Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

Acoustic characteristics of rough voice: Subharmonics

This study investigates the relationship between rough voice and the presence of Subharmonics, which correspond to smaller yet distinct peaks located between two consecutive harmonic peaks in the power spectrum. Spectrum analysis was undertaken in 389 pathologic voices, of which 20 had subharmonics. Although all 20 voices had roughness perceptually, 8 had normal jitter and/or shimmer. The degree of roughness had a significant inverse relationship with the frequency of subharmonics. By digital signal processing, sound samples with various types of subharmonics were synthesized and perceptually analyzed. Power and frequency of subharmonics in the synthesized sound also had significant relationships with the degree of roughness. Rough voice is acoustically characterized not only by jitter and shimmer but also by the presence of subharmonics in the power spectrum. Subharmonics are important acoustic properties for objective evaluation of rough voices.     

A stratospheric chemical reaction controlling climatic change

It has been established from geological studies that change in the atmospheric content of carbon dioxide gas commenced about one hundred million years ago. The likely origin of this change is advanced as being the onset of the Brewer circulation caused by the rise in terrain induced by tectonic plate movement. It is demonstrated that tectonic plate movement can be affected by impacts from external bodies which penetrate the crust of the Earth. The consequences of the change in atmospheric concentration of carbon dioxide are proposed as first, extinctions and reductions in animal numbers, including primates, as a result of changes in body chemistry of these animals and second, a change in the rate of weathering of rocks giving rise to changes in the availability of chemicals such as calcium and potassium which are essential for plant and animal life. This latter change contributing to the extinctions and reductions in animal numbers. It is shown that the change in weathering can account for the rise to dominance of angiosperm plants. It is concluded that there were several simultaneous evolutionary environments on Earth which were a function of altitude which gave rise to a vertical variation in atmospheric content of carbon dioxide. This variation disappeared with rise of terrain and the onset of the Brewer circulation. Such changes are advanced and being much more important than any changes in temperature caused by greenhouse effects since the disappearance of atmospheric variations in carbon dioxide allowed animal migration. It is demonstrated that the conditions of extinction could be reintroduced by human activities.     

Supremizers of inner <Emphasis Type="Italic">γ</Emphasis>-convex functions

A real-valued function f defined on a convex subset D of some normed linear space is said to be inner γ-convex w.r.t. some fixed roughness degree γ > 0 if there is a such that holds for all satisfying ||x ₀ − x ₁|| = νγ and . This kind of roughly generalized convex functions is introduced in order to get some properties similar to those of convex functions relative to their supremum. In this paper, numerous properties of their supremizers are given, i.e., of such satisfying lim . For instance, if an upper bounded and inner γ-convex function, which is defined on a convex and bounded subset D of some inner product space, has supremizers, then there exists a supremizer lying on the boundary of D relative to aff D or at a γ-extreme point of D, and if D is open relative to aff D or if dim D ≤ 2 then there is certainly a supremizer at a γ-extreme point of D. Another example is: if D is an affine set and is inner γ-convex and bounded above, then for all , and if 2 ≤ dim D < ∞ then each is a supremizer of f.      

具有粗糙核的Marcinkiewicz积分交换子在齐次Herz空间中的有界性

该文证明了一类由Marcinkiewicz积分和BMO(Rn)函数生成的交换子在齐次Herz空间上的有界性．     

Laplace's method for the laws of heat processes on loop spaces

In this paper, we will consider Laplace's method for a class of heat processes on loop spaces. We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate. This kind of process was first introduced by P. Malliavin in 1990 for the loop group case and then gradually generalized by various authors. Our tool is the rough path theory of T. Lyons. This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.     

关于集合的粗相似度量的注记

举例说明文献"集合的粗相似度量"中定理3.1(2)的结论是不严谨的,从而给出一个严谨的结论。     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.