Attracting and invariant sets for a class of impulsive functional differential equations

AbstractIn this article, a class of nonlinear and nonautonomous functional differential systems with impulsive effects is considered. By developing a delay differential inequality, we obtain the attracting set and invariant set of the impulsive system. An example is given to illustrate the theory

Input-to-State Stability for Dynamical Neural Networks with Time-Varying Delays

A class of dynamical neural network models with time-varying delays is considered. By employing the Lyapunov-Krasovskii functional method and linear matrix inequalities (LMIs) technique, some new sufficient conditions ensuring the input-to-state stability (ISS) property of the nonlinear network systems are obtained. Finally, numerical examples are provided to illustrate the efficiency of the derived results

The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations

This paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulations are given to illustrate the effectiveness of our results. In addition, we show that the impulsive effects may play a key role to these asymptotical properties even though the solutions of corresponding nonimpulsive systems are unbounded

The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations

This paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulations are given to illustrate the effectiveness of our results. In addition, we show that the impulsive effects may play a key role to these asymptotical properties even though the solutions of corresponding nonimpulsive systems are unbounded

The Character Transformation of Henry Fleming in The Red Badge of Courage

The Red Badge of Courage, written by Stephen Crane, is one of the representative works of American naturalism. It describes and evaluates the American Civil War through the eyes of the protagonist, Henry Fleming. This thesis mainly focuses on the character transformation of the protagonist, and it also briefly analyzes the reasons for his transformation.Key words: The Red Badge of Courage; Henry Fleming; Character transformatio

Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the subset defined by one of the constraints, our algorithm only requires projecting onto a half-space approximation of the subset, which significantly reduces the computational cost as it admits a closed-form formula. Second, to exploit the structure that the objective is a sum, variance reduction is incorporated into our algorithm to further improve the performance. As theoretical contributions, under an error bound condition and other standard assumptions, we prove that the proposed RPM converges to an optimal solution and that both optimality and feasibility gaps vanish at a sublinear rate. We also provide sufficient conditions for the error bound condition to hold. Experiments on a beamforming problem and a robust classification problem are also presented to demonstrate the superiority of our RPM over existing ones

Effect of annealing in O2 or N2 on the aging of Fe0.5Mn1.84Ni0.66O4 NTC-ceramics

Fe0.5Mn1.84Ni0.66O4 NTC ceramic thermistors were annealed in nitrogen or oxygen atmosphere at 600 °C. The change of the electrical properties of the thermistors with time was reduced sharply by annealing in N2, whereas it was enhanced upon annealing in O2. N2-annealed samples exhibited a less degree of redistribution of cations in the lattice as compared with O2-annealed samples. The aging of the electrical properties is believed to result from the cation redistribution which in turn is favoured by the presence of cation vacancies. And the improved aging behaviour of the N2-annealed thermistor is explained by the reduction of the concentration of the cation vacancy upon annealing under lower oxygen partial pressure and the suppression of cation redistribution