Asian-European Journal of Mathematics

In [M. Chandramouleeswaran and P. Muralikrishna, The recipotent abelian group, Int. J. Math. Sci. 5(4) (2010) 191–200], the concept of a recipotent matrix was introduced. A matrix $A$ of order $n$ is called recipotent matrix if $A\circ A^R=0_n$ where $A^R$ is reversible matrix of $A$, defined by each nonzero element of $A$ is replaced by its reciprocal. The aim of this paper is to improve and complete that paper.

In this paper, we study the following fractional order three-point boundary value problem

We prove (local and global) differential Harnack inequalities for all positive solutions to the geometric conjugate heat equation coupled to the forward in time Ricci flow. In this case, the diffusion operator is perturbed with the curvature operator, precisely, the Laplace–Beltrami operator is replaced with “$\Delta -R(x,t)$”, where $R$ is the scalar curvature of the Ricci flow, which is well generalized to the case of nonlinear heat equation with potential. Our estimates improve on some well known results by weakening the curvature constraints. As a by-product, we obtain some Li–Yau-type differential Harnack estimate. The localized version of our estimate is very useful in extending the results obtained to noncompact case.

In this paper, we introduce the concept of a $2$-absorbing primary submodule over a commutative ring with nonzero identity which is a generalization of primary submodule. Let $M$ be an $R$-module and $N$ be a proper submodule of $M$. Then $N$ is said to be a $2$-absorbing primary submodule of $M$ if whenever $a,b\in R$, $m\in M$ and $abm\in N$, then $am\in N$ or $bm\in N$ or $ab\in \sqrt{(N{:}_{R}M)}$. We have given an example and proved number of results concerning $2$-absorbing primary submodules. We have also proved the $2$-absorbing primary avoidance theorem for submodules.

We present a local convergence analysis of a sixth-order Jarratt-type method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies such as [X. Wang, J. Kou and C. Gu, Semilocal convergence of a sixth-order Jarratt method in Banach spaces, Numer. Algorithms 57 (2011) 441–456.] require hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.

Let $M$ be a lattice module over a $C$-lattice $L$ and $\sigma (M)$ be the set of all prime elements in lattice modules $M$. In this paper, we study the generalization of the Zariski topology of multiplicative lattices [N. K. Thakare, C. S. Manjarekar and S. Maeda, Abstract spectral theory II: Minimal characters and minimal spectrums of multiplicative lattices, Acta Sci. Math. 52 (1988) 53–67; N. K. Thakare and C. S. Manjarekar, Abstract spectral theory: Multiplicative lattices in which every character is contained in a unique maximal character, in Algebra and Its Applications (Marcel Dekker, New York, 1984), pp. 265–276.] to lattice modules. Also we investigate the interplay between the topological properties of $\sigma (M)$ and algebraic properties of $M$.

In this paper, we consider the series of Fibonacci $n$-step numbers $F_k^{(n)}$. Thereby, we establish some properties and theorems of these numbers for $k=0,\pm 1,\pm 2,\dots$ and $n>1$.

In this paper we present the results on the existence of fixed points of system of mappings in generalized metric spaces generalizing the result of Diaz and Margolis. Also the “local fixed point theorems” of a system of such mappings both in generalized and ordinary metric spaces are stated. Banach fixed point theorem and many others are consequences of our results.

In this paper, some general two parameters perturbed Ostrowski type inequalities for functions of bounded variation are established.

In this paper, we define a new graph ${\Gamma }_d(G)$ on a finite group $G$, where $d$ is a divisor of $\left|G\right|$. The vertices of ${\Gamma }_d(G)$ are the subgroups of $G$ of order $d$ and two subgroups $H_1$ and $H_2$ of $G$ are said to be adjacent if there exists $S_i\in {𝒯}(G,H_i)$ $(i=1,2)$ such that $S_1\cong S_2$, where ${𝒯}(G,H_i)$ $(i=1,2)$ denote the set of all NRTs of $H_i$ in $G$. We shall discuss the completeness of ${\Gamma }_d(G)$ for various groups like finite abelian groups, dihedral groups and some finite $p$-groups.

