Demonstratio Mathematica

In this study, we will express the 2-crossed module of groups from a higher-dimensional categorical perspective. According to simplicial homotopy theory, a 2-crossed module is the Moore complex of a 2-truncated simplicial group. Therefore, the 2-crossed module is an algebraic homotopy model for the homotopy 3-types. Tricategories are a three-dimensional generalization of the bicategory concept. Any tricategory is triequivalent to the Gray category, where Gray is a category enriched over the monoidal category 2Cat equipped with the Gray tensor product. Briefly, a Gray category is a semi-strict 3-category for homotopy 3-types. Naturally, the tricategory perspective is used in homotopy theory. The 2-crossed module is associated with the concept of the Gray category. The aim of this study is to obtain a single object tricategory from any 2-crossed module of groups.

In the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional. From the obtained result, we also deduce the qualitative order of approximation, by considering functions in suitable Lipschitz classes. This allows us to apply the above results in certain Orlicz spaces of particular interest, such as the interpolation spaces, the exponential spaces and the {L}^{p} -spaces, 1\le p\lt +\infty . In particular, in the latter case, we also provide an estimate established using a direct proof based on certain properties of the {L}^{p} -modulus of smoothness, which are not valid in the general case of Orlicz spaces. The possibility of using a direct approach allows us to improve the estimate that can be deduced as a consequence of the one achieved in Orlicz spaces. In the final part of the article, we furnish some estimates and the corresponding qualitative order of approximation in the space of uniformly continuous and bounded functions.

In this article, based on the real representation and Kronecker product, Cramer’s rule for a class of coupled Sylvester commutative quaternion matrix equations is studied and its expression is obtained. The proposed algorithm is very simple and convenient because it only involves real operations. Some numerical examples are provided to illustrate the feasibility of the proposed algorithm.

The present study is related to the existence and the asymptotic behavior of the solution of a nonlinear elliptic Steklov problem imposed on a nanostructure depending on the thickness parameter \varepsilon (nano-scale), distributed on the boundary of the domain when the parameter \varepsilon goes to 0, under some appropriate conditions on the data involved in the problem. We use epi-convergence method in order to establish the limit behavior by characterizing the weak limits of the energies for the solutions. An intermediate step in the proof provides a homogenization result for the considered structure.

In the field of civil engineering education, accurately evaluating the effectiveness of budget courses is crucial. However, traditional methods of evaluation tend to be cumbersome and subjective. In recent years, machine learning technology has demonstrated immense potential in educational evaluation. Nevertheless, in practical application, the machine learning-based evaluation model for civil engineering budget courses faces the predicament of inadequate evaluation accuracy. To solve this problem, the squirrel search algorithm technology was used to establish support vector machine parameters and create optimization algorithms. The performance of the proposed optimization algorithm was tested, and the results showed that the accuracy of the proposed algorithm was 0.927, which was better than similar prediction algorithms. Then, the empirical analysis of the proposed civil engineering budget course evaluation model showed that student satisfaction and student examination scores had increased to 92 and 94 points, respectively. The above results reveal that the proposed optimization algorithm and course evaluation model have good performance. Therefore, the implementation of the proposed curriculum evaluation method can significantly improve the learning efficiency of students and the teaching quality of civil engineering budgeting methods courses.

The primary focus of this work lies in the exploration of the limiting dynamics governing fractional stochastic discrete wave equations with nonlinear noise. First, we establish the well-posedness of solutions to these stochastic equations and subsequently demonstrate the existence of periodic measures for the considered equations.

We prove the nonexistence of global solutions for the following wave equations with structural damping and nonlinear memory source term {u}_{tt}+{\left(-\Delta )}^{\tfrac{\alpha }{2}}u+{\left(-\Delta )}^{\tfrac{\beta }{2}}{u}_{t}=\underset{0}{\overset{t}{\int }}{\left(t-s)}^{\delta -1}{| u\left(s)| }^{p}{\rm{d}}s and {u}_{tt}+{\left(-\Delta )}^{\tfrac{\alpha }{2}}u+{\left(-\Delta )}^{\tfrac{\beta }{2}}{u}_{t}=\underset{0}{\overset{t}{\int }}{\left(t-s)}^{\delta -1}{| {u}_{s}\left(s)| }^{p}{\rm{d}}s, posed in \left(x,t)\in {{\mathbb{R}}}^{N}\times \left[0,\infty ) , where u=u\left(x,t) is the real-valued unknown function, p\gt 1 , \alpha ,\beta \in \left(0,2) , \delta \in \left(0,1) , by using the test function method under suitable sign assumptions on the initial data. Furthermore, we give an upper bound estimate of the life span of solutions.

