Based on previous researches, the H-proper hypersurfaces of Riemannian space forms include a wide range of minimal ones. In this paper, we study an extended version of H-properness condition on Lorentz hypersurfaces with three distinct principal curvatures in the 5-dimensional Lorentz pseudosphere. The main goal is to prove the 1-minimality of such a hypersurface.
In order to apply the DM (DM)'s preferred information in the fixed cost allocation process, the production trade-off method in data envelopment analysis (DEA) can be used. In this paper, we present a fair fixed cost allocation scheme among decision-making units (DMUs) in the presence of production trade-offs from inputs and outputs based on a single-stage DEA model. The model simultaneously considers the importance of inputs and outputs in the fixed cost allocation model. An algorithm is also presented for the fixed cost allocation scheme in the presence of production trade-offs based on the principle of efficiency invariance. In this algorithm, the fixed cost allocation to DMUs is a function of the efficiency scores, the scale of inputs and outputs, and the production trade-offs between their inputs and outputs. We apply the presented algorithm to allocate fixed costs to a set of refineries in Iran which operate under the same management.
In this paper, we will see some new results about the weak integral closure and the asymptotic prime divisors of a filtration relative to a module. Especially, we obtain some new results for the weak integral closure of a filtration relative to an injective module. For example, if f = {In}n >= 0 is a Noetherian filtration on a Noetherian ring R and E is an injective R-module, then it is shown that the asymptotic prime divisors of the filtration f relative to E can be characterized by the asymptotic prime divisors of the filtration f and also it is shown that the sequence (AssR(R/ClosR(f(n), E)))n is an element of N is ultimately constant.
In this article, we present two new sequences of Ernst-type that mark a significant step in the theoretical exploration of such mathematical constructions. Specifically, we develop the concept of Ernst and Ernst-Lucas tricomplex numbers, offering a detailed analysis of their properties and their links to classical Ernst numbers. We establish several fundamental identities that clarify the properties and structure of these sequences. In addition, we derive the generating function for this new class of sequences and propose a Binet-type formula. Our research also validates several classical identities related to Ernst tricomplex numbers, including those attributed to Tagiuri-Vajda, d'Ocagne, Catalan, and Cassini. This research not only improves our understanding of these distinctive sequences, but also provides a solid foundation for future research in this emerging domain.
Integral equations, and in particular Generalized Abel's Integral equations (GAIEs), have been widely used to model various phenomena in applied science. Several numerical methods have been proposed to solve GAIEs, many of which require significant computational effort to achieve convergence. In this paper, we develop a stable method for solving GAIEs using Bernoulli orthogonal polynomials constructed via the Gram-Schmidt orthogonalization algorithm. Since our method does not rely on collocation points, the computational time is significantly reduced. Moreover, the proposed method demonstrates several advantages over existing approaches in terms of both accuracy and performance. Under certain conditions, we also establish the error bounds and provide a convergence analysis. To evaluate the effectiveness of the method, several numerical examples are presented. The results indicate that, on average, our method yields lower absolute errors compared to other techniques.
This paper aims to extend the concept of ideals in Sheffer stroke Hilbert algebras to the framework of intuitionistic fuzzy set theory. We introduce and define the notion of intuitionistic fuzzy ideals using intuitionistic fuzzy points and examine their structural properties. We provide several characterizations of these ideals and identify the necessary and sufficient conditions under which an intuitionistic fuzzy set qualifies as an ideal. Furthermore, we construct the (0, 1)-set associated with an intuitionistic fuzzy set and investigate the circumstances under which it forms an ideal. The study also explores the roles of intuitionistic level sets and intuitionistic q-sets in the context of ideals, offering a detailed analysis supported by illustrative examples.
In this paper, we investigate the topological aspects of n-ary polygroups, a generalization of classical group-like structures within the framework of algebraic hyperstructures. We introduce the definition of n-ary polygroups. Then develop the theory of n-ary topological poly-groups by equipping these structures with compatible topologies, and examine their continuity properties. Special attention is given to the subclass of connected n-ary topological polygroups, where we explore the influence of topological connectedness on the algebraic behavior. In particular, we prove some results about the quotient topological n-ary polygroups. Finally, we study the connection between the fundamental relation-a key concept in the theory of hyperstructures-and the topology of n-ary polygroups, providing new insights into their structural decomposition. Our results contribute to a deeper understanding of the interplay between topology and generalized algebraic operations. By using the notion of fundamental relation we make a connection between topological n-ary polygroups and topological n-ary groups.
