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A Python Framework for Neutrosophic Sets and Mappings

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Neutrosophic Sets and Systems 2024年 65卷 199-236页

作者： Nordo, Giorgio Jafari, Saeid Mehmood, Arif Basumatary, Bhimraj MIFT Department – Mathematical and Computer Science Physical Sciences and Earth Sciences University of Messina Sant’Agata Messina98166 Italy Mathematical and Physical Science Foundation Slagelse4200 Denmark Department of Mathematics Institute of Numerical Sciences Gomal University KPK Dera Ismail Khan29050 Pakistan Department of Mathematical Sciences Bodoland University BTAD Kokrajhar India

In this paper we present an open source framework developed in Python and consisting of three distinct classes designed to manipulate in a simple and intuitive way both symbolic representations of neutrosophic sets over universes of various types as well as mappings between them. The capabilities offered by this framework extend and generalize previous attempts to provide software solutions to the manipulation of neutrosophic sets such as those proposed by Salama et al. [21], Saranya et al. [23], El-Ghareeb [7], Topal et al. [29] and Sleem [26]. The code is described in detail and many examples and use cases are also provided. © (2023), (University of New Mexico). All Rights Reserved.

关键词： Python

Existence of solutions to the generalized periodic fractional boundary value problem

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Existence of solutions to the generalized periodic fractiona...

作者： Fečkan, Michal Marynets, Kateryna Wang, JinRong Department of Mathematical Analysis and Numerical Mathematics Comenius University in Bratislava Bratislava Slovakia Mathematical Institute of Slovak Academy of Sciences Bratislava Slovakia Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Delft Netherlands Department of Mathematics Guizhou University Guiyang China

We study a boundary value problem for a Caputo-type fractional differential equation subjected to periodic boundary conditions. For an auxiliary problem with the simplified right-hand side, we explicitly construct its unique solution. In addition, based on the theory of the topological index, we prove existence of at least one solution to the original problem. © 2023 The Authors. Mathematical Methods in the Applied sciences published by John Wiley & Sons Ltd.

关键词： Boundary value problems

ON POSITIVITY PRESERVATION OF HYBRID DISCONTINUOUS GALERKIN METHODS ON HYPERGRAPHS

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arXiv 2025年

作者： Knobloch, Petr Lederer, Philip L. Rupp, Andreas Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic Department of Mathematics University of Hamburg Germany Department of Mathematics Faculty of Mathematics and Computer Science Saarland University Saarbrücken Germany

Hybrid finite element methods, particularly hybridized discontinuous Galerkin (HDG) methods, are efficient numerical schemes for discretizing the diffusion equation, which encompasses two main physical principles: mass conservation and positivity preservation. While the former has been extensively analyzed in the literature, this paper investigates the latter. We state a theorem that guarantees the positivity of both the bulk and skeleton approximations to the primary unknown (concentration) and provide counterexamples for nonpositive discretizations. The theoretical findings are confirmed by numerical experiments. Copyright © 2025, The Authors. All rights reserved.

关键词： Finite element method

The injectivity radius of the compact Stiefel manifold under the Euclidean metric

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arXiv 2024年

作者： Zimmermann, Ralf Stoye, Jakob Department of Mathematics and Computer Science University of Southern Denmark Odense Denmark Institute for Numerical Analysis TU Braunschweig Germany

The injectivity radius of a manifold is an important quantity, both from a theoretical point of view and in terms of numerical applications. It is the largest possible radius within which all geodesics are unique and length-minimizing. In consequence, it is the largest possible radius within which calculations in Riemannian normal coordinates are well-defined. A matrix manifold that arises frequently in a wide range of practical applications is the compact Stiefel manifold of orthogonal p-frames in Rn. We observe that geodesics on this manifold are space curves of constant Frenet curvatures. Using this fact, we prove that the injectivity radius on the Stiefel manifold under the Euclidean metric is π.MSC Codes 15B10, 15B57, 65F99, 53C30, 53C80 © 2024, CC BY-NC-SA.

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HIGH CURVATURE MEANS LOW-RANK: ON THE SECTIONAL CURVATURE OF GRASSMANN AND STIEFEL MANIFOLDS AND THE UNDERLYING MATRIX TRACE INEQUALITIES

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arXiv 2024年

作者： Zimmermann, Ralf Stoye, Jakob University of Southern Denmark Department of Mathematics and Computer Science Odense Denmark TU Braunschweig Institute for Numerical Analysis Braunschweig Germany

Methods and algorithms that work with data on nonlinear manifolds are collectively summarized under the term ‘Riemannian computing’. In practice, curvature can be a key limiting factor for the performance of Riemannian computing methods. Yet, curvature can also be a powerful tool in the theoretical analysis of Riemannian algorithms. In this work, we investigate the sectional curvature of the Stiefel and Grassmann manifold. On the Grassmannian, tight curvature bounds are known since the late 1960ies. On the Stiefel manifold under the canonical metric, it was believed that the sectional curvature does not exceed 5/4. Under the Euclidean metric, the maximum was conjectured to be at 1. For both manifolds, the sectional curvature is given by the Frobenius norm of certain structured commutator brackets of skew-symmetric matrices. We provide refined inequalities for such terms and pay special attention to the maximizers of the curvature bounds. In this way, we prove for the Stiefel manifold that the global bounds of 5/4 (canonical metric) and 1 (Euclidean metric) hold indeed. With this addition, a complete account of the curvature bounds in all admissible dimensions is obtained. We observe that ‘high curvature means low-rank’, more precisely, for the Stiefel and Grassmann manifolds under the canonical metric, the global curvature maximum is attained at tangent plane sections that are spanned by rank-two matrices, while the extreme curvature cases of the Euclidean Stiefel manifold occur for rank-one matrices. numerical examples are included for illustration *** Codes 15B10, 15B57, 15B30, 65F99, 22E70, 53C30, 53C80 © 2024, CC BY-NC-SA.

关键词： Matrix algebra

Optimization of Interval Type-2 Fuzzy Logic System Using Grasshopper Optimization Algorithm

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computers, Materials & Continua 2022年第5期71卷 3513-3531页

作者： Saima Hassan Mojtaba Ahmadieh Khanesar Nazar Kalaf Hussein Samir Brahim Belhaouari Usman Amjad Wali Khan Mashwani Institute of Computing Kohat University of Science and TechnologyKohatPakistan Department of Mechanical Materials and Manufacturing EngineeringFaculty of EngineeringUniversity of NottinghamUK College of Computer Sciences and Mathematics Tikrit UniversityIraq Division of Information and Computing Technology College of Science and EngineeringHamad Bin Khalifa UniversityQatar Department of Computer Science Sir Syed University of Engineering and TechnologyPakistan Institute of Numerical Sciences Kohat University of Science and TechnologyKohatPakistan

The estimation of the fuzzy membership function parameters for interval type 2 fuzzy logic system(IT2-FLS)is a challenging task in the presence of uncertainty and *** optimization algorithm(GOA)is a fresh population based meta-heuristic algorithm that mimics the swarming behavior of grasshoppers in nature,which has good convergence ability towards *** main objective of this paper is to apply GOA to estimate the optimal parameters of the Gaussian membership function in an *** antecedent part parameters(Gaussian membership function parameters)are encoded as a population of artificial swarm of grasshoppers and optimized using its *** of the consequent part parameters are accomplished using extreme learning *** optimized IT2-FLS(GOAIT2FELM)obtained the optimal premise parameters based on tuned consequent part parameters and is then applied on the Australian national electricity market data for the forecasting of electricity loads and *** forecasting performance of the proposed model is compared with other population-based optimized IT2-FLS including genetic algorithm and artificial bee colony optimization *** of the performance,on the same data-sets,reveals that the proposed GOAIT2FELM could be a better approach for improving the accuracy of the IT2-FLS as compared to other variants of the optimized IT2-FLS.