We present and analyze two kinds of nonconforming finite element methods for three-field Biot’s consolidation model in poroelasticity. We employ the Crouzeix-Raviart element for one of the displacement component and conforming linear element for the remaining component, the lowest order Raviart-Thomas element (or the first-order Brezzi-Douglas-Marini element) for the fluid flux, and the piecewise constant for the pressure. We provide the corresponding analysis, including the well-posedness and a priori error estimates, for the fully discrete scheme coupled with the backward Euler finite difference for the time discretization. Such scheme ensures that the discrete Korn’s inequality is satisfied without adding any stabilization terms. In particular, it is free of poroelasticity locking. Numerical results are presented to compare the accuracy and locking-free performance of the two introduced schemes.

In this article, a family of delay differential equations with pseudo compact almost automorphic coefficients is considered. By introducing a concept of Bi-pseudo compact almost automorphic functions and establishing the properties of these functions, and using Halanay’s inequality and Banach fixed point theorem, some results on the existence, uniqueness and global exponential stability of pseudo compact automorphic solutions of the equations are obtained. Our results extend some recent works. Moreover, an example is given to illustrate the validity of our results.

In this study, subordination, superordination, and sandwich theorems are established for a class of p-valent analytic functions involving a generalized integral operator that has as a special case p-valent Sălăgean integral operator. Relevant connections of the new results with several well-known ones are given as a conclusion for this investigation.

The problem of common solutions for nonlinear equations has significant theoretical and practical value. In this article, we first introduce a new concept of a pair of \left(\alpha ,\Theta ) -type contractions, and then, we present some common fixed point results for the contractions in complete metric spaces. Finally, our results are applied to consider the existence, uniqueness and approximation of common solutions for two classes of nonlinear fractional differential equations.

This study deals with the limiting dynamics for stochastic complex Ginzburg-Landau systems with time-varying delays and multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of pullback tempered random attractors for the systems and then establish the upper semicontinuity of these attractors when the thin domains collapse onto {\mathbb{R}} .

In a dynamic market marked by disruptions like pandemics and recessions, organizations face significant challenges in efficiently managing logistics processes and activities. The primary objective of this article is to propose an integrated four-phase model for assessing the efficiency of retail distribution warehouses based on principal component analysis-data envelopment analysis-improved fuzzy step-wise weight assessment ratio analysis-combined compromise solution (PCA-DEA-IMF SWARA-CoCoSo). The model provides a synergistic effect of all positive sides of the considered methods. PCA-DEA methods are used to reduce the number of variables and to identify efficient warehouses. IMF SWARA is applied to determine criteria weights, while the CoCoSo method is employed in the last phase for ranking efficient warehouses. The model incorporates 18 inputs and 3 outputs, derived from both literature and real-world systems. The proposed model identifies the most efficient warehouses, which can serve as benchmarks for improving the performance of less efficient ones. After implementing PCA-DEA, only seven warehouses were identified as efficient. Subsequently, fixed and variable costs are identified as the two most important criteria. Results of the considered case study indicate that warehouse A4 emerges as the best one, whereas A6 is the least preferred warehouse. This research offers valuable insights and practical implications for organizations operating in dynamic markets, assisting them in achieving operational excellence and improving their supply chain performance.

This article aims to provide a modified Noor iterative scheme to approximate the fixed points of generalized nonexpansive mappings with property ( E ) called MN-iteration. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical experiments of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Ultimately, an illustrative analysis regarding Noor, SP-, and MN-iteration procedures is obtained via polysomnographic techniques. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. The obtained graphs describe the pattern of complex polynomials and also the convergence properties of the iterative method. They can also be used to increase the functionality of the existing polynomiography software.

In this study, we introduce the following additive functional equation: g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all \lambda \in {\mathbb{C}} , all unitary elements u,v in a unital Poisson {C}^{* } -algebra P , and all y\in P . Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson {C}^{* } -algebras. Furthermore, we apply to study Poisson {C}^{* } -algebra homomorphisms and Poisson {C}^{* } -algebra derivations in unital Poisson {C}^{* } -algebras.

The shrinking of support in non-linear parabolic p -Laplacian equations with a positive initial condition {u}_{0} that decayed as | x| \to \infty was explored in the Cauchy problem. Proofs were provided for establishing exact local estimates for the boundary of the support of the solutions.

This article is focused on deriving the approximate model for surface wave propagation on an elastic isotropic half-plane under the effects of the rotation and magnetic field along with the prescribed vertical and tangential face loads. The method of study depends on the slow time perturbation of the prevalent demonstration for the Rayleigh wave eigen solutions through harmonic functions. A perturbed pseudo-hyperbolic equation on the interface of the media is subsequently derived, governing the propagation of the surface wave. The established asymptotic formulation is tested by comparison with the exact secular equation. In the absence of the magnetic field, the specific value of Poisson’s ratio, \nu =0.25 , is highlighted, where the rotational effect vanishes at the leading order.

