Existence of non-oscillatory solutions of a kind of first-order neutral differential equation

This paper deals with the existence of non-oscillatory solutions to a kind of first-order neutral equations having both delay and advance terms. The new results are established using the Banach contraction principle

Finite-time stabilization of discontinuous fuzzy inertial Cohen–Grossberg neural networks with mixed time-varying delays

This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results

A Topological Method for Comparing Document Semantics

Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from the statistic or the vector space model perspectives but nearly none from a topological perspective. In this paper, we hope to make a different sound. A novel algorithm based on topological persistence for comparing semantics similarity between two documents is proposed. Our experiments are conducted on a document dataset with human judges' results. A collection of state-of-the-art methods are selected for comparison. The experimental results show that our algorithm can produce highly human-consistent results, and also beats most state-of-the-art methods though ties with NLTK.Comment: 9 pages, 3 tables, 9th International Conference on Natural Language Processing (NLP 2020

Solitary wave and periodic wave solutions for a class of singular p-laplacian systems with impulsive effects

This work deals with the existence of periodic wave solutions and nonexistence of solitary wave solutions for a class of second-order singular p-Laplacian systems with impulsive effects. A su_cient criterion for the solutions of the considered system is provided via an innovative method of the mountain pass theorem and an approximation technique. Some corresponding results in the literature can be enriched and extended

Research on the impact of the development of green finance in the China region on residents’ health

In the context of implementing the strategy of “double carbon” and “healthy China,” this paper firstly measures the level of green finance development and the comprehensive index of health care accessibility in each province by using the entropy weight method based on 30 provincial panel data from 2007 to 2021. A panel fixed effects model was also used to empirically analyze the effect of regional green finance development on the improvement of residents’ health. In addition, a panel threshold model was constructed to empirically test the threshold effect of green finance on residents’ health under the influence of four external environments: carbon intensity level, healthcare accessibility, residents’ living standard and human capital level. The empirical results show that the regional green financial development in China significantly improves the health level of residents. And the impact has significant regional heterogeneity, as shown in the improvement effect is more significant for the provinces in the central and western regions. In addition, the impact of green financial development on the health level of residents in China is non-linearly influenced by external environmental factors. The improvement effect of green finance on residents’ health level is more significant in the provinces with higher carbon intensity level, residents’ living standard, human capital level and lower accessibility to medical services. In this regard, regional governments should continue to build and optimize a synergistic development ecosystem of green finance and public health, give full play to the advantages of financial leverage, promote green, low-carbon and high-quality economic and social development, and realize the beautiful vision of harmonious coexistence between human beings and nature

Two homoclinic solutions of anonperiodic fourth-order impulsive differential equation

In this paper, we are concerned with a kind of nonperiodic fourth-order impulsive differential equation. By applying the mountain pass theorem, we shall establish several new criteria for the existence of at least two nontrivial homoclinic solutions of the addressed equation. Some recent results in the literature are generalized and improved. In addition, a numerical example is provided to show the applicability and effectiveness of our main results.Mathematics Subject Classification (2010): 34C37, 37J45.Keywords: Homoclinic solutions, fourth-order impulsive differential equation, nonperiodic, mountain pass theore

Positive periodic solutions for p-Laplacian neutral differential equations with a singularity

Abstract In this paper, we study the positive periodic solutions of a kind of p-Laplacian neutral differential equation with a singularity. By applying the continuation theorem and some analytic techniques, we shall establish several new criteria for the existence of positive periodic solutions for the considered problem. Some recent results in the literature are generalized and improved. Three examples are given to illustrate the effectiveness of our results

Robust fixed-time synchronization of discontinuous Cohen–Grossberg neural networks with mixed time delays

This paper aims to investigate the fixed-time synchronization (i.e., synchronization in fixed-time sense) of Cohen–Grossberg drive-response neural networks with discontinuous neuron activations and mixed time delays (both time-varying discrete delay and distributed delay). To accomplish the target of fixed-time synchronization, a novel discontinuous feedback control procedure is firstly designed for the response neural networks. Then, under the framework of Filippov solutions, by means of functional differential inclusions theory, inequality technique and the nonsmooth analysis theory with Lyapunov-like approach, some sufficient criteria are derived to design the control parameters for achieving fixed-time synchronization of the proposed drive-response systems. Finally, two numerical examples are presented to illustrate the proposed methodologies