Asian-European Journal of Mathematics

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEGPCD’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of the proposed results. We end the paper with a brief conclusion.

This paper explains a numerical scheme based on the moving least squares (MLS) method to solve Volterra-Fredholm integro-differential equations in one-dimensional space. The method is a meshless method, since it does not need any background interpolation or approximation cells, so it does not depend on the geometry of domain. The demand of meshless techniques increases because of its meshless nature and simplicity of usage in higher dimensions. We show the convergence analysis for this technique to stress its reliability, and eventually some examples are presented to indicate the applicability of the method. The approximate results of this technique are compared with the correct solutions, which reveals that this technique meets with the approval of the correct solutions to the problems.

In this paper, we characterize left (right) magnifying elements in the semigroups of linear transformations with restricted range which nullity or co-rank are infinite. Furthermore, we also show that every left (right) magnifier in these semigroups is very good.

In this paper, we propose a new algorithm for finding a common element of the set of fixed points of Bregman asymptotically regular quasi-nonexpansive mappings and the set of zeros of maximal monotone mappings and the set of solutions of equilibrium problems for pseudomonotone and Bregman Lipschitz-type continuous bifunctions in reflexive Banach spaces. Moreover, the strong convergence of the sequence generated by this algorithm is established under some suitable conditions.

In this paper, we propose and analyze a nonlinear deterministic malaria disease model for the impact of temperature variability on malaria epidemics. Firstly, we analyzed the invariant region and the positivity solution of the model. The basic reproduction number with respect to disease free-equilibrium is calculated by the next-generation matrix method. The local stability and global stability of the equilibrium points are shown using the Routh–Hurwitz criterion and the Lyapunov function, respectively. A disease-free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one and endemic equilibrium exists otherwise. Moreover, we have shown the sensitivity analysis of the basic reproduction number and the model exhibits forward and backward bifurcation. Secondly, we apply the optimal control theory to describe the model with incorporates three controls, namely using treated bed nets, treatment of infected with anti-malaria drugs and for vector killing using insecticide spray strategy. Pontraygin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the simulation result of optimal control problem and analysis of cost-effectiveness show that a combination of using treated bed nets and treatment is the most effective and least-cost strategy to prevent the malaria disease.

For a simple connected graph $G,$ let $c:V(G)\to \mathbb{N}$ be a coloring of $G,$ where two adjacent vertices may be assigned the same color. Let $\sigma (v)$ be the sum of colors of neighbors of any vertex $v\in V(G).$ The coloring $c$ is a sigma coloring of $G$ if for any two adjacent vertices $u,v\in V(G),$ $\sigma (u)\ne \sigma (v).$ The least number of colors required in a sigma coloring of $G$ is the sigma chromatic number of $G$ and is denoted by $\sigma (G).$ A sigma coloring of a graph is a neighbor-distinguishing type of coloring and it is known that the sigma chromatic number of a graph is bounded above by its chromatic number. It is also known that for a path $P_n$ and a cycle $C_n$ where $n\ge 4,$ $\sigma (P_n)=2$ and $\sigma (C_n)=2$ if $n$ is even. Let $G={\sum }_{i=1}^k{G}_i,$ the join of the graphs $G_i$, where $G_i=P_{n_i}$ or $G_i=C_{n_i},$ $6\le n_1\le \cdots \le n_k$ and $G_i$ is not an odd cycle for any $i$. It has been shown that if $n_{i+2}-n_i\ge 2$ for $1\le i\le k-2$ and $(G_1,G_2)\ne (C_6,C_6)$ then $\sigma (G)=2$. In this study, we give necessary and sufficient conditions under which $\sigma (G)=2,$ where $G$ is the join of copies of $P_n$ and/or $C_n$ for the same value of $n$. Let $n$ and $k$ be positive integers with $n\ge 3$ and $k\ge 2.$ In this paper, we show that $\sigma (k{P}_n)=2$ if and only if $n\ge 6k-6-(nmod4),$ or $n$ is odd, $k$ is even and $n\ge 6k-10-(nmod4)$; and $\sigma (k{C}_n)=2$ if and only if $n$ is even and $n\ge 6k-6+(nmod4).$ We also obtain necessary and sufficient conditions on $n\ge 8$ and $k\ge 2$, so that $\sigma (G)=2$ for $G={\sum }_{i=1}^k{G}_i,$ where $G_i=P_n$ or $C_n,$ other than the cases $G=k{P}_n$ and $G=k{C}_n.$

