On the search for a narrow penta-quark Z+-baryon in NN interactions

The possibility for an observation of a narrow penta-quark Z⁺-baryon in NN reactions is discussed. It is shown that the pp↦nΣ⁺ K ⁺ reaction at excess energies around 100 MeV above threshold provides optimal conditions for Z⁺-baryon detection by an analysis of the nK⁺ invariant mass spectrum, if the Z⁺ mass is located around 1.5 GeV involving a rather narrow width. Received: 24 May 2000 / Accepted: 3 August 2000     

Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST

A characterization of the standard models of ZFC set theory that are embeddable as the class of standard sets in models of the internal set theory IST and some of its versions is proposed. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 202–210, August, 1999.     

Nonstandard finite difference schemes for reaction‐‐diffusion equations having linear advection

We extend previous work on nonstandard finite difference schemes for one‐space dimension, nonlinear reaction–diffusion PDEs to the case where linear advection is included. The use of a positivity condition allows the determination of a functional relation between the time and space step‐sizes, and provides schemes that are explicit. The Fisher equation is used to illustrate the method. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 361–364, 2000     

Finite element solution of vector Poisson equation with a coupling boundary condition

The vector Poisson equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. A rigorous analysis of such a vector Poisson problem and uncoupled solution methods have been presented for domains of C^1,1 and Lipschitz regularity in [1] and [2], respectively. In this work, the finite element approximation of the two uncoupled solution methods is studied, and a convergence analysis of the numerical schemes is provided together with some numerical results. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 71–83, 2000     

Synthesis of macrocyclic lactones with methoxysulfonyl side chain

Two representative macrocyclic lactones with methoxysulfonyl side chain（5a and 5b）were synthesized employing Michael addition with acrolein and ring enlargement as the key steps,starting from potassium,α-oxocycloaikylsulfonates（1）in total yields of 45 and 57%,respectively.     

各向异性增长拟线性椭圆型方程广义解最大模的先验估计

本文我们第一次给出了几类各向异性增长拟线性椭圆型方程广义解的最大模的先验估计。     

Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition

An essential feature of nonstandard finite difference schemes for differential equations is the precise manner in which the discretization of derivatives is made. We demonstrate, for differential equations modeling systems where the solutions satisfy a positivity condition, that procedures can be formulated to calculate the so‐called denominator functions that appear in the discrete derivatives. These procedures are applied to a number of both ordinary and partial model differential equations to illustrate their use. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Nonstandard solvability for linear operators between sections of vector bundles

Given a certain kind of linear operator (possibly a differential operator or a properly supported pseudodifferential operator) between sections of Hermitian vector bundles over a Riemannian manifold, a necessary and sufficient condition is obtained for the operator to be solvable in a class of nonstandard sections in a generalized sense of weak solutions. The existence of a fundamental-solution-like internal section is established in the solvable case.

     

Alpha-theory: An elementary axiomatics for nonstandard analysis

The methods of nonstandard analysis are presented in elementary terms by postulating a few natural properties for an infinite “ideal” number . The resulting axiomatic system, including a formalization of an interpretation of Cauchy's idea of infinitesimals, is related to the existence of ultrafilters with special properties, and is independent of ZFC. The Alpha-Theory supports the feeling that technical notions such as superstructure, ultrapower and the transfer principle are definitely not needed in order to carry out calculus with actual infinitesimals.     

Nonstandard Set Theory in ∈-Language

A sufficiently convenient set theory in the standard -language applicable to nonstandard analysis is proposed.