Space Setting Research Articles

On Beta Generalized Star Pre-I-Closed Sets in Ideal Topological Spaces

On Beta Generalized Star Pre-I-Closed Sets in Ideal Topological Spaces

Attribute reduction using self-information uncertainty measures in optimistic neighborhood extreme-granulation rough set

The pessimistic and optimistic neighborhood multi-granulation rough sets (PNMRS and ONMRS) have been applied to attribute reduction. Nonetheless, the setting of the granulation space in both models is usually based on expert experience or continuous trials, which are poorly interpretable. Besides, the dependency, an important attribute evaluation function in PNMRS and ONMRS, only considers classification information in the lower approximation and ignores that of the upper approximation, affecting its evaluation effect. Thus, we firstly propose the pessimistic and optimistic neighborhood extreme-granulation rough sets (PNERS and ONERS) based on the minimum granulation space, avoiding the unobjective setting of the granulation space. However, PNERS describes knowledge with low accuracy, and therefore we construct two self-information uncertainty measures in ONERS and propose the joint self-information that is more suitable for attribute reduction as it takes full consideration of classification information in the lower and upper approximations. Then, an attribute reduction method using the joint self-information is designed, and Fisher Score is introduced into our method to decrease time cost when processing high dimensional data. Extensive experiments validate that our method is able to achieve superior reduction and classification results on different dimensional datasets.

Compact Extended Formulations for Low-Rank Functions with Indicator Variables

We study the mixed-integer epigraph of a special class of convex functions with nonconvex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions. Extended formulations describing the convex hull of such sets can easily be constructed via disjunctive programming although a direct application of this method often yields prohibitively large formulations, whose size is exponential in the number of variables. In this paper, we propose a new disjunctive representation of the sets under study, which leads to compact formulations with size exponential in the dimension of the nonlinear function but polynomial in the number of variables. Moreover, we show how to project out the additional variables for the case of dimension one, recovering or generalizing known results for the convex hulls of such sets (in the original space of variables). Our computational results indicate that the proposed approach can significantly improve the performance of solvers in structured problems. Funding: This work was supported by the National Science Foundation Division of Computing and Communication Foundations [Grant 2006762].

$$\lambda $$-Limited Sets in Banach and Dual Banach Spaces

$$\lambda $$-Limited Sets in Banach and Dual Banach Spaces

The Influence of Format Readability on Children’s Reading Speed and Comprehension

Background: Format readability, including font and spacing, impacts reading metrics in adults, but will the research generalize to children? We examined how eight fonts (four serif and four sans serif) and three-character spacing variations influenced children’s reading comprehension and reading speed. Methods: Fifty-one students in third–fifth grade read 11 narrative text passages on a computer and answered comprehension questions. Passages were randomized in terms of order. First, the font in which the text of each passage was presented was manipulated. Then passages were presented in three spacing manipulations (narrow, normal, and wide). Results: A linear mixed effects model demonstrated that, on a group-level, passages presented in Roboto and Arial font were read significantly faster (words-per-minute) than other fonts. On the individual level, students experienced significant boosts in reading speed (words-per-minute) between their best and worst fitting font, and spacing. A chi-square test showed no one font or spacing setting that was most likely to be a students’ font fit or clash. For reading comprehension, no speed–comprehension tradeoff was observed. Conclusions: Changes to text format at the group and individual level may yield boosts in reading speed for students, without negatively impacting reading comprehension.

COUPLED AND COMMON COUPLED FIXED POINT THEOREMS UNDER NEW COUPLED IMPLICIT RELATION IN PARTIAL METRIC SPACES

The purpose of this paper is to study existence and uniqueness of coupledand common coupled fixed point theorems for self-mappings satisfying a new coupledimplicit relation in the setting of partial metric spaces and give some corollaries ofTheorem 3.1. Furthermore, we prove well-posedness of a coupled fixed point problem.We also provide some applications of our result to a mapping with a contraction ofintegral type. The results of findings in this paper extend and generalize several resultsfrom the existing literature.