Let $P_k:={𝔽}_2[x_1,x_2,\dots ,x_k]$ be the polynomial algebra in $k$ variables with the degree of each $x_i$ being $1,$ regarded as a module over the mod-$2$ Steenrod algebra ${𝒜},$ and let $G{L}_k$ be the general linear group over the prime field ${𝔽}_2$ which acts naturally on $P_k$. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for the polynomial algebra $P_k$ as a module over the mod-2 Steenrod algebra, ${𝒜}$. These results are used to study the Singer algebraic transfer which is a homomorphism from the homology of the mod-$2$ Steenrod algebra, ${\text{Tor}}_{k,k+n}^{{𝒜}}({𝔽}_2,{𝔽}_2),$ to the subspace of ${𝔽}_2{\otimes }_{{𝒜}}{P}_k$ consisting of all the $G{L}_k$-invariant classes of degree $n.$ In this paper, we explicitly compute the hit problem for $k=5$ and the degree $7.2^s-5$ with $s$ an arbitrary positive integer. Using this result, we show that Singer’s conjecture for the algebraic transfer is true in the case $k=5$ and the above degree.

Recently, there are many works that proposed modeling approaches to describe the random movement of individuals for COVID-19 infection. However, these models have not taken into account some key aspects for disease such the prediction of expected time of patients remaining at certain health state before entering an absorption state (e.g., exit out of the system for ever such as death state or recovery). Therefore, we propose a dynamical model approach called the absorbing Markov chains for analyzing COVID-19 infections. From this modeling approach, we seek to focus and predict two states of absorption: recovery and death, as these two conditions are considered as important indicators in assessment of the health level. Based on the absorbing Markov model, the study suggested that there is a gradually increase in the predicted death number, while a decrease in the number of recovered individuals.

A starlike univalent function $f$ is characterized by $z{f}^{\prime }(z)/f(z)$; several subclasses of starlike functions were studied in the past by restricting $z{f}^{\prime }(z)/f(z)$ to take values in a region $\mathrm{\Omega }$ on the right-half plane, or, equivalently, by requiring $z{f}^{\prime }(z)/f(z)$ to be subordinate to the corresponding mapping of the unit disk $𝔻$ to the region $\mathrm{\Omega }$. The mappings $w_i$, $i=1,2,3$, defined by $w_1(z):=z+\sqrt{1+z^2},w_2(z):=\sqrt{1+z}$ and $w_3(z):=e^z$ map the unit disk $𝔻$ to certain nice regions in the right-half plane. For normalized analytic functions $f$ with $f(z)/g(z),g(z)/(zp(z))$ and $p(z)$ are subordinate to the function $w_i$ for some analytic functions $g$ and $p$, we determine the sharp radius for them to belong to various subclasses of starlike functions.

The aim of this research work is to define a new class of multi-algebras that is called ternary $\mathrm{\Gamma }$-semihyperrings as a generalization of $\mathrm{\Gamma }$-semihyperrings and semihyperrings. Then, we define and study the concepts of ideals, mutual ideals, spectrum ideals, strong prime ideals and ultra-prime ideals of them. Also, we define a topology on the set of strong prime ideals. Finally, we introduce the concept of ideal extensions and obtain some related results.

In this paper, discrete cubic spline method based on central differences is developed to solve one-dimensional (1D) Bratu’s and Bratu’s type highly nonlinear boundary value problems (BVPs). Convergence analysis is briefly discussed. Four examples are given to justify the presented method and comparisons are made to confirm the advantage of the proposed technique.

In this paper, we propose several new lower and upper bounds for the functions $sinx/x$ and $cosx.$ In particular, we refine by generalizing some known inequalities involving these functions. To attain this aim, monotonicity rules and ratio of consecutive even indexed Bernoulli numbers play an important role. Graphic evidence of the results is provided.

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation

In [Tense operators on De Morgan algebras, Log. J. IGPL 22(2) (2014) 255–267], Figallo and Pelaitay introduced the notion of tense operators on De Morgan algebras. Also, other notions of tense operators on De Morgan algebras were given by Chajda and Paseka in [De Morgan algebras with tense operators, J. Mult.-Valued Logic Soft Comput. 1 (2017) 29–45; The Poset-based logics for the De Morgan negation and set representation of partial dynamic De Morgan algebras, J. Mult.-Valued Logic Soft Comput. 31(3) (2018) 213–237; Set representation of partial dynamic De Morgan algebras, in 2016 IEEE 46th Int. Symp. Multiple-Valued Logic (IEEE Computer Society, 2016), pp. 119–124]. In this paper, we introduce a new notion of tense operators on De Morgan algebras and define the class of tense De Morgan $S4$-algebras. The main purpose of this paper is to give a discrete duality for tense De Morgan $S4$-algebras. To do this, we will extend the discrete duality given in [W. Dzik, E. Orłowska and C. van Alten, Relational Representation Theorems for Lattices with Negations: A Survey, Lecture Notes in Computer Science (2006), pp. 245–266], for De Morgan algebras.