Assessing decision-making units frequently involves managing undesirable outputs that impair performance. While reducing these outputs improves efficiency, their total removal is infeasible in practice. This research presents two models: the first determines the minimum unavoidable undesirable outputs while keeping other inputs and outputs constant, and a second one that measures efficiency under uncertainty. Most current models depend on exact data, yet actual situations often include uncertainties when information is only accessible through expert opinions. Recognizing that such information inherently contains inexactness, Liu's uncertainty theory effectively manages this imprecise data. Using this axiomatic foundation, employing the directional distance function with individual proportion weak disposability, we suggest an uncertain framework for decision-making units. Unlike earlier models, constrained to either radial or non-radial forms, our technique flexibly allows both radial and non-radial efficiency calculations, contracting inputs and undesirable outputs while expanding desirable outputs. We transform uncertain models into a deterministic counterpart using be-lief degrees as a solution method. Our examination of the impact of desirable and undesirable outputs on inefficiency delivers superior de-tail, exceeding prior research. The results indicate that greater belief degrees increase efficiency, differing from deterministic outcomes. We confirm our method by evaluating the environmental efficiency of renew-able energy in 20 OECD countries in 2020. This framework performs well in handling data imprecision, assisting policymakers in optimizing sustainability and resource utilization.
Let R be a commutative ring. A right R-module M is said to be endo-Artinian if it is Artinian with regard to the left L-module structure, where L = EndR(M). This study demonstrates that if R is a Dedekind domain, then all injective R-modules with finitely many simple components, all unfaithful modules, and arbitrary direct sums of an endo-Artinian module are endo-Artinian modules. Moreover, the following result is established: if R is a Dedekind domain and M is an indecomposable injective torsion right R-module, then M is an Artinian module. It can therefore be demonstrated, on the basis of the preceding arguments, that if S is a simple R-module, then its injective hull E(S) is an Artinian module. Finally, assuming that the ring R is a Dedekind domain, we will present a necessary and sufficient condition for an Rmodule to be an endo-Artinian module.
Infectious diseases pose a significant threat to global health, and mathematical modeling can be highly useful for understanding their transmission dynamics. Fractional differential equations have emerged as a powerful tool for modeling complex systems with memory and long-term interactions. In this paper, we provide a mathematical model of generalized viral infection with cure rate via FDEs. The basic reproduction number will be obtained and positivity and uniformly boundedness of solutions will be controlled. Three equilibrium points: infection-free equilibrium, immune-free equilibrium and chronic equilibrium, will also be calculated. It will be shown that the infection-free equilibrium is globally asymptotically stable if the reproduction number is less than one and if it is more than one, within certain conditions on humoral immune response reproduction rate, then the immune-free and the chronic equilibria are globally asymptotically stable. Finally, numerical simulations will be presented to establish the analytical calculations.
For a locally compact group G with a closed subgroup H, we define and study Beurling-Fourier algebras on the homogeneous space G/H, which consists of the left cosets of H in G. The cornerstone of our approach is the definition of Beurling-Fourier algebras in terms of the weight inverses. For G with closed subgroup H and weight omega : G -> [1, infinity), we study Beurling-Fourier algebras on G/H. We show that our construction on G/H, denoted by A(G : H,omega) and equipped with the norm parallel to.parallel to omega, forms a Banach algebra. In particular, we establish a version of Leptin theorem: if H is compact, then G is amenable, if and only if Beurling-Fourier algebra on G/H has a bounded approximate identity.
Suppose that PG(2)(Z(2n)p(m)) is the prime graph with the vertex set of the finite ring Z(2n)p(m) , where p is a prime number greater than two and n, m are positive integers. In this paper, we decompose PG(2)(Z(2n)p(m) ) and obtain neighborhood metric dimension and Wiener index of the graph.
Z-differential equations are used to model phenomena under uncertainty and partial reliability in scientific and engineering fields. Most existing methods for z-differential equations that involve z-numbers are based on discrete forms; however, the continuous form of z-numbers is more representative of the behavior of many phenomena. In this work, we examine z+-numbers with triangular distributions as initial conditions in uncertain differential equations. The numerical method, called the Modified Euler method, is generalized to solve z+-initial value problems, with proofs provided for its convergence and stability. Several examples are provided to demonstrate the accuracy and efficiency of the proposed method.
Let H(D) be the set of analytic functions on D and for 1 <= p <= infinity, H(p )be the Hardy space. For m is an element of N suppose that I-m be mth iteration. Let g(->) = (g(0), & centerdot; & centerdot; & centerdot;, g(m-1)) where {g(i)}(i=0 )(m-1) subset of H(D) and I(f) = integral(z )(0)f(w)dw. If I-m for m is an element of N be the mth iteration, then the generalized Volterra-type operators I ->(m)(g) on H(D) is defined as follows I-g(m)->(f) = I-m(Sigma(m-1)(i=0) f((i))g(i)). In this paper, we investigate boundedness and compactness of generalized Volterra-type operators from Hardy space into iterated weighted-type spaces, V-n = {f is an element of H(D): sup(z is an element of D)(1-|z|(2)) f((n))(z) < infinity}.