关键词： Parameter optimization grasshopper optimization algorithm interval type-2 fuzzy logic system extreme learning machine electricity market forecasting

Approximate stationarity in disjunctive optimization: concepts, qualification conditions, and application to MPCCs

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arXiv 2025年

作者： Käming, Isabella Mehlitz, Patrick Technische Universität Dresden Institute of Numerical Mathematics Dresden01062 Germany Philipps-Universität Marburg Department of Mathematics and Computer Science Marburg35032 Germany

In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, optimization problems with complementarity, vanishing, or switching constraints which are notoriously challenging due to their highly combinatorial structure. The focus of our study is twofold. First, we investigate approximate stationarity conditions and the associated strict constraint qualifications which can be used to infer stationarity of local minimizers. While such concepts are already known in the context of so-called Mordukhovich-stationarity, we introduce suitable extensions associated with strong stationarity. Second, a qualification condition is established which, based on an approximately Mordukhovich- or strongly stationary point, can be used to infer its Mordukhovich- or strong stationarity, respectively. In contrast to the aforementioned strict constraint qualifications, this condition depends on the involved sequences justifying approximate stationarity and, thus, is not a constraint qualification in the narrower sense. However, it is much easier to verify as it merely requires to check the (positive) linear independence of a certain family of gradients. In fact, it provides a characterization of stationarity and, thus, is weaker than these strict constraint qualifications. In order to illustrate the obtained findings, they are applied to optimization problems with complementarity constraints where they can be naturally extended to the well-known concepts of weak and *** Codes 49J53, 90C30, 90C33, 90C46 © 2025, CC BY-NC-ND.

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Formulas for the h-mass on 1-currents with coefficients in Rm

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arXiv 2024年

作者： Lohmann, Julius Schmitzer, Bernhard Wirth, Benedikt Department of Mathematics and Statistics University of Helsinki Finland Institute for Computer Science University of Göttingen Germany Institute for Numerical and Applied Mathematics University of Münster Germany

We consider the minimization of the h-mass over normal 1-currents in Rn with coefficients in Rm and prescribed boundary. This optimization is known as multi-material transport problem and used in the context of logistics of multiple commodities, but also as a relaxation of nonconvex optimal transport tasks such as so-called branched transport problems. The h-mass with norm h can be defined in different ways, resulting in three functionals Mh, | · |H, and Mh, whose equality is the main result of this article: Mh is a functional on 1-currents in the spirit of Federer and Fleming, norm | · |H denotes the total variation of a Radon measure with respect to H induced by h, and Mh is a mass on flat 1-chains in the sense of Whitney. On top we introduce a new and improved notion of calibrations for the multi-material transport problem: we identify calibrations with (weak) Jacobians of optimizers of the associated convex dual problem, which yields their existence and natural regularity. © 2024, CC BY.

关键词： Convex optimization

Research on Heterogeneous Parallel Algorithms for Radar Signal Processing in OpenCL Platform

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Research on Heterogeneous Parallel Algorithms for Radar Sign...

2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022

作者： Wang, Yingfei Xue, Xiaoqin Wang, Wei Xi'an Polytechnic University Department of Computer Science Xi'an China Beijing Institute of Space Long March Vehicle National Key Laboratory of Science and Technology on Test Physics and Numerical Mathematics Beijing China

ISBN: (纸本)9781665452366

An efficient radar signal processing parallel algorithm for Open Computing Language (OpenCL) is presented in this paper, which reveals a rational allocation schema of tasks between the central processing unit (CPU) and the graphics processing unit (GPU). The powerful parallel processing ability of GPU is used to replace the traditional serial processing method by the way of pipeline acceleration and algorithm parallel acceleration, and the real-time performance of the proposed algorithm is improved by the design idea of intra-module parallelism and inter-module flow processing. The algorithm is applied to CPU-GPU heterogeneous computing platform and has a good portability. The effectiveness and real-time performance of the algorithm are verified through simulation data. © 2022 IEEE.

关键词： Graphics processing unit