We define a Hom-Leibniz 2-algebra, which can be considered as the deformation and categorification of Leibniz algebras. We give the notion of 2-term strongly homotopy (sh) Hom-Leibniz algebras. We prove that the 2-term sh Hom-Leibniz algebras are equivalent to the Hom-Leibniz 2-algebras. We show that there exists a one-to-one correspondence between crossed modules of Hom-Leibniz algebras and 2-term Hom-differential graded Leibniz algebras. We also prove that the skeletal 2-term sh Hom-Leibniz algebras can be classified by using the third cohomology group of Hom-Leibniz algebras. We construct a Hom-Leibniz 2-algebra from an Omni-Hom-Lie 2-algebra. Moreover, we also give the construction of Hom-Leibniz 2-algebras from Hom-associative Rota–Baxter algebras.

Let $G$ be a finite group and $A$ a subgroup of $G$. We say that $A$ is strongly$𝔘$-subnormal in $G$ if either $A$ is normal in $G$ or $A_G\ne A^G$ and every chief factor of $G$ between $A_G$ and $A^G$ is cyclic; strongly$\pi$-permutable in $G$ if $A$ permutes with all Hall $\pi$’-subgroups and with all Sylow $p$ -subgroups of $G$ for all $p\in \pi$; partially$\pi$-subnormal in $G$ if $A=〈L,T〉$, where $L$ is a strongly $𝔘$-subnormal subgroup and $T$ is a $\pi$-subnormal subgroup of $G$. In this paper, we study finite groups whose 3-maximal or 2-maximal subgroups are partially $\pi$-subnormal (strongly $\pi$-permutable).

In the modern theory of elliptic curves, one of the important problems is the determination of the number of rational points on an elliptic curve. The Mordel–Weil theorem [T. Shioda, On the Mordell–Weil lattices, Comment. Math. University St. Paul. 39(2) (1990) 211–240] points out that the elliptic curve defined above the rational points is generated by a finite group. Despite the knowledge that an elliptic curve has a final number of rational points, it is still difficult to determine their number and the way how to determine them. The greatest progress was achieved by Birch and Swinnerton–Dyer conjecture, which was included in the Millennium Prize Problems [A. Wiles, The Birch and Swinnerton–Dyer conjecture, The Millennium Prize Problems (American Mathematical Society, 2006), pp. 31–44]. This conjecture uses methods of the analytical theory of numbers, while the current knowledge corresponds to the assumptions of the conjecture but has not been proven to date. In this paper, we focus on using a tangent line and the osculating circle for characterizing the rational points of the elliptical curve, which is the greatest benefit of the contribution. We use a different view of elliptic curves by using Minkowki’s theory of number geometry [H. F. Blichfeldt, A new principle in the geometry of numbers, with some applications, Trans. Amer. Math. Soc. 15(3) (1914) 227–235; V. S. Miller, Use of elliptic curves in cryptography, in Proc. Advances in Cryptology — CRYPTO ’85, Lecture Notes in Computer Science, Vol. 218 (Springer, Berlin, Heidelberg, 1985), pp. 417–426; E. Bombieri and W. Gubler, Heights in Diophantine Geometry, Vol. 670, 1st edn. (Cambridge University Press, 2007)].

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some matrix algebras. Using this tool, we characterize strong pseudo-amenability of ${\ell }^1(S)$, provided that $S$ is a uniformly locally finite inverse semigroup. As an application, we show that for a Brandt semigroup $S=M^0(G,I)$, ${\ell }^1(S)$ is strong pseudo-amenable if and only if $G$ is amenable and $I$ is finite. We give some examples to show the differences between strong pseudo-amenability and the other classical notions of amenability.

Let $G$ be a graph of order $n$, and $d_u$ be the degree of vertex $u$ in a graph $G$. The Zagreb matrix of $G$ is the square matrix of order $n$ whose $(i,j)$-entry is equal to $d_u+d_v$ if the vertex $u$ and the vertex $v$ of $G$ are adjacent, and $0$ otherwise. This matrix, related closely to the Zagreb (abbreviated as $Z$) index. The Zagreb eigenvalues of $G$ are the eigenvalues of its $Z$ matrix and the Zagreb energy of $G$ is the sum of the absolute values of its Zagreb eigenvalues. In this paper, we obtain some new results for the eigenvalues of the Zagreb matrix, the spread of the Zagreb matrix. Moreover, we obtain some new bounds for the Zagreb energy of a graph.

In this paper, we introduce the concept of right semi-harmonically $(\gamma ,\eta )$-convex, (RHS $(\gamma ,\eta )$-convex) function by the inequality