Weaker Sufficient Conditions Research Articles

Impulsive-Based Almost Surely Synchronization for Neural Network Systems Subject to Deception Attacks.

This article is dedicated to investigating the impulsive-based almost surely synchronization issue of neural network systems (NSSs) with quality-of-service constraints. First, the communication network considered suffers from random double deception attacks, which are modeled as a nonlinear function and a desynchronizing impulse sequence, respectively. Meanwhile, the impulsive instants and impulsive gains are randomly and only their expectations are available. Second, by taking two different types of random deception attacks into consideration, a novel mathematical model for vulnerable NSSs is constructed. Then, almost surely synchronization criteria are established by using Borel-Cantelli lemma. Furthermore, based on the derived strong and weak sufficient conditions, the almost surely synchronization of NSSs is achieved. Finally, the section of numerical example is shown to illustrate the effectiveness of the proposed method.

Stability Analysis for Semi-Infinite Vector Optimization Problems under Functional Perturbations

This paper aims to study the stability of a class of semi-infinite vector optimization problems (SVOP) under functional perturbations. By using an important hypothesis a necessary and sufficient condition of Hausdorff continuity for weak efficient solution mappings and certain sufficient conditions for Painlevé-Kuratowski convergence of weak efficient solution sets for SVOP are established under the perturbations of both constraint sets and objective functions.

Persistence of excitation for identifying switched linear systems

This paper investigates the uniqueness of parameters via persistence of excitation for switched linear systems. The main contribution is a much weaker sufficient condition on the regressors to be persistently exciting that guarantees the uniqueness of the parameter sets and also provides new insights in understanding the relation among different subsystems. It is found that for uniquely determining the parameters of switched linear systems, the needed minimum number of samples derived from our sufficient condition is much smaller than that reported in the literature.

THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE

In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.

On unique solvability and Picard’s iterative method for absolute value equations

In this paper, we deal with unique solvability and numerical solution ofabsolute value equations (AVE),Ax−B|x|=b, (A,B∈Rn×n,b∈Rn).Under some weaker conditions, a simple proof is given for unique solvabilityof AVE. Furthermore, we demonstrate with an example that these results arereliable to detect unique solvability of AVE. These results are also extendedto unique solvability of standard and horizontal linear complementarity prob-lems. Finally, we suggest a Picard iterative method to compute an approx-imated solution of some uniquely solvable AVE problems where its globallylinear convergence is guaranteed via one of our weaker sufficient condition.

General and weak sufficient condition for Hamiltonian systems

General and weak sufficient condition for Hamiltonian systems

Ground state solutions for Schrödinger–Poisson system with critical exponential growth in [formula omitted

This paper gives weak sufficient conditions to get the existence of ground state solutions for the following planar Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(x,u),x∈R2,Δϕ=u2,x∈R2,where V∈C(R2,[0,∞)) is axially symmetric and f∈C(R2×R,R) is of critical exponential growth in the sense of Trudinger–Moser inequality. Especially, some new estimates involving the Moser’s sequence of functions are given to get some suitable upper bound for the mountain pass level. Our theorem extends and improves the results of de Figueiredo et al. (1995) and of Chen and Tang (2020).

A microscopic approach to Souslin-tree construction, Part II

In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known ⋄-based constructions of Souslin trees with various additional properties may be rendered as applications of our approach. In this paper, we show that constructions following the same approach may be carried out even in the absence of ⋄. In particular, we obtain a new weak sufficient condition for the existence of Souslin trees at the level of a strongly inaccessible cardinal.We also present a new construction of a Souslin tree with an ascent path, thereby increasing the consistency strength of such a tree's nonexistence from a Mahlo cardinal to a weakly compact cardinal.Section 2 of this paper is targeted at newcomers with minimal background. It offers a comprehensive exposition of the subject of constructing Souslin trees and the challenges involved.

On Feller and strong Feller properties and irreducibility of regime-switching jump diffusion processes with countable regimes

This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small fluctuations as well as big spikes coexist and are intertwined. The paper provides weak sufficient conditions for Feller and strong Feller properties and irreducibility for such processes. The conditions are presented in terms of the coefficients of the associated stochastic differential equations.

Souslin trees at successors of regular cardinals

AbstractWe present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.

Iterated elimination procedures

We study the existence and uniqueness (i.e., order independence) of any arbitrary form of iterated elimination procedures in an abstract environment. By allowing for a transfinite elimination, we show a general existence of the iterated elimination procedure. Inspired by the seminal work of Gilboa et al. (OR Lett 9:85–89, 1990), we identify a fairly weak sufficient condition of Monotonicity* for the order independence of iterated elimination procedure. Monotonicity* requires a Monotonicity property along any elimination path. Our approach is applicable to different forms of iterated elimination procedures used in (in)finite games, for example iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, rationalizability, and so on. We introduce a notion of CD* games, which incorporates Jackson’s (Rev Econ Stud 59:757–775, 1992) idea of “boundedness,” and show the iterated elimination procedure is order independent in the class of CD* games. In finite games, we also formulate and show an “outcome” order-independence result suitable for Marx and Swinkles’s (Games Econ Behav 18:219–245, 1997) notion of nice weak dominance.

