Asian-European Journal of Mathematics

In this paper, we discuss a new definition of $w_A$-compatible maps in a modular metric space, prove a common fixed point theorem and utilize them to get a solution of a Volterra type integral equation.

In this paper, we introduce the notion of prime hyperideals and maximal hyperideals in ternary hypersemirings and we study some of their properties. We construct a ternary semiring $P_{\circ }(S)$, corresponding to a strongly distributive ternary hypersemiring $S$ and obtain various results among them. We also establish an inclusion preserving bijection between the set of all prime hyperideals of $S$ and collection of all prime total k-ideals of $P_{\circ }(S)$.

In this paper, we introduce a generalization of the well-known notion of weak coherent rings, which we call weak $P$-coherent rings. We investigate the stability of this property under direct products and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions and amalgamated algebras along an ideal. We conclude with various examples of weak $P$-coherent rings.

Let $(N,G)$ be a pair of groups, in which $N$ is a normal subgroup of $G$ and $1\to R\to F\to G\to 1$ is a free presentation of $G$. Suppose that $N$ admits a complement in $G$, Ellis defined the notion of the Schur multiplier of the pair $(N,G)$ as ${ℳ}(N,G)\cong R\cap [S,F]/[R,F]$, where $S$ is a normal subgroup in a free group $F$ such that $N\cong S/R$. In this paper, we give some inequalities for the order of the Schur multiplier of a pair of groups.

In this paper, we introduce and study the notion of a (positive implicative) left ray in groupoids, and we show that every normal subgroup of a group is a left ray of a group, and in every finite group, left rays are normal subgroups. Further, left absorptive subsets of groupoids are discussed and several examples for these definitions provided. The relationship between left rays and zero semigroups is discussed.

A B-algebra is an algebra $(X;\ast ,0)$ of type (2, 0) satisfying: (I) $x\ast x=0$, (II) $x\ast 0=x$, (III) $(x\ast y)\ast z=x\ast (z\ast (0\ast y))$. A B${}_{po}$-algebra is an algebra $(X;\ast ,\preccurlyeq ,0)$ such that $(X;\ast ,0)$ is a B-algebra and $(X,\preccurlyeq )$ is a poset with $\preccurlyeq$ compatible on $X$. In this paper, we introduce and characterize lattice ordered B-algebras (or B${}_{lo}$-algebras). A B${}_{lo}$-algebra is a B${}_{po}$-algebra which is a lattice under its partial order. We show that a B${}_{lo}$-algebra is both distributive and torsion-free.

Let $𝔉$ be a hereditary saturated formation such that $𝔉\subseteq {𝔗}_{\prec }\cap {𝔑}^2$ (${𝔗}_{\prec }$ denotes the class of all Sylow tower groups of type $\prec$). In this paper, the concept of a fan of a subgroup of a group $G$, introduced in 1979 by Borevich, is used to prove that $G$ belongs to $𝔉$. We proved that a finite group $G\in 𝔉$ if and only if $\pi (G)\subseteq \pi (𝔉)$ and every basic subgroup of the fan of every Sylow subgroup in $G$ is $𝔉$-subnormal. We have also obtained that the group $G$ lies in $𝔉$ if and only if all the basic subgroups of the fans of all Sylow subgroups in $G$ lie in $𝔉$.

The power graph is a special type undirected simple graph of a finite group G which has the group elements as its vertex set and two distinct vertices $x,y\in G$ are adjacent if one is non-negative integral power of other. Vertex labeling of graph $\mathrm{\Gamma }$ is a process of assigning integers to all its vertices subject to certain conditions. In simple words, vertex (edge) labeling is a function of all vertices (edges) to set of labels. Frequently, integers are used in labeling of vertices and edges. A graph $G$ is said to be divisor graph if all vertices of graph can be labeled with positive integers such that any two distinct vertices $x,y\in G$ are adjacent if and only if either $x|y$ or $y|x$. In this research paper, we prove that every power graph of finite group is always a divisor graph, but converse is not true.

Pneumonia affects 7% of the population worldwide and results in about four million deaths worldwide. The mortality caused by pneumonia can be prevented, as the treatment is low-tech and low-cost, yet it often goes unrecognized. The chest X-ray is the most reliable diagnostic imaging technique for pneumonia. Yet, often it is not used for lack of trained diagnosticians. However, this can be overcome with deep learning computer-aided diagnostic technology, which is shown in this study as well is in previous research to be able to achieve high performance in detecting and classifying between healthy and pneumonia radio graph images. This study presents a comparison between a transfer learning model based on NASNet-Mobile and a custom custom convolutional neural network (CNN) topology. Transfer learning has enhanced the model performance with an average of 5% for accuracy and lowered the loss with 15%. The experiments point to the fact that with fine-tuning, transfer learning can greatly improve custom CNN models. These results are significant as building transfer learning models based on simpler models can be faster and cheaper to industrialize and can be a viable option for providing the needed computer-aided diagnostic support system for pneumonia detection in chest radio graphs.