This article uses genetic algorithms and geometric properties of hyperplanes and a constructive way to determine strong and weak hyperplanes in the collection entitled Efficient Frontier. To this end, a mapping with domain Rm+s >= 0 to the space of real numbers is defined. This function is introduced in such a way that it's optimal points, which are also Multiple, correspond to the normal vectors of the strong and weak supporting hyperplanes of the Production Possibility Set (PPS). The optimal points of this function are determined through an optimization algorithm, specifically a genetic algorithm. There exists a one-to-one correspondence between the optimal points of the introduced function and the set of supporting hyperplanes. Using the proposed method, the production function under PPS conditions is obtained. It is evident that accurately determining the boundaries of the Production Possibility Set provides useful and valuable information, including returns to scale, benchmarks, and also the stability region.
Cross-efficiency evaluation in data envelopment analysis is a useful tool for evaluating the performance of decision-making units (DMUs). Using secondary goals is one way to overcome the issue of the existence of multiple optimal solutions in the cross-efficiency evaluation method. This paper proposes two secondary goals with a neutral aspect that focuses only on the interests of the DMU being evaluated and is indifferent to other DMUs. In the proposed models, unlike many of the existing neutral models, the weights are selected without defining virtual DMUs and by defining the range of changes for the efficiency of each output of the DMU being evaluated. In the first proposed model, the efficiency of all the outputs of the unit under evaluation becomes of all outputs of the evaluated unit moves closer to the upper limit, away from the lower limit. Finally, using two numerical examples, the effectiveness of the proposed models is shown by comparing them with the previously proposed models. Also, the TOPSIS model is used to integrate the efficiency scores obtained from different models, resulting in a unique score for ranking the units.
A U-shaped assembly line (UAL) is an assembly line (AL) effective type that offers many advantages over straight AL. It can be installed in a smaller physical space with fewer number of stations. This study investigates a bi-objective model that incorporates station installation costs, variable operating costs, and equipment purchasing costs into a typical cost-based UAL balancing problem. For the first time, the possibility of selecting equipment types is considered in such AL, where task operating duration is determined by the sort of equipment needed for that task. As the problem has a high degree of complexity, we employ several classical meta-heuristics and hyper-heuristics, enhance them with new logic, and hybridize them to form our solution approach. The Taguchi approach is used to tune the parameters of each algorithm. According to the obtained outcomes, the GD, VNS, and their hybrid version obtain better results than other algorithms.
In recent years, there has been a growing interest in developing mathematical models that can better inform treatment strategies for complex health conditions. Distinct from traditional modeling approaches, which often consider immunotherapy, optimal control, and nutritional interventions as isolated factors in the dynamics of stomach cancer, we introduce an integrative mathematical framework that concurrently incorporates: center dot Externally delivered anti-tumor immunotherapy, center dot Dynamically controlled ACI (Adoptive Cell Immunotherapy) protocols, center dot Precision nutritional management strategies. We conduct a rigorous analysis of the dynamical properties of this proposed model, placing special emphasis on the stability of treatment outcomes. Through the construction of an appropriate Lyapunov function, we establish both necessary and sufficient conditions for global asymptotic stability. This theoretical foundation guarantees the model's reliability in predicting long-term therapeutic effects. Building upon the stability analysis, we formulate an optimal control problem to systematically determine the most effective treatment regimens. This framework enables quantitative identification of strategies that maximize cancer cell population reduction while accounting for physiological constraints. Comprehensive numerical simulations validate our theoretical results, exploring a spectrum of treatment strategies within our modeling framework.
In this paper, we present examples contrasting the two main results of the theory of (phi, psi)-amenability which were introduced in [3]. In particular, we show that being (phi, psi)-biflatness does not imply (phi, psi)-approximate biprojectivity, and thus prove that [3, Theorem 3.4] is false. Our main example shows that for an infinite discrete amenable semigroup G, the Banach algebra & ell;(1)(G) is (id, psi)-biflat for any psi is an element of triangle(& ell;(1)(G)), but not (id, psi)-approximately biprojective. The reason for this is that we can prove that (id, psi)-approximately biprojective implies the left psi-contractivity of & ell;(1)(G), which in turn implies that G is finite-a contradiction. Using an essentially identical argument, we show that [3, Theorem 3.7], which connects (phi, psi)-pseudo-amenability with (phi, psi)approximate biprojectivity, is also false. Our examples thus point to the need for more structural hypotheses in the theory of generalized amenability.
We investigate a class of (2+1)-dimensional nonlinear fractional wave-diffusion equations with Caputo derivatives using Lie symmetry analysis. First, we derive a prolongation formula for the infinitesimal generators of the symmetry group acting on Caputo-type fractional derivatives of arbitrary order alpha generalizing earlier results for Riemann-Liouville derivatives by Gazizov et al. [13]. By constructing an optimal system of subalgebras, we classify all symmetry reductions for this class of equations. As a key application, we obtain exact invariant solutions and solitary wave solutions for the (2+1)-dimensional fractional Burgers' equation. This framework opens avenues for extending Lie analysis to other fractional PDEs in continuum mechanics, plasma physics, and transport processes where Caputo operators play a crucial role.