A Class of Nonautonomous Schistosomiasis Transmission Model with Incubation Period

A nonautonomous schistosomiasis model with latent period and saturated incidence is investigated. Further, we study the long-time behavior of the epidemic model. The weaker sufficient conditions for the permanence and extinction of infectious population of the model are obtained by constructing some auxiliary functions. Numerical simulations show agreement with the theoretical results.

Resilient guaranteed cost control for uncertain T–S fuzzy systems with time-varying delays and Markov jump parameters

This paper aims to investigate the problem of resilient guaranteed cost control for uncertain Takagi–Sugeno fuzzy systems with Markov jump parameters and time-varying delay. A resilient mode-dependent fuzzy controller is designed and a weak sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples of the single-link robot arm system are provided to demonstrate the performance of the proposed approach.

Divide-and-choose with nonmonotonic preferences

I consider the divide-and-choose method for allocating fixed quantities of infinitely divisible commodities among two agents when their preferences are commonly known but need not be monotonic. First, I show that with single-dipped preferences, the outcome may not be envy-free (or efficient). Also, it may be advantageous to be the chooser rather than the divider. I then show that if preferences are single-peaked, the divide-and-choose outcome is envy-free. This establishes a significantly weaker sufficient condition for no-envy than monotonicity. Moreover, it shows that it is not the lack of monotonicity per se that may cause the divide-and-choose outcome to be envious but rather a particular type.

A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems

We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In order to control the feasibility violation induced by the discretization, error estimates for the semilinear partial differential equation are derived. Based upon these estimates, it can be shown that any local minimizer of the semilinear parabolic optimization problems satisfying a weak second-order sufficient condition can be approximated by the discretized problem. Rates for this convergence in terms of temporal and spatial discretization mesh sizes are provided. In contrast to other results in numerical analysis of optimization problems subject to semilinear parabolic equations, the analysis can work with a weak second-order condition, requiring growth of the Lagrangian in critical directions only. The analysis can then be conducted relying solely on the resulting quadratic growth condition of the continuous problem, without the need for similar assumptions on the discrete or time semidiscrete setting.

Recovery of signals under the condition on RIC and ROC via prior support information

In this paper, the sufficient condition in terms of the RIC and ROC for the stable and robust recovery of signals in both noiseless and noisy settings was established via weighted l 1 minimization when there is partial prior information on support of signals. An improved performance guarantee has been derived. We can obtain a less restricted sufficient condition for signal reconstruction and a tighter recovery error bound under some conditions via weighted l 1 minimization. When prior support estimate is at least 50% accurate, the sufficient condition is weaker than the analogous condition by standard l 1 minimization method, meanwhile the reconstruction error upper bound is provably to be smaller under additional conditions. Furthermore, the sufficient condition is also proved sharp. • A weaker sufficient condition and a tighter recovery error bound are obtained. • The sufficient condition on RIC and ROC is sharp. • The achievable performance of signal recovery is better than the work in [5]. • Our work can be seen a supplement of Friedlander et al. [18].

Strong convergence rates of modified truncated EM method for stochastic differential equations

Motivated by truncated Euler–Maruyama (EM) method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler–Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time T and over a time interval [0,T] under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions.

Finite Convergence for Feasible Solution Sequence of Variational Inequality Problems

We establish the notion of augmented weak sharpness of solution sets for the variational inequality problems which can be abbreviated to VIPs. This notion of augmented weak sharpness is an extension of the weak sharpness of the solution set of monotone variational inequality, and it overcomes the defect of the solution set not satisfying the weak sharpness in many cases. Under the condition of the solution set being augmented weak sharp, we present a necessary and sufficient condition for finite convergence for feasible solution sequence of VIP. The result is an extension of published results, and the augmented weak sharpness also provides weaker sufficient conditions for the finite convergence of many optimization algorithms.

Global dynamics of a stochastic ratio-dependent predator–prey system

The dynamical properties of a stochastic non-autonomous ratio-dependent predator–prey system are studied by applying the theory of stochastic differential equations, Itô’s formula and the method of Lyapunov functions. First, the existence, the uniqueness and the positivity of the solution are discussed. Second the boundedness of the moments and the upper bounds for growth rates of prey and predator are studied. Moreover, the global attractivity of the system under some a weaker sufficient conditions are investigated. Finally, the theoretical results are confirmed by the special examples and the numerical simulations.

Recurrence Principles and Their Application to Stability Theory for a Class of Stochastic Hybrid Systems

In this paper, we establish results similar in nature to the invariance principle for a class of stochastic hybrid systems modeled by set-valued mappings. In particular, we characterize the set to which bounded random solutions converge in terms of a new concept called weak total recurrence. A refinement of the result under the existence of a non-increasing on average Lyapunov-like function is also established. A comparison between weak total recurrence and the frequently studied invariance concepts are presented. Finally, application of the main results to establish weak sufficient conditions for certifying stochastic stability properties like uniform global asymptotic stability in probability for compact sets and uniform global recurrence for open, bounded sets are discussed.