测定晶体结构的系统试差法的研究(II)系统位相超解方程得改进

本文证明了|E(k)E(h-k)|的大小是由结构决定的。与原点无关, 在这种认识的基础上, 提出了用归一化结构振幅|E|估量它的三种模式。特别是通过四位相结构不变量的二级Noighborhood~[1,2]原理解决三位相不变量间的匹配问题而算出的|E(k)E(h-k)|_(QE), 这是在没有位相数据的情况下对它的理想的估量。予期它能改进系统试差法中位相超解方程的功能, 提高测得位相的准确性。     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.     

A two-step estimator of the extreme value index

In this paper, we build a two-step estimator , which satisfies , where is the well-known maximum likelihood estimator of the extreme value index. Since the two-step estimator can be calculated easily as a function of the observations, it is much simpler to use in practice. By properly choosing the first step estimator, such as the Pickands estimator, we can even get a shift and scale invariant estimator with the above property. The author thanks Laurens de Haan for motivating this work and giving helpful comments. The author also thanks two anonymous referees for their useful comments.     

Almost positive curvature on the Gromoll-Meyer sphere

Gromoll and Meyer have represented a certain exotic 7-sphere as a biquotient of the Lie group . We show for a 2-parameter family of left invariant metrics on that the induced metric on has strictly positive sectional curvature at all points outside four subvarieties of codimension which we describe explicitly.

     

Slice knots with distinct Ozsváth-Szabó and Rasmussen invariants

As proved by Hedden and Ording, there exist knots for which the Ozsváth-Szabó and Rasmussen smooth concordance invariants, and , differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice. It is shown in this note that a simple manipulation of the Hedden-Ording examples yields a topologically slice Alexander polynomial one knot for which and differ. Manolescu and Owens have previously found a concordance invariant that is independent of both and on knots of polynomial one, and as a consequence have shown that the smooth concordance group of topologically slice knots contains a summand isomorphic to . It thus follows quickly from the observation in this note that this concordance group contains a summand isomorphic to .

     

Semiclassical analysis for highly degenerate potentials

This paper characterizes the semi-classical limit of the fundamental energy,

and ground state of the Schrödinger operator in a bounded domain , in the highly degenerate case when and consists of two components, say and . The main result establishes that

and that approximates in the ground state of in if

     

Norm Inequalities for Commutators of Self-adjoint Operators

Let A, B, and X be bounded linear operators on a complex separable Hilbert space. It is shown that if A and B are self-adjoint with and for some real numbers a ₁, a ₂, b ₁, and b ₂, then for every unitarily invariant norm|||·|||,

Stability problem for the Go?a?b-Schinzel type functional equations

Let X be a vector space over a field K of real or complex numbers, n∈N and λ∈K?{0}. We study the stability problem for the Go?a?b-Schinzel type functional equations

f(x+fn(x)y)=λf(x)f(y)     

Some isoperimetric inequalities and eigenvalue estimates in weighted manifolds

In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative linear isoperimetric inequality for such submanifolds. We also prove an extrinsic upper bound to the first non-zero eigenvalue of the drift Laplacian on closed submanifolds of weighted manifolds.     

Optimum life testing plans in presence of hybrid censoring: A cost function approach

Hybrid censoring scheme is a combination of Type‐I and Type‐II censoring schemes. Determination of optimum hybrid censoring scheme is an important practical issue in designing life testing experiments to enhance the information on reliability of the product. In this work, we consider determination of optimum life testing plans under hybrid censoring scheme by minimizing the total cost associated with the experiment. It is shown that the proposed cost function is scale invariant for some selected distributions. Optimum solution cannot be obtained analytically. We propose a method for obtaining the optimum solution and consider Weibull distribution for illustration. We also studied the sensitivity of the optimal solution to the misspecification of parameter values and cost components through a well‐designed sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.