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By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We also compute the entropies of various intersections of the…

Dynamical Systems · Mathematics 2015-10-23 Yiwei Dong , Xueting Tian

A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…

Optimization and Control · Mathematics 2016-11-04 Jiawang Nie , Li Wang , Jane Ye

This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.

General Mathematics · Mathematics 2012-08-07 S. S. Kutateladze

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure, interior and neighbourhood are introduced here and established some important…

General Mathematics · Mathematics 2017-06-06 Manash Jyoti Borah , Bipan Hazarika

In this paper, we introduce the notions of I and I*-soft convergence of sequences of soft points in soft topological spaces and study some basic properties of these notions. Also we introduce the notions of I-soft limit points and I-soft…

General Topology · Mathematics 2025-12-18 Prasanta Malik , Anirban Paul

Information algebra is algebraic structure for local computation and inference. Given an initial universe set and a parameter set, we show that a soft set system over them is an information algebra. Moreover, in a soft set system, the…

Information Theory · Computer Science 2012-01-17 Xuechong Guan , Yongming Li

Many interpretable AI approaches have been proposed to provide plausible explanations for a model's decision-making. However, configuring an explainable model that effectively communicates among computational modules has received less…

Machine Learning · Computer Science 2023-11-09 Jinyung Hong , Keun Hee Park , Theodore P. Pavlic

In this paper, we study maximal antipodal sets in simply connected exceptional compact symmetric spaces. Combining our results with the existing literature, we obtain a complete classification of maximal antipodal sets in all such spaces.…

Differential Geometry · Mathematics 2025-12-15 Yuuki Sasaki

The purpose of this paper is to introduce the notion of noncommutative BiHom-pre-Poisson algebra. Also we establish the bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras and related relevant properties are also…

Rings and Algebras · Mathematics 2021-02-24 Ismail Laraiedh

The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…

Algebraic Topology · Mathematics 2023-08-01 Nazmiye Alemdar , Hasan Arslan

The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems.…

Artificial Intelligence · Computer Science 2012-06-07 Mohamed Nazih Omri , Mohamed Ali Mahjoub

In this paper, we define concept of approximate fixed point property of a function and a set in intuitionistic fuzzy normed space. Furthermore, we give intuitionistic fuzzy version of some class of maps used in fixed point theory and…

Functional Analysis · Mathematics 2015-09-10 Müzeyyen Ertürk , Vatan Karakaya , M. Mursaleem

We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an…

Dynamical Systems · Mathematics 2010-02-11 Daniel Thompson

Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…

Category Theory · Mathematics 2022-03-24 Bartosz Milewski

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of…

General Mathematics · Mathematics 2015-09-28 Florentin Smarandache

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study…

Combinatorics · Mathematics 2018-12-10 Bostjan Brešar , Jérémie Chalopin , Victor Chepoi , Tanja Gologranc , Damian Osajda

We explore a more general class of soft supersymmetry-breaking masses and interactions than that usually considered, both in general and in the MSSM context, where our results for the one-loop $\beta$-functions correct some errors in the…

High Energy Physics - Phenomenology · Physics 2009-10-31 I. Jack , D. R. T. Jones

We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…

Machine Learning · Computer Science 2018-06-04 Andrew Cotter , Maya Gupta , Heinrich Jiang , James Muller , Taman Narayan , Serena Wang , Tao Zhu

The paper is a naive introduction to descriptive set theory. It is aimed mathematicians without a background in logic. The goal is to provide the basic facts used for applications of descriptive set theory to other areas of mathematics,…

Logic · Mathematics 2021-10-19 Matthew Foreman

In present paper, the definition of new metric space with neutrosophic numbers is given. Several topological and structural properties have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given…

General Mathematics · Mathematics 2019-07-02 Murat Kirişci , Necip Şimşek