In this article, we study the following nonlinear k -Hessian system with singular weights \left\{\begin{array}{ll}{S}_{k}^{\frac{1}{k}}(\sigma ({D}^{2}{u}_{1}))=\lambda b\left(| x| )f\left(-{u}_{1},-{u}_{2}),& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ {S}_{k}^{\frac{1}{k}}(\sigma ({D}^{2}{u}_{2}))=\lambda h\left(| x| )g\left(-{u}_{1},-{u}_{2}),& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ {u}_{1}={u}_{2}=0,& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial \Omega ,\end{array}\right. where \lambda \gt 0 , 1\le k\le N is an integer, \Omega stands for the open unit ball in {{\mathbb{R}}}^{N} , and {S}_{k}(\sigma ({D}^{2}u)) is the k -Hessian operator of u . By using the fixed point index theory, we prove the existence and nonexistence of negative k -convex radial solutions. Furthermore, we establish the multiplicity result of negative k -convex radial solutions based on a priori estimate achieved. More precisely, there exists a constant {\lambda }^{\ast }\gt 0 such that the system admits at least two negative k -convex radial solutions for \lambda \in \left(0,{\lambda }^{\ast }) .

Krasnoselskii’s iteration is a classical and important method for approximating the fixed point of an operator that satisfies certain conditions. Many authors have used this approach to obtain several famous fixed point theorems for different types of operators. It is well known that Kirk’s iteration can be seen as a generalization of Krasnoselskii’s iteration, in which the iterates are generated by a certain generalized averaged mapping. This approximation method is of great practical significance because the iterative formula contains more information related to the operator in question. The purpose of this study is to define weak \left({\alpha }_{n},{\beta }_{i}) -convex orbital Lipschitz operators. These concepts not only extend the previously introduced Popescu-type convex orbital \left(\lambda ,\beta ) -Lipschitz operators in Fixed-point results for convex orbital operators, (Demonstr. Math. 56 (2023), 20220184), but also encompass many classical contractive operators. Popescu also proved a fixed point result for his proposed operator using the graphic contraction principle and obtained an approximation of the fixed point with Krasnoselskii’s iterates. To extend Popescu’s main results from Krasnoselskii’s iterative scheme to Kirk’s iterative scheme, several fixed point theorems are established, in which an appropriate Kirk’s iterative algorithm can be used to approximate the fixed point of a k -fold averaged mapping associated with our presented convex orbital Lipschitz operators. These results not only generalize, but also complement the existing results documented in the previous literature.

The purpose of this article is to discuss about the so-called semi-greedy bases in p -Banach spaces. Specifically, we will review existing results that characterize these bases in terms of almost-greedy bases, and, also, we analyze quantitatively the behavior of certain constants. As new results, by avoiding the use of certain classical results in p -convexity, we aim to quantitatively improve specific bounds for bi-monotone 1-semi-greedy bases.

This article is concerned with the following Kirchhoff equation: − a + b ∫ R 3 ∣ ∇ u ∣ 2 d x Δ u = g ( u ) + h ( x ) in R 3 , -\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3}, where a a and b b are positive constants and h ≠ 0 h\ne 0 . Under the Berestycki-Lions type conditions on g g , we prove that the equation has at least two positive solutions by using variational methods. Furthermore, we obtain the existence of ground state solutions.

In this study, we introduce the \lambda -analogue of Lah numbers and \lambda -analogue of r -Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of \lambda -analogue of Lah numbers arising from degenerate differential operators. Using these new identities, we study the normal ordering of degenerate integral power of the number operator in terms of boson operators, which is represented by means of \lambda -analogue of Lah numbers and \lambda -analogue of r -Lah numbers, respectively.

In this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are absent in conventional time-frequency transforms, especially for dealing with the time-varying quaternion-valued signals. First, we propose the definition of Q-QPST and then we explore some mathematical properties of the of quaternion Q-QPST, including the linearity, modulation, shift, orthogonality relation, and reconstruction formula. Second, we derive the associated Heisenberg’s uncertainty inequality and the corresponding logarithmic version for Q-QPST. Finally, an illustrative example and some potential applications of the Q-QPST are introduced.

In this article, we investigate the behavior of weak solutions for the three-dimensional Navier-Stokes-Voigt-Brinkman-Forchheimer fluid model with memory and Tresca friction law within a thin domain. We analyze the asymptotic behavior as one dimension of the fluid domain approaches zero. We derive the limit problem and obtain the specific Reynolds equation, while also establishing the uniqueness of the limit velocity and pressure distributions.

Let f be a function defined on the real line, and {T}_{f} be the corresponding superposition operator which maps h to {T}_{f}\left(h) , i.e., {T}_{f}\left(h)=f\circ h . In this article, the sufficient and necessary conditions such that {T}_{f} maps periodic Hölder-Lipschitz spaces {H}_{p}^{\alpha } into itself with 0\lt \alpha \lt \frac{1}{p} and \frac{1}{p}\lt \alpha \lt 1 , where \alpha is the smoothness index, are shown. Our result in the case 0\lt \alpha \lt \frac{1}{p} may be the first result about the superposition operator problems of smooth function space containing unbounded functions.