Asian-European Journal of Mathematics

Characterizations of $\alpha$-prime ideals, weakly $\alpha$-prime ideals in a semiring $R$ are investigated. If $I$ is a $Q$-ideal of a semiring $R$, then a relation between the set of $\alpha$-prime ideals (weakly $\alpha$-prime ideals) in $R$ and the set of $\alpha$-prime ideals (weakly $\alpha$-prime ideals) in the quotient semiring $R/I_{(Q)}$ is obtained.

In this paper, we classify the modular group algebra $KG$ of a group $G$ over a field $K$ of characteristic $p>0$ having upper Lie nilpotency index $t^L(KG)=\left|G^{\prime }\right|-k(p-1)+1$ for $k=14$ and $15$. Group algebras of upper Lie nilpotency index $\left|G^{\prime }\right|-k(p-1)+1$ for $k\le 13$, have already been characterized completely.

We prove that a Ricci almost soliton on a Kenmotsu manifold of dimension $>3$ reduces to an expanding Ricci soliton satifying certain condition on the potential vector field or on the soliton function. Next, we show that any Ricci almost soliton on a Kenmotsu manifold is trivial (Einstein) if the soliton vector leaves the contact form $\eta$ invariant. Finally, we classify (locally) a Kenmotsu manifold admitting an almost Yamabe soliton. Some examples have been constructed of almost Yamabe solitons on different class of warped product spaces.

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a completely elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century and this century.

We introduce Kähler-like, G-Kähler-like almost Hermitian metrics. We characterize the Kähler-likeness and the G-Kähler-likeness, and show that these properties are equivalent on nearly Kähler manifolds. Furthermore, we prove that a nearly Kähler manifold with the Kähler-likeness is Kähler.

We study screen conformal lightlike submersions of semi-transversal lightlike submanifolds of indefinite Kaehler manifolds, which can be considered as a lightlike version of horizontally conformal submersions. We establish necessary and sufficient conditions for a screen conformal lightlike submersion to be harmonic.

Let $G$ be a $(p$, $q)$- graph, $D(G)$ the detour diameter of $G$, and cdn$(G)$ is the connected detour number of $G$. Santhakumaran and Athisayanathan are characterized by the graphs of $D(G)\le$ 4 and cdn$(G)=p$, $p-1$ and $p-2$. In this paper, we obtain a necessary and sufficient condition for a graph $G$, $p(G)\ge$ 2, of $D(G)\le$ 8 to have cdn$(G)=p$. Moreover, graphs G of $p(G)\ge$ 6, and $D(G)$ = 5 and 6, such that cdn$(G)=p-1$, are characterized in this research.

Let $G$ be a finite group and $H$ a subgroup of $G$. Then $H$ is said to be $s$-permutably embedded in $G$ if a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$ for every prime dividing the order of $H$. We say that $H$ is nearly$S\mathrm{\Phi }$-embedded in $G$ if $G$ has a normal subgroup $N$ such that $HN$ is $s$-permutable in $G$ and $H\cap N\le \mathrm{\Phi }(H)H_{seG}$, where $H_{seG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-permutably embedded in $G$. In this paper, we study the properties of the nearly $S\mathrm{\Phi }$-embedded subgroups and use them to determine the structure of finite groups. Some known results are generalized.

Let $R$ and $S$ be two commutative rings with unity, let $J$ be an ideal of $S$ and $\phi :R\to S$ be a ring homomorphism. In this paper, we give a characterization for the amalgamated algebra $R{\bowtie }^{\phi }J$ to be a Nagata ring, a strong S-domain, and a catenarian. Also, we investigate the conditions that the ring of Hurwitz series over $R{\bowtie }^{\phi }J$ has a complete comaximal factorization.

In this paper, we study the problem of finding a common element of the solution set of monotone equilibrium problem and the fixed point set of relatively nonexpansive multi-valued mappings in uniformly convex and uniformly smooth Banach spaces. We introduce a Halpern-S-iteration for solving the problem and establish a strong convergence theorem. Some consequences and applications of our main results are discussed. Some numerical experiments are performed to illustrate the convergence and computational performance of our algorithm in comparison with others having similar features. The numerical results have confirmed that the proposed algorithm has a competitive advantage over the existing methods. Our results extend and generalize some results in the literature in this direction.

