“混合元”的有限元法

大家知道,用有限元求解微分方程时,如果微分方程的解足够光滑,边界比较接近拆线,采用高阶元比采用低阶元网格可以稀得多,因此这时采用高阶元比低阶元有利得多,但在实际计算中,边界常常比较复杂,解在边界附近变化较大,这时只采用高阶元在边界     

Factorization method for second order functional equations

We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the change of variables. Some examples of applications are presented.     

Nucleation of bulk superconductivity close to critical magnetic field

We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC₂ and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L^∞-bound which is of independent interest.     

Generalization of the simplest equation method for nonlinear non-autonomous differential equations

It is known that the simplest equation method is applied for finding exact solutions of autonomous nonlinear differential equations. In this paper we extend this method for finding exact solutions of non-autonomous nonlinear differential equations (DEs). We applied the generalized approach to look for exact special solutions of three Painlevé equations. As ODE of lower order than Painlevé equations the Riccati equation is taken. The obtained exact special solutions are expressed in terms of the special functions defined by linear ODEs of the second order.     

Unimodality of uniform generalized order statistics,with applications to mean bounds

We prove that uniform generalized order statistics are unimodal for an arbitrary choice of model parameters. The result is applied to establish optimal lower and upper bounds on the expectations of generalized order statistics based on nonnegative samples in the population mean unit of measurement. The bounds are attained by two-point distributions.     

Solvability of a boundary-value problem with an integral boundary condition of the second kind for equations of odd order

We study the solvability of a boundary-value problem for equations of odd order subject to a boundary condition relating the values of the conormal derivative with those of an integral operator applied to the solution. We prove the existence and uniqueness theorems for regular solutions.     

On the Behavior of the Four Order Iteration in Euler's Family Near a Zero

The aim of this paper is to study the local convergence of the four order iteration of Euler's family for solving nonlinear operator equations. We get the optimal radius of the local convergence ball of the method for operators satisfying the weak third order generalized Lipschitz condition with L-average. We also show that the local convergence of the method is determined by a period 2 orbit of the method itself applied to a real function.     

On the regularity of second order cone programs and an application to solving large scale problems

We prove the nonsingularity of the standard primal–dual system for second order cone programs assuming Slater’s condition, uniqueness and strict complementarity. This result is applied to the analysis of the augmented primal–dual method for solving linear programs over second order cones.     

D-CONVERGENCE OF ONE-LEG METHODS FOR STIFF DELAY DIFFERENTIAL EQUATIONS

1. IntroductionIn recent yeaJrs, many paPers discussed numerical methods for the solution of delay deential equation (DDE)y,(t) = f(t,y(t),y(t -- T)). (1.1)For linear stability of ntunerical methods, a sedcant nUIner of results have aiready beenfound for both Rase--Kutta methods and linear mchistev mehods (cf[4] [7] [8]).Recently wefurther established the relationship between G-stability and llonhnear stability (cf[3]). Erroranalysis of DDE sobors is another imPortant issue. In faCt, ma…     

Moments of integral-type downward functionals for single death processes

We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes. Meanwhile, main results are applied to more general integral-type downward functionals.     

Hyperbolic 3-manifolds with geodesic boundary: Enumeration and volume calculation

We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be applied in order to analyze simultaneously compact manifolds and finite-volume manifolds with toric cusps. In contrast, we show that if one allows annular cusps, the number of manifolds grows very rapidly and our strategy cannot be employed to obtain a complete list. We also carefully describe how to compute the volume of our manifolds, discussing formulas for the volume of a tetrahedron with generic dihedral angles in hyperbolic space.     

A Zienkiewicz-type finite element applied to fourth-order problems

This paper deals with convergence analysis and applications of a Zienkiewicz-type (Z-type) triangular element, applied to fourth-order partial differential equations. For the biharmonic problem we prove the order of convergence by comparison to a suitable modified Hermite triangular finite element. This method is more natural and it could be applied to the corresponding fourth-order eigenvalue problem. We also propose a simple postprocessing method which improves the order of convergence of finite element eigenpairs. Thus, an a posteriori analysis is presented by means of different triangular elements. Some computational aspects are discussed and numerical examples are given.     

Symplectic invariants and covariants of matrices

This paper deals with symplectic algebraic invariants and covariants of matrices. We adapt the Aronhold symbolic method to characterize and compute the generators of algebras of symplectic invariants and covariants. New symplectic identities are obtained and applied to construct minimal generator systems of a matrix of order 4 and a Hamiltonian matrix of order 2n.     

Fixed point theorem of Leggett-Williams type and its application

We establish a norm-type cone expansion and compression fixed point theorem for completely continuous operators. Our theorem is then applied to prove the existence of positive solution of second order three-point boundary value problem.     

A Doubly Adaptive Integration Algorithm Using Stratified Rules

A doubly adaptive integration algorithm chooses between a higher order rule applied on the current subinterval or the subdivision of the interval. We describe one such algorithm using a stratified sequence of integration rules. We present a criterion to select the suitable strategy, depending on the type of integrand, using available information.     

不确定性对混合CVaR约束库存系统的影响

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的“风险偏好系数”,得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。     

On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations

We present a modified method for solving nonlinear systems of equations with order of convergence higher than other competitive methods. We generalize also the efficiency index used in the one-dimensional case to several variables. Finally, we show some numerical examples, where the theoretical results obtained in this paper are applied.     

Stability of Order Statistics under Dependence

We precisely evaluate the upper and lower deviations of the expectation of every order statistic from an i.i.d. sample under arbitrary violations of the independence assumption, measured in scale units generated by various central absolute moments of the parent distribution of a single observation. We also determine the distributions for which the bounds are attained. The proof is based on combining the Moriguti monotone approximation of functions with the Hölder inequality applied for proper integral representations of expected order statistics in the independent and dependent cases. The method allows us to derive analogous bounds for arbitrary linear combinations of order statistics.     

Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications

We discuss the existence of fixed point for a class of nonlinear operators by a combination of topological and variational method. The theoretical results are applied to second order dynamic equation with homogeneous Dirichlet boundary conditions.     

Relaxing convergence conditions for an inverse-free Jarratt-type approximation

We consider an inverse-free Jarratt-type approximation of order four in a Banach space (Argyros et al., 1996). We establish a convergence theorem by using recurrence relations. The purpose of this note is to relax convergence conditions and give an example where our convergence theorem can be applied but not the other ones.