Novel and stereocontrolled asymmetric synthesis of a new naturally occurring styryllactone, (+)-cardiobutanolide

An efficient and stereodefined strategy is described for the asymmetric synthesis of a new styryllactone from the stem bark of Goniothalamus cardiopetalus, cardiobutanolide. The synthetic process is based on requisite manipulation of the functionalized bicyclic lactol-lactone intermediate incorporating the glucuronolactone-derived skeleton in a complete stereoselective manner.     

图有分数因子的度条件

本文研究了图有分数因子的度条件,得到了下面的结果：令k(?)1是一个整数,G是一个连通的n阶图,n(?)4k-3且最小度δ(G)(?)k,若对于每一对不相邻的顶点u,v∈V(G)都有max{d_G(u),d_G(v)}(?)n/2,则G有分数k-因子．并指出该结果在一定意义上是最好可能的。     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.     

Coupled intervals in the discrete calculus of variations: necessity and sufficiency

In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: The nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [R. Hilscher, V. Zeidan, Comput. Math. Appl., to appear], where the right endpoint is fixed.     

On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

A Modified Quasi-Newton Method for Structured Optimization with Partial Information on the Hessian

This paper develops a modified quasi-Newton method for structured unconstrained optimization with partial information on the Hessian, based on a better approximation to the Hessian in current search direction. The new approximation is decided by both function values and gradients at the last two iterations unlike the original one which only uses the gradients at the last two iterations. The modified method owns local and superlinear convergence. Numerical experiments show that the proposed method is encouraging comparing with the methods proposed in [4] for structured unconstrained optimization Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040