In this paper, we establish some nontrivial and effective upper bounds for the least common multiple of consecutive terms of a finite arithmetic progression. Precisely, we prove that for any two coprime positive integers $a$ and $b$, with $b\ge 2$, we have

Over the past four decades an extensive literature covered the properties of $S$-acts. However, only few studies had generalized some known properties of $S$-acts to the $S$-posets. The reversible, and indecomposable properties in $S$-posets have been addressed previously but connectivity has not been defined in $S$-posets yet. Connectivity property was found to be related to those of reversibility and flatness in the category of $S$-acts. The primary objective of this paper is to define connectivity in the category of $S$-posets for both versions: ordered “poconnected” and unordered “connected”. Examples are presented to show the difference between the two versions. The relationship between connectivity with other properties such as reversibility, and indecomposability had also been investigated. We show that the poconnected in $S$-posets is always indecomposable, but the inverse is not true. We also find that the weakly reversible is always connected and indecomposable. These relations among these properties in $S$-posets are different from their corresponding relations in $S$-acts.

We have shown that a variety of left(right) normal bands is closed in some homotypical varieties. Further, we partially generalize a result of Isbell from the class of commutative semigroups to some generalized classes of commutative semigroups by showing that dominion of such semigroups belongs to same classes.

A semigroup $S$ is said to have the Basis Property if for any subsemigroup $T$ of a semigroup $S$, any two bases for $T$ have the same cardinality. The structure of completely $0$-simple semigroup with the Basis Property is described. In particular, we proved that each completely $0$-simple semigroup $S$ has the Basis Property if and only if $S$ satisfies one of the following conditions:

• (1)$S$ is produced from a completely simple semigroup with adjoint zero.
• (2)$S$ is an isomorphic to Rees’s semigroup $M^0(G;I,\mathrm{\Lambda };P)$ over a group $G^0$ with sandwich matrix $P$ such that $\left|G\right|=1$, $min\{|I|,|\mathrm{\Lambda }|\}=2$, in addition $P$ has a zero in every row and column.

In this paper, we study the problem of reconstructing an unknown initial condition for nonlinear diffusion from integral observations which have many practical meanings. We reformulate this problem as a variational one to minimizing objective functional. We prove the existence of this minimized problem in our main result.

This paper presents a nonconvex approach for computing a Nash equilibrium in bimatrix games. It relies on the Linear Complementarity Problem (LCP) formulation of the game and follows the Difference of Convex Algorithm (DCA) general scheme. To measure the performance of the proposed approach, numerical experiments as well as a comparative study with the Lemke Howson (LH) algorithm are carried out.

In this paper, a hybrid method between Variational Iteration Method (VIM) and gray wolf optimization algorithm (GWO) was proposed to solve the fractional differential equations (FDE), where the optimal parameter value ($\lambda )$ for the VIM was estimated by the GWO. The solutions in the proposed method, GWO-VIM, demonstrated the efficiency and reliability compared to the default method VIM, by calculating the maximum absolute errors (MAE) and mean square error (MSE).

In this paper, we present new cubically convergent Newton-type iterative methods with dynamics for solving nonlinear algebraic equations under weak conditions. The proposed methods are free from second-order derivative and work well when $f^{\prime }(x)=0$. Numerical results show that the proposed method performs better when Newton’s method fails or diverges and competes well with same order existing method. Fractal patterns of different methods also support the numerical results and explain the compactness regarding the convergence, divergence, and stability of the methods to different roots.

In this paper, we determine the relative rank of the semigroup ${𝒪}{𝒫}(X)$ of all orientation-preserving transformations on infinite chains modulo the semigroup $Ø(X)$ of all order-preserving transformations.

The aim of this paper is to investigate the solvability of infinite systems of nonlinear functional integral equations of $N$-variables in $C(I\times I\times \cdots \times I,m(\varphi ))$ by using the Hausdorff measure of noncompactness with the help of Meir–Keeler condensing operators. We also provide an illustrative example in support of our existence theorems.