Asymptotic profiles of zero points of solutions to the heat equation

In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the high-order asymptotic expansion theory for the heat equation. This reveals a previously unknown asymptotic profile of zero points diverging at O ( t ) O(t) . In a one-dimensional spatial case, we show the zero point’s second and third-order asymptotic profiles in a general situation. We also analyze a zero level set in high-dimensional spaces and obtain results that extend the results for the one-dimensional spatial case.

A Bregman proximal point algorithm without convexity in Banach spaces

ABSTRACT In this paper, we first introduce a Bregman prox-convexity notion as the generalization of the convexity for Bregman prox-convexity in Banach spaces. We verify the single-valudeness and Bregman firm nonexpansiveness of the Bregman proximity operator of the functions and provide examples of the notion. Using this notion, we show that the Bregman proximal point scheme remains convergent under appropriate conditions on the functions to be minimized in the setting of Banach spaces.

Representation Learning and Reinforcement Learning for Dynamic Complex Motion Planning System.

Indoor motion planning challenges researchers because of the high density and unpredictability of moving obstacles. Classical algorithms work well in the case of static obstacles but suffer from collisions in the case of dense and dynamic obstacles. Recent reinforcement learning (RL) algorithms provide safe solutions for multiagent robotic motion planning systems. However, these algorithms face challenges in convergence: slow convergence speed and suboptimal converged result. Inspired by RL and representation learning, we introduced the ALN-DSAC: a hybrid motion planning algorithm where attention-based long short-term memory (LSTM) and novel data replay combine with discrete soft actor-critic (SAC). First, we implemented a discrete SAC algorithm, which is the SAC in the setting of discrete action space. Second, we optimized existing distance-based LSTM encoding by attention-based encoding to improve the data quality. Third, we introduced a novel data replay method by combining the online learning and offline learning to improve the efficacy of data replay. The convergence of our ALN-DSAC outperforms that of the trainable state of the arts. Evaluations demonstrate that our algorithm achieves nearly 100% success with less time to reach the goal in motion planning tasks when compared to the state of the arts. The test code is available at https://github.com/CHUENGMINCHOU/ALN-DSAC.

NANO g* sr CLOSED SETS IN NANO TOPOLOGICAL SPACES

The primary focus of this article is to develop, a fresh concept of sets namely Ng*sr closed sets. The goal of this research is to go over the concepts of Ng*sr closed sets and open sets in nano topological spaces. An appropriate illustration is given to study the properties of the above sets. The present relations between some of these sets in nano topological space are provided.

A new concept of semistrict quasiconvexity for vector functions

We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when Y = R and C = R + . Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.

Solving Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions Using Covariant JS-Contractions

This paper investigates the existence, uniqueness, and symmetry of solutions for Φ–Atangana–Baleanu fractional differential equations of order μ∈(1,2] under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant JS-contractions within a generalized framework of a sequential extended bipolar parametric metric space. As a consequence, we obtain the results on covariant and contravariant Ćirić, Chatterjea, Kannan, and Reich contractions as corollaries. Additionally, we substantiate our fixed-point findings with specific examples and derive similar results in the setting of sequential extended fuzzy bipolar metric space.

Continuous imbedding theorems in Musielak spaces

We provide continuous Sobolev-type imbedding results for Musielak spaces. In the first result the target space is a Musielak space bigger than the considered one, while the second is that of bounded and continuous functions. Continuous imbeddings into a particular Musielak space built upon Sobolev conjugate functions generate serious difficulties and does not holds in general for arbitrary Musielak functions, as it is well known in variable exponent Sobolev spaces. We overcome this problem by imposing only a regularity assumption on the Musielak functions without resorting to other restrictions such as the Δ2/∇2 conditions. Nevertheless, the continuous embedding in the space of bounded continuous functions is obtained by using the convex envelope, which then allows us to use a result already obtained in Orlicz spaces. The results we obtain extend and unify those obtained in classical Sobolev spaces, variable exponent Sobolev spaces as well as those obtained by Donaldson-Trudinger in the setting of Orlicz spaces.