We give a simplified analysis and an improved iteration bound of a full Nesterov–Todd (NT) step infeasible interior-point method for solving symmetric optimization. This method shares the features as, it (i) requires strictly feasible iterates on the central path of a perturbed problem, (ii) uses the feasibility steps to find strictly feasible iterates for the next perturbed problem, (iii) uses the centering steps to obtain a strictly feasible iterate close enough to the central path of the new perturbed problem, and (iv) reduces the size of the residual vectors with the same speed as the duality gap. Furthermore, the complexity bound coincides with the currently best-known iteration bound for full NT step infeasible interior-point methods.

A dual Gabor window pair has two functions that can reconstruct any function in $L^2(ℝ)$ using certain systems of their modulated and translated forms. Few explicit examples of dual Gabor window pairs are known. This paper constructs explicit examples with trigonometric form in one dimension as well as higher dimensions. Also, in the discrete time domain, the trigonometric form allows us to evaluate the Gabor coefficients efficiently using the Discrete Fourier Transform. The windows have fixed support and arbitrary smoothness.

Inextensible flows of timelike curves plays an important role in practical applications. In this paper, we construct a new method for inextensible flows of timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. With this new representation, we derive the necessary and sufficient condition for the given curve to be the inextensible flow. By using curvature tensor field, we give some characterizations for curvatures of a timelike curve in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. Finally, we obtain flows of some associated curves of timelike curves.

In this paper, we tell about some results and open problems concerning Armendariz rings.

In this paper, we determine necessary and sufficient conditions for Bruck–Reilly and generalized Bruck–Reilly ∗-extensions of monoids to be unit regular, completely regular and orthodox. In addition, we characterize the congruences on generalized Bruck–Reilly ∗-extension of a monoid.

In this paper, a set of non-standard discrete models were constructed for the solution of non-homogenous second-order ordinary differential equation. We applied the method of non-local approximation and renormalization of the discretization functions to some problems and the result shows that the schemes behave qualitatively like the original equation.

A congruence relation $\theta$ on an ADL $R$ is defined such that the quotient lattice $R/\theta$ is a distributive lattice and the prime spectrum of $R$ and of $R/\theta$ are homeomorphic. Also it is proved that the minimal prime spectrum of $R$ is homeomorphic with the minimal prime spectrum of $R/\theta$.

This is a further study of reflexive rings over polynomial rings and monoid rings. The concepts of strongly reflexive rings and strongly $M$-reflexive rings are introduced and investigated. Some characterizations of various extensions of the two classes of rings are obtained. It is proved that a ring $R$ is strongly reflexive if and only if $R[x]$ is strongly reflexive if and only if $R[x,x^{-1}]$ is strongly reflexive. For a right Ore ring $R$ with classical right quotient ring $Q$, we show that $R$ is strongly reflexive if and only if $Q$ is strongly reflexive. Moreover, we prove that if $M$ is a unique product monoid (u.p.-monoid) and $R$ is a reduced ring, then $R$ is strongly $M$-reflexive. It is shown that finite direct sums of strongly $M$-reflexive rings are strongly $M$-reflexive.

In this paper, we introduce some ${\lambda }_2$-convergence spaces of double difference sequences of interval numbers with Musielak–Orlicz function ${ℳ}=(M_{kl})$ over $n$-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. Furthermore, we study ${\lambda }_2$-statistical convergence of double difference sequences of interval numbers.

A Vogan superdiagram is a set of involution and painting on a Dynkin diagram. It selects a real form, or equivalently an involution, from a complex simple Lie superalgebra. We introduce the double Vogan superdiagram, which comprises of two sets of Vogan superdiagrams superimposed on an affine Dynkin diagram. They correspond to pairs of commuting involutions on complex simple Lie superalgebras, and therefore provide an independent classification of the simple locally symmetric or semisymmetric superpairs.

