investigated. By using an expression of the $C$-radius stability, we obtain a lower bound which involves the distance of $\mathrm{\Omega }$ from the connected components of the $C$-numerical range of $P(\lambda )$.

Hypersubstitutions for algebraic systems are mappings which send operation symbols to terms and relational symbols to formulas preserving arities (see [D. Phusanga, Derived Algebraic Systems, Ph.D. thesis, Potsdam (2013)]). In the non-deterministic case, i.e. if one operation symbol is sent to several terms of the same arity and also one relational symbol is sent to several quantifier free formulas of the same arity, we can consider a mapping from the set of operation symbols into the power set of the set of all terms and from the set of relational symbols into the power set of the set of all quantifier free formulas of the considered type. These mappings are called non-deterministic hypersubstitutions for algebraic systems. We consider sets of algebraic systems which are invariant under non-deterministic hypersubstitutions and apply the result to $M$-$nd$-solid classes of algebraic systems. In this paper, we consider an extension of non-deterministic hypersubstitutions which is based on deterministic ones.

If $S$ is a semigroup without identity, then the deleted diagonal act of $S$ is the right $S^1$-act $D_d(S):={(S\times S)}_{S^1}$. In [S. Bulman-Fleming and A. Gilmour, Flatness properties of diagonal acts over monoids, Semigroup Forum 79 (2009) 298–314] the authors answered the question of when $D_d(S)$ is flat, satisfies Condition $(P)$ or $(E)$ for a completely $(0\text{-})$ simple semigroup (always represented here in regular Rees matrix form). In this paper we answer similar question for some other properties. There are also some results that can arise.