Compactness and Connectedness in Beta Weakly Semi – Closed Sets in Topological Spaces

Compactness and Connectedness in Beta Weakly Semi – Closed Sets in Topological Spaces

On obtaining convergence order of a fourth and sixth order method of Hueso et al. without using Taylor series expansion

Hueso et al. (2015) studied the fourth and sixth order methods to approximate a solution of a nonlinear equation in Rn, where the convergence analysis needs the involved operator to be five times differentiable and seven times differentiable for fourth-order and sixth-order methods, respectively. Also, they found no error estimate for those methods, as the Taylor series expansion played a leading role in proving the convergence. In this paper, we extended the method in the Banach space settings and relaxed the higher order derivative of the involved operator so that the methods can be used in a bigger class of problems which were not covered by the analysis in Hueso et al. (2015). Also, we obtained an error estimate without Taylor series expansion. This error estimate helps to get the number of iterations to achieve a given accuracy. Moreover, new sixth-order method is introduced by small modification and numerical examples were discussed for all these methods to validate our theoretical results and to study the dynamics.

An event-triggered and dimension learning scheme WOA for PEMFC modeling and parameter identification

Aiming at the high dimension and complexity of parameters identification problem, a whale optimization algorithm based on event-triggered and dimension learning scheme (EDWOA) is presented, which is specifically designed for the proton exchange membrane fuel cell (PEMFC) model. Drawing inspiration from group optimization strategies, a novel dimensional learning method is introduced to enhance the dynamic search capabilities of the algorithm. To assess the efficacy of the proposed algorithm, benchmark function testing was conducted, and its fitness surpassed common heuristic algorithms on over 15 objective functions. The results clearly indicate that the EDWOA algorithm outperforms its counterparts in terms of global search performance. Its ability to navigate complex search spaces sets it apart from other algorithms. Finally, the proposed EDWOA algorithm is successfully applied to parameter identification in the PEMFC model. Through a comparative analysis with existing research findings, it was found that the identified PEMFC model exhibited a notable enhancement in fitness, ranging from 0.02 to 0.93. This underscores the effectiveness of the EDWOA algorithm in improving the performance and dynamic output of PEMFC models.

On GeneralizedNanoℕ?̌-Closed andNanoℕα̂-OpenSetsin Nano-Topological Spaces

This work aims to define a new class of sets in nano topological spaces called Nano (Nα) ̌- closed and (Nα) ̂-open sets, and to prove its verifiable properties and theorems.

Some algebras and logics from quasiorder-generated covering-based approximation spaces

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, ∼ 1 -complemented and ∼ 2 -complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics.

REGULARITY OF POISSON QUADRATIC STOCHASTIC OPERATOR GENERATED BY 2-PARTITION OF A SINGLETON

The theory of quadratic stochastic operator (QSO) was developed by Bernstein in 1924 when he presented about population genetics. The research on QSO is still ongoing as researchers have not yet studied various classes, conditions, and measures. In this paper, we introduce a new class of Poisson QSO generated by the 2-partition of a singleton defined on the set of all integers state space. We illustrate the trajectory behaviour of the constructed QSO by cases. Lastly, we show that it is a regular transformation for some parameters’ values.

Applications of semi-pre-c-open sets

Semi-pre-c-open sets are a subtle development in topology that has a substantial impact on both theoretical investigations and real-world applications. This study explores the several uses of semi-pre-c-open sets in diverse fields. First, we look into how they may be used to improve the structure of generalized topological spaces and give a more comprehensive framework for studying compactness, continuity, and convergence. A more precise categorization of functions is made possible by semi-pre-c-open sets, opening up new function spaces and expanding on previously established findings. Furthermore, their significant applications in digital topology help to advance digital continuity notions and more efficient picture processing methods. We develop and study semi-pre-c-open sets, a novel class of generalized open sets in a topological space. The semi-pre-open sets class includes this class. It is demonstrated that the topology generated by semi-pre-c-open sets is the same. Semi-pre-c-derived set, semi-pre-c-interior points, semi-pre-c-closure, semi-pre-c-closure, semi-pre-c-frontier, and semi-pre-c-exterior are among the topological aspects of these sets that we present and examine. Using examples and counterexamples, the existence of their relationship is also examined.