Some properties on the star order of bounded operators

In this paper, we give various characterizations of star order and present some new relationships between the logic order and the star order. We present some necessary and sufficient conditions for which the infimum or upper bound exists with respect to given orders.     

Fixed point theorems for mixed monotone operators and applications to integral equations

The purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. We also present an application to integral equations.     

Artificial boundary conditions to compute correctors in linear elasticity

We present the derivation of a transparent boundary condition of order two to solve the equations of linear elasticity in a half plane. The resolution of the boundary value problem leads to a noncoercive variational formulation. We also present some numerical examples.     

Further results on the reverse order law for the Moore-Penrose inverse in rings with involution

We present some equivalent conditions of the reverse order law for the Moore-Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C^∗-algebras.     

推广的相关序及其一些性质

本文考虑相关风险序，首先，把Dhaene和Goovaerts于1996年提出的相关序由二维随机向量推广到了多维随机向量的情况；然后，我们讨论了推广的相关序的一些性质；最后作为推论，我们还得到：由相关序可以推出指数序．     

On orders of approximation of plane curves by parametric cubic splines

The aim of the present paper is to show that the convergence rate of the parametric cubic spline approximation of a plane curve is of order four instead of order three. For the first and second derivatives, the rates are of order three and two, respectively. Finally some numerical examples are given to illustrate the predicted error behaviour.     

Explicit One-Step P-Stable Methods for Second Order Periodic Initial Value Problems

In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.     

NUMERICAL METHODS FOR MAXWELL＇S EQUATIONS IN INHOMOGENEOUS MEDIA WITH MATERIAL INTERFACES

In this paper, we will present some recent results on developing numerical methods for solving Maxwell‘s equations in inhomogeneous media with material interfaces. First,we will present a second order upwinding embedded boundary method - a Cartesian grid based finite difference method with special upwinding treatment near the material interfaces. Second, we will present a high order discontinuous spectral element with Dubinar orthogonal polynomials on triangles. Numerical results on electromagnetic scattering and photonic waveguide will be included.     

Linear Complementarity Problems on Extended Second Order Cones

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.     

Partial algebras—survey of a unifying approach towards a two-valued model theory for partial algebras

In this survey, with no proofs included, we collect some material scattered through recent papers and a planned monograph, which shows that partial algebras do have a two-valued first order model theory which is simpler and nicer than one might have expected it to be. In section 1 we comment and present some basic definitions. In section 2 a correct and complete two-valued first order logic is developed. In section 3 the three main concepts of “varieties” are presented, while sections 4 and 5 contain some additional axiomatizability results and some applications, respectively. Section 6 contains some additional remarks. Presented by E. Fried.     

A simplified view of first order methods for optimization

We discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms, with a focus on non-Euclidean proximal distances of Bregman type, which are central to the analysis of many other fundamental first order minimization relatives. We stress simplification and unification by highlighting self-contained elementary proof-patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings, which in turn also allows to present some novel results.     

Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus

We introduce a new class of smooth pseudodifferential operators on the torus whose calculus allows us to show that global hypoellipticity with a finite loss of derivatives of certain systems of pseudodifferential operators is stable under perturbations by lower order systems of pseudodifferential operators whose order depends on the loss of derivatives. We also present some applications.     

Generalized contractions in partially ordered metric spaces

We present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption.     

Bifurcation analysis and feedback control of a 3D chaotic system

In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcritical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results.     

论Bézier曲线的仿射不变量

本文的目的是按照[1]的理论找出n次平面Bezier曲线的内在仿射不变量,特别是,对于3次Bezier曲线的保凸性作出其充要条件的几何解释。对于一般的情况下的保凸性问题,至今还没有解决。著者仅在4次的场合详尽地讨论了曲线段上是否存在拐点的分析的(而不是几何的)充要条件,而最后举出几个实例,以说明特征多角形的凸性是充分条件,而不是必要条件。     

Some eighth-order root-finding three-step methods

In this paper, we present an improvement of the local order of convergence to increase the efficiency of some fourth-order iterative methods and the order can be improved from four to eight. Per iteration the present methods require three evaluations of the function and one evaluation of its first derivative and therefore have the efficiency index equal to 1.682. Numerical tests verifying the theory are given.     

On order bounded disjointness preserving operators

The paper is aimed at demonstrating that some properties of order bounded operators in vector lattices are just Boolean valued interpretations of elementary properties of order bounded functionals. We present the general machinery and illustrate it with a few new results on order bounded disjointness preserving and n-disjoint operators.     

OSCILLATION CRITERIA FOR SECOND ORDER QUASILINEAR NEUTRAL EQUATION

We present some new oscillation criteria for second order neutral delay differential equations with distributed deviating argument using the Riccati technique and some inequalities. The results obtained improve and extend some known results.     

Approximation of the rth differential operator by means of linear shape preserving operators of finite rank

In this paper, we present some results estimating the order of approximation of the rth derivative of a function by means of linear operators under different assumptions related to shape preserving properties. We give an example of an operator with the best order of approximation.