正螺面的两个由特殊曲线刻画的特征

通过对曲线主法线面的研究,得到了正螺面的两个由特殊曲线刻画的特征.     

Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.     

Collocation method using sinc and Rational Legendre functions for solving Volterra’s population model

This paper proposes two approximate methods to solve Volterra’s population model for population growth of a species in a closed system. Volterra’s model is a nonlinear integro-differential equation on a semi-infinite interval, where the integral term represents the effect of toxin. The proposed methods have been established based on collocation approach using Sinc functions and Rational Legendre functions. They are utilized to reduce the computation of this problem to some algebraic equations. These solutions are also compared with some well-known results which show that they are accurate.     

Fixed-time stabilization control for port-Hamiltonian systems

Nonlinear Dynamics - In this paper, the locally fixed-time and globally fixed-time stabilization problems for the port-Hamiltonian (PH) systems via the interconnection and damping assignment...     

Dark two-soliton solutions for nonlinear Schrödinger equations in inhomogeneous optical fibers

In this paper, the variable coefficient nonlinear Schrödinger equation is investigated analytically. With the bilinear method, the bilinear forms and analytic soliton solutions are obtained. Based on the obtained analytic solutions, the effect of free parameters on the control of soliton transmission is studied. Influences of second-order and third-order dispersion coefficients on dark solitons are discussed. Results in this paper would be of great significance in the generation of dark solitons.     

Stochastic exponential synchronization for delayed neural networks with semi-Markovian switchings: Saturated heterogeneous sampling communication

By implementing heterogeneous sampling communication mechanism, this article addresses the exponential synchronization issue of drive–response chaotic neural networks (CNNs) with interval time-varying delays by simultaneously taking into account the semi-Markovian switchings and saturating actuators. More specifically, a semi-Markovian jumping model whose transition rates (TRs) are not constant but depends on the sojourn time (ST) is introduced to characterize the stochastic changing among the interaction of CNNs, which makes the NNs model under consideration more suitable for some actual circumstances. More particularly, we assume that the sampling intervals are heterogeneous and time-varying, which may be more practical in real-life applications than homogeneous sampling policy. Additionally, by introducing some new terms, one novel time-dependent Lyapunov–Krasovskii function (LKF) is ingeniously constructed, which can fully capture the characteristic information of heterogeneous sampling pattern. Benefitting from the introduced relaxed free-weighting matrices (FWM) and resorting to the formed LKF, some sampling-interval-dependent sufficient conditions for controller design of the resulting semi-MJNNs error system are established and expressed by linear matrix inequalities (LMIs). These LMIs-based constraints can be effectively checked by utilizing the available software packages. Therein, the developed synchronization criteria dependent on both the lower and upper bounds of sampling periods, and the available information about the actual sampling pattern is fully considered. Ultimately, two numerical examples are provided to demonstrate the feasibility and practicability of our theoretical findings.     

Nonlinear instability for nonhomogeneous incompressible viscous fluids

We investigate the nonlinear instability of a smooth steady density profile solution to the three-dimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor steady-state solution with heavier density with increasing height (referred to the Rayleigh-Taylor instability). We first analyze the equations obtained from linearization around the steady density profile solution. Then we construct solutions to the linearized problem that grow in time in the Sobolev space H ^k , thus leading to a global instability result for the linearized problem. With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations, we can then demonstrate the instability of the nonlinear problem in some sense. Our analysis shows that the third component of the velocity already induces the instability, which is different from the previous known results.