Optimal training sample allocation and asymptotic expansions for error rates in discriminant analysis

The sample-based rule obtained from Bayes classification rule by replacing the unknown parameters by ML estimates from a stratified training sample is used for the classification of a random observationX into one ofL populations. The asymptotic expansions in terms of the inverses of the training sample sizes for cross-validation, apparent and plug-in error rates are found. These are used to compare estimation methods of the error rate for a wide range of regular distributions as probability models for considered populations. The optimal training sample allocation minimizing the asymptotic expected error regret is found in the cases of widely applicable, positively skewed distributions (Rayleigh and Maxwell distributions). These probability models for populations are often met in ecology and biology. The results indicate that equal training sample sizes for each populations sometimes are not optimal, even when prior probabilities of populations are equal.     

Study of photoreaction in dichromated gelatin by laser photoacoustic technique

 An experimental method to study the photochemical reaction in solid-state dichromated gelatin during exposure is proposed, in which two laser sources with different wavelengths are used to induce photoreaction and to excite photoacoustic signal, respectively. This method is to obtain the real-time characteristics during the formation of the photoreaction product. The curve is fitted using the Rosencwaig-Gersho (R-G) theory and chemical kinetics. The reaction order and the rate of reaction may be obtained by fitting the parameters. The results show that photochemical reaction in dichromated gelatin conforms to the mechanism suggested by Watanable-Westheimer, and the photosensitivity of the samples, prepared under different conditions, is dependent on the initial concentration of photoactive ions. Received: 18 April 1995/Revised version: 3 May 1996     

Production of fumaric acid by immobilized rhizopus using rotary biofilm contactor

Rotary biofilm contactor (RBC) is a reactor consisting of plastic discs that act as supports for micro-organisms. The discs are mounted on a horizontal shaft and placed in a medium-containing vessel. During nitrogen-rich growth phase, mycelia ofRhizopus oryzae ATCC 20344 grew on and around the discs and formed the “biofilm” of self-immobilized cells on the surface of the plastic discs. During the fermentation phase, the discs are slowly rotated, and the biofilms are exposed to the medium and the air space, alternately. With RBC, in the presence of CaCO₃,Rhizopus biofilm consumes glucose and produces fumaric acid with a volumetric productivity of 3.78 g/L/h within 24 h. The volumetric productivity is about threefolds higher with RBC than with a stirred-tank fermenter with CaCO₃. Furthermore, the duration of fermentation is one-third of the stirred-tank system. The immobilized biofilm is active for over a 2-wk period with repetitive use without loss of activity.

     

Effects of a Degeneracy in the Competition Model: Part II. Perturbation and Dynamical Behaviour

This is the second part of our study on the competition model where the coefficient functions are strictly positive over the underlying spatial region Ω except b(x), which vanishes in a nontrivial subdomain of Ω, and is positive in the rest of Ω. In part I, we mainly discussed the existence of two kinds of steady-state solutions of this system, namely, the classical steady-states and the generalized steady-states. Here we use these solutions to determine the dynamics of the model. We do this with the help of the perturbed model where b(x) is replaced by b(x)+ε, which itself is a classical competition model. This approach also reveals the interesting relationship between the steady-state solutions (both classical and generalized) of the above system and that of the perturbed system.     

Coloring of Double Disk Graphs

We study the problem of minimizing the number of colors for vertex-coloring of double disk graphs and in this note, show a polynomial-time 31-approximation for the problem, which improves an existing result.     

Kp,q-factorization of complete bipartite graphs

Let K _m,nbe a complete bipartite graph with two partite sets having m and n vertices, respectively. A K _p,q-factorization of K _m,n is a set of edge-disjoint K _p,q-factors of K _m,n which partition the set of edges of K _m,n. When p = 1 and q is a prime number, Wang, in his paper “On K _1,k -factorizations of a complete bipartite graph” (Discrete Math, 1994, 126: 359—364), investigated the K _1,q -factorization of K _m,nand gave a sufficient condition for such a factorization to exist. In the paper “K _1,k -factorizations of complete bipartite graphs” (Discrete Math, 2002, 259: 301—306), Du and Wang extended Wang’s result to the case that q is any positive integer. In this paper, we give a sufficient condition for K _m,n to have a K _p,q-factorization. As a special case, it is shown that the Martin’s BAC conjecture is true when p : q = k : (k+ 1) for any positive integer k.     

水母雪莲化学成分的研究（Ⅱ）

前文已报道从水母雪莲(Saussurea Medusa Maxim)中分得4种黄酮甙,本文报道另外6种化合物的分离和鉴定。 1 化合物Ⅰ—Ⅳ物化性质及分离鉴定 1.1 化合物Ⅰ 黄色结晶,m.p.:249～251℃,水解所得甙元鉴定为木樨草素,纸层析检出鼠李糖和葡萄糖。MS(FAB):m/z 595(M~++1),287(M~++H-葡萄糖基-鼠李糖)。化合物I与木樨草素的~(13)C NMR比较,C_6、C_8、C_(10)分别向低场位移1.1、1.0、1.8 ppm,而C,向高场移动     

A modal analysis for the dynamic response of fluid-structure systems

In this paper a theory of modal analysis for the dynamic response of fluid-structure systems is presented. A pair of generalized eigenvalue equations with three real symmetric matrices and their relationships are derived from the finite element equations in the form of structural displacements and fluid velocity potential. Generalized orthogonality relations of modal vectors are then developed. The response of the system to external excitation is derived in closed form by modal expansion. Two examples of the solution are given for illustration.     

Temperature elevation generated by a focused Gaussian ultrasonic beam at a tissue-bone interface

When a focused Gaussian ultrasonic beam in soft tissue normally impinges on the boundary of a contiguous bone, reflection and transmission occur. Taking account of the reflection, the steady-state temperature elevation along the beam axis for this case was calculated. The effect of perfusion is also included.