Throughout this paper, using the fixed point and direct methods, the generalized Hyers–Ulam stability of the following $m$-Appolonius type functional equation

Let $R$ be a prime ring of characteristic not equal to $2$, $U$ be the Utumi quotient ring of $R$ and $C$ be the extended centroid of $R$. Let $G$ and $F$ be two generalized derivations on $R$ and $L$ be a non-central Lie ideal of $R$. If $F(G(u))u=uG(u)$, for all $u\in L$, then one of the following holds :

• ⁽¹⁾$G=0$.
• ⁽²⁾there exists $\lambda \in C$ such that $F(x)=x$, and $G(x)=\lambda x$ for all $x\in R$.
• ⁽³⁾$R$ satisfies the standard identity $s_4$.

In this paper, we introduce a new notion of module strong pseudo-amenability for Banach algebras. We study the relation between this new concept to other various notions at this issue, module pseudo-contractibility, module pseudo-amenability and module approximate amenability. For an inverse semigroup $S$ with the set of all idempotents $E$, we show that ${\ell }^1(S)$ is module strong pseudo-amenable as an ${\ell }^1(E)$-module if and only if $S$ is amenable. For specific types of semigroups such as Brandt semigroups and bicyclic semigroups, we investigate the module strong pseudo-amenability of ${\ell }^1(S)$. We show that for every non-empty set $I$, ${𝕄}_I(ℂ)$ under this new notion is forced to have a finite index as an $𝔄$-module, where $𝔄=\{[a_{i,j}]\in {𝕄}_{\mathrm{\Lambda }}(ℂ)|\forall i\ne j,a_{i,j}=0\}$.

In this paper, we first introduce the concept of tempered sequence space $m^{\beta }(\phi ,p)$. Then, we construct a Hausdorff measure of noncompactness on this sequence space. Furthermore, by employing this measure of noncompactness we discuss the existence of solutions for an infinite system of nonlinear convolution differential equations in the tempered sequence space $m^{\beta }(\phi ,p)$. Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.

O. A. S. Karamzadeh et al. [On rings with a unique proper essential right ideal, Fund. Math. 183 (2004) 229–244] introduced a class of modules with unique proper essential submodule, such modules are called as ue-modules. A. Azarang and F. Shahrisvand [Rings with only finitely many essential right ideals, Comm. Algebra 47 (2019) 2843–2854] introduced the idea of fe-module and called a module with finitely many essential submodules as a fe-module. Here, we introduce and study the classes of modules dual to them. The class of modules with finitely many small submodules is defined as fs-modules and modules with a unique nonzero small submodule are defined as us-modules.

A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring $S$ is uniserial if and only if the matrix semiring $M_n(S)$ is uniserial. As a generalization of valuation semirings, we also investigate those semirings whose prime ideals are linearly ordered by inclusion. For example, we prove that the prime ideals of a commutative semiring $S$ are linearly ordered if and only if for each $x,y\in S$, there is a positive integer $n$ such that either $x|y^n$ or $y|x^n$. Then, we introduce and characterize pseudo-valuation semidomains. It is shown that prime ideals of pseudo-valuation semidomains and also of the divided ones are linearly ordered.

In this paper, microtubules nonlinear dynamics has been investigated through two different approaches — the first integral method and the $\left(\right.\frac{G^{\prime }}{G}\left)\right.$ expansion method — with an objective of deriving traveling wave solutions to the considered model governed by nonlinear partial differential equation by first reducing it to nonlinear ordinary differential equation. The classes of solutions, furnished by these two methods, form a completely new contribution. In some cases, we also demonstrate that various solutions reported earlier in literature can also be recovered as special cases from the solutions constructed in this study.

New numerical radius inequalities for Hilbert space operators are given. We give an improvement of the inequality presented by Kittaneh for numerical radius, in fact we show that if $A\in {ℬ}({\mathscr{H}}),$ then

We use the theory of first-order differential subordination for meromorphic functions with fixed second coefficient to reform and improve some well-known results of this class of functions. Also, some applications in integral operators and sufficient condition for starlikeness of meromorphic functions with fixed second coefficient are investigated.

Fixed point iterations of some contraction mappings with variations in cone metric space (CMS) domains have been discussed in this paper. More specifically, an increasing sequence of subsets of an order complete CMSs has been considered such that one member of the sequence is mapped into the next member of the sequence by a map for which a contraction condition is satisfied. The usual iteration method has been considered to establish generalized fixed point results in CMSs. Furthermore, some examples are provided to illustrate our main results.

In this paper, we classify completely the negacyclic codes of length $3p^s$ over ${𝔽}_{p^m}+u{𝔽}_{p^m}+u^2{𝔽}_{p^m}$ when $u^3=0$ by using six-cyclotomic codes.