Abstract: Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is said to be a 1-absorbing primary submodule if whenever non-unit elements a, b ∈ R and m ∈ M with abm ∈ N, then either ab ∈ (N :RM) or m ∈ M − rad(N). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ -derivation. We give criteria for skew polynomials f ∈ R of degree less or equal to four to be irreducible. We apply them to low degree polynomials in quantized Weyl algebras and the quantum planes. We also consider f(t) = tm − a ∈ R. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: We consider the existence of solutions of the following weighted problem:{L:=-div(ρ(x) ∇u N-2∇u)+ξ(x) u N-2u=f(x,u)inBu>0inBu=0on∂B,\left\{ {\matrix{{L: = - div\left( {\rho \left( x \right){{\left {\nabla u} \right }^{N - 2}}\nabla u} \right) + \xi \left( x \right){{\left u \right }^{N - 2}}} \hfill & {u = f\left( {x,u} \right)} \hfill & {in} \hfill & B \hfill \cr {} \hfill & {u > 0} \hfill & {in} \hfill & B \hfill \cr {} \hfill & {u = 0} \hfill & {on} \hfill & {\partial B,} \hfill \cr } } \right.where B is the unit ball of ℝN, N #62; 2, ρ(x)=(loge x )N-1\rho \left( x \right) = {\left( {\log {e \over {\left x \right }}} \right)^{N - 1}} the singular logarithm weight with the limiting exponent N − 1 in the Trudinger-Moser embedding, and ξ(x) is a positif continuous potential. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities of double exponential type. We prove the existence of positive solution by using Mountain Pass theorem. In the critical case, the function of Euler Lagrange does not fulfil the requirements of Palais-Smale conditions at all levels. We dodge this problem by using adapted test functions to identify this level of compactness. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the line graph L(Fm,n). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Let I be a homogeneous ideal in a polynomial ring S. In this paper, we extend the study of the asymptotic behavior of the minimum distance function δI of I and give bounds for its stabilization point, rI, when I is an F -pure or a square-free monomial ideal. These bounds are related with the dimension and the Castelnuovo–Mumford regularity of I. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction equations. An implicit finite difference method was used to discretize the mathematical model equations. The algorithm used to solve the non-linear system resulted for each time step is the modified Picard iteration. The numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) in solving the linear systems of the modified Picard iteration were analysed in detail. The numerical results obtained show good numerical performances. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Bone is a complex material that can be regarded as an anisotropic elastic composite material. The problem of crack propagation in human bone is analyzed by using a generalization of the maximum tensile stress criterion (MTS). The results concern the critical stress for crack propagation and the direction of the crack path in Iliac bone. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Let R be a commutative ring with nonzero identity. Let 𝒥(R) be the set of all ideals of R and let δ : 𝒥 (R) → 𝒥 (R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of δ -primary ideals. A proper ideal I of R is said to be a 1-absorbing δ -primary ideal if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ δ (I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing δ-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: The subject of this paper is an analytic approximate method for a class of stochastic functional differential equations with coefficients that do not necessarily satisfy the Lipschitz condition nor linear growth condition but they satisfy some polynomial conditions. Also, equations from the observed class have unique solutions with bounded moments. Approximate equations are defined on partitions of the time interval and their drift and diffusion coefficients are Taylor approximations of the coefficients of the initial equation. Taylor approximations require Fréchet derivatives since the coefficients of the initial equation are functionals. The main results of this paper are the Lp and almost sure convergence of the sequence of the approximate solutions to the exact solution of the initial equation. An example that illustrates the theoretical results and contains the proof of the existence, uniqueness and moment boundedness of the approximate solution is displayed. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Session centered recommender systems has emerged as an interesting and challenging topic amid researchers during the past few years. In order to make a prediction in the sequential data, prevailing approaches utilize either left to right design autoregressive or data augmentation methods. As these approaches are used to utilize the sequential information pertaining to user conduct, the information about the future context of an objective interaction is totally ignored while making prediction. As a matter of fact, we claim that during the course of training, the future data after the objective interaction are present and this supplies indispensable signal on preferences of users and if utilized can increase the quality of recommendation. It is a subtle task to incorporate future contexts into the process of training, as the rules of machine learning are not followed and can result in loss of data. Therefore, in order to solve this problem, we suggest a novel encoder decoder prototype termed as space filling centered Recommender (SRec), which is used to train the encoder and decoder utilizing space filling approach. Particularly, an incomplete sequence is taken into consideration by the encoder as input (few items are absent) and then decoder is used to predict these items which are absent initially based on the encoded interpretation. The general SRec prototype is instantiated by us employing convolutional neural network (CNN) by giving emphasis on both e ciency and accuracy. The empirical studies and investigation on two real world datasets are conducted by us including short, medium and long sequences, which exhibits that SRec performs better than traditional sequential recommendation approaches. PubDate: Tue, 23 Nov 2021 00:00:00 GMT

Abstract: Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1). PubDate: Thu, 08 Jul 2021 00:00:00 GMT

Abstract: We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b.The multiplicative version of the above example is shown too.The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ byg(x):=max{ y∈ℤ+ Iy⊆Ix⋅Ix }g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + } {I_y} \subseteq {I_x} \cdot {I_x}} \right\}for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev.Finally, we formulate some questions concerning the above topics. PubDate: Thu, 08 Jul 2021 00:00:00 GMT

Abstract: In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given. PubDate: Thu, 08 Jul 2021 00:00:00 GMT

Abstract: In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals. PubDate: Thu, 08 Jul 2021 00:00:00 GMT

Abstract: We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models. PubDate: Thu, 08 Jul 2021 00:00:00 GMT