A mapping $\sigma$ from $\{f_i|i\in I\}$, the set of all co-operation symbols of type $\tau$, into $C{T}_{\tau }$, the set of all coterms of type $\tau$, is said to be a generalized cohypersubstitution of type $\tau$. Every generalized cohypersubstition $\sigma$ of type $\tau$ induces a mapping $\widehat{\sigma }$ on the set of all coterms of type $\tau$. The set of all generalized cohypersubstitutions of type $\tau$, ${\mathrm{\text{Cohyp}}}_G(\tau )$, under the binary operation ${\circ }_{CG}$, which is defined by ${\sigma }_1{\circ }_{CG}{\sigma }_2:={\widehat{\sigma }}_1\circ {\sigma }_2$ for all ${\sigma }_1,{\sigma }_2\in {\mathrm{\text{Cohyp}}}_G(\tau )$, forms a monoid which is called the monoid of generalized cohypersubstitution of type $\tau$. In this research, we characterize all idempotent and regular elements of ${\mathrm{\text{Cohyp}}}_G(\tau )$, where $\tau =(3)$.

Recently, Opps, Saad and Srivastava [Recursion formulas for Appell’s hypergeometric function $F_2$ with some applications to radiation field problems, Appl. Math. Comput. 207 (2009) 545–558] presented the recursion formulas for Appell’s function $F_2$ and also gave its applications to radiation field problems. Then Wang [Recursion formulas for Appell functions, Integral Transforms Spec. Funct. 23(6) (2012) 421–433] obtained the recursion formulas for Appell functions $F_1,F_2,F_3$ and $F_4$. In our investigation here, we derive the recursion formulas for 14 three-variable Lauricella functions, three Srivastava’s triple hypergeometric functions and four $k$-variable Lauricella functions.

Let $T$ be a tilting module. In this paper, Gorenstein $\sigma [T]$-injective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein $\sigma [T]$-injective are given. For instance, we show that every $R$-module is Gorenstein $\sigma [T]$-injective if and only if every flat $R$-module is Gorenstein $\sigma [T]$-injective if and only if $R$ is a $\sigma [T]$-injective module on itself.

In this paper, we have shown that any complemented modular poset of finite length can be reduced to a weakly modular $M_P$-symmetric poset called Wilcox poset. The concept of parallelism has been generalized to posets. The properties of singular elements, modularity and parallelism are studied in a Wilcox poset.

Quasi-cyclic (QC) codes are a natural generalization of cyclic codes. In this paper, we study some structural properties of QC codes over $R={𝔽}_p+u{𝔽}_p$, where $p$ is a prime and $u^2=u$. By exploring their structure, we determine the one generator QC codes over $R$ and the size by giving a minimal spanning set. We discuss some examples of QC codes of various length over $R$.

In this paper, the justification of application of averaging method on a final interval for impulse differential inclusions with the fuzzy right-hand side with small parameter when the average is absent is considered.

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler’s totient function. This determines an interesting class of finite groups.

It is proved that every $\tau$-closed solubly saturated formation contained in a compact element of the lattice of all $\tau$-closed saturated formations of finite groups is also contained in some compact element of the lattice of all $\tau$-closed solubly saturated formations of finite groups.

Jean-Louis Loday and María O. Ronco introduced the notion of a trioid and constructed a free trioid of rank 1. In this paper, we give a survey of results on trioids. Different examples of trioids and new trioid theoretical constructions are given, combinatorial properties of operations on trioids are studied and some congruences on trioids are characterized. We also introduce the notion of a triband of subtrioids and in terms of tribands of subtrioids describe the structure of trioids. Moreover, we describe a free trioid of an arbitrary rank and for this trioid give an isomorphic construction. In addition, we introduce and study the notion of a semiretraction of a trioid and give some applications of semiretractions to the study of congruences on trioids. The main references are the papers by J.-L. Loday and M. O. Ronco as well as the author.