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.
