Unavoidable sequences in constructive analysis

Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic (choice) sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π¹₁ formula is unavoidable (cannot fail to exist) and that no sequence can fail to be classically Δ¹₁. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A generalization of ekellandz’s variational principle

This paper presents a vector valued variational principle by using a general concept of ?-efficiency and a nonconvex separation theorem     

基于广义最大熵原理和遗传算法的多指标权重确定方法研究

本文探讨了多目标评价的实现过程,针对评价过程的权重确定问题,提出了基于广义最大熵原理和遗传算法的赋权方法,该方法把不同赋权方法有机地集成在一起,并可以对各种赋权方法进行优劣比较。最后用实例验证了该方法的准确性、可靠性和有效性。     

Existence and Uniqueness of Stationary Solutions for 3D Navier–Stokes System with Small Random Forcing via Stochastic Cascades

We consider the 3D Navier–Stokes system in the Fourier space with regular forcing given by a stationary in time stochastic process satisfying a smallness condition. We explicitly construct a stationary solution of the system and prove a uniqueness theorem for this solution in the class of functions with Fourier transform majorized by a certain function h. Moreover we prove the following “one force—one solution” principle: the unique stationary solution at time t is presented as a functional of the realization of the forcing in the past up to t. Our explicit construction of the solution is based upon the stochastic cascade representation.     

小波变换-主成分回归分光光度法同时测定邻苯二酚、间苯二酚和对苯二酚三组分

根据小波变换具有将信号分频的特点,本文提出了将小波变换与主成分回归(PCR)相结合的一种多元校正算法。该法能更有效地去除噪声,提取有用信息,并将其用于分析邻苯二酚、间苯二酚、对苯二酚三组分体系。实验结果表明,本法比直接用主成分回归处理效果好,得到的平均相对误差从2．24％降低到1．19％。     

基于化学模式识别的大蒜傅里叶变换红外光谱指纹图谱多样性

以不同地理居群的大蒜为研究对象,采用傅里叶变换红外光谱法获取各样品的红外谱图及不同波数下各样品的透过率数据,运用主成分分析及聚类分析等统计学方法对谱图数据进行了比较分析。结果发现,不同地理居群大蒜的红外指纹图谱存在差异,统计学分析结果显示25个品种大致可分为4大类(其中2个样品,4号及25号与这4类间有较大差异),此现象一定程度上反映了大蒜种植地居群环境对大蒜理化性质的影响。     

A proof of the Generalized Banach Contraction Conjecture

We introduce the notion of -continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any -continuous self-map on a scattered compact space, has an invariant finite set. We use the results and the techniques to prove the Generalized Banach Contraction Conjecture.

     

Is the thermodynamic behavior of the noble fluids consistent with the principle of corresponding states?

The applicability of the Principle of Corresponding States (PCS) for the noble fluids is discussed. We give the thermodynamic evidence for the dimerization of the liquid phase in heavy noble gases like argon, krypton etc. which manifests itself in deviations from the PCS. The behavior of the diameter of the entropy and the density is analyzed. It is shown that these characteristics are very sensitive to the dimerization process which takes place in the liquid phase of heavy noble gases.     

The structure of shift invariant spaces on a locally compact abelian group

We investigate shift invariant subspaces of L²(G), where G is a locally compact abelian group. We show, among other things, that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame.