Dynamic investigation of triangles inscribed in a circle,which tend to an equilateral triangle

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner.

First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics.     

Hα∞到Hβ∞复合算子的线性组合

设B是N维复空间C^N中的开单位球,φ_i为B上的解析自映射,H_α^∞表示定义在单位球上的加权解析函数空间.本文主要研究的是从空间H_α^∞到H_β^∞上的复合算子线性组合■的紧致性,其中λ_i(i=1,2,…,M)是非零常数.另外,根据紧致性等价条件,得出算子差分对(C_φ1-C_φ2)-(C_φ3-C_φ1)是紧致的当且仅当C_φ1-C_φ2与C_φ3-C_φ1都是紧致的算子.     

An algorithm for constrained convex optimization

This paper presents a feasible direction algorithm for the minimization of a pseudoconvex function over a smooth, compact, convex set. We establish that each cluster point of the generated sequence is an optimal solution of the problem without introducing anti-jamming procedures. Each iteration of the algorithm involves as subproblems only one line search for a zero of a continuously differentiable convex function and one univariate function minimization on a compact interval.     

Exploring Effects of Protease Choice and Protease Combinations in Enzymatic Protein Hydrolysis of Poultry By-Products

A study of the effects of single and combined protease hydrolysis on myofibrillar versus collagenous proteins of poultry by-products has been conducted. The aim was to contribute with knowledge for increased value creation of all constituents of these complex by-products. A rational approach was implemented for selecting proteases exhibiting the most different activity towards the major protein-rich constituents of mechanically deboned chicken residue (MDCR). An initial activity screening of 18 proteases on chicken meat, turkey tendons and MDCR was conducted. Based on weight yield, size exclusion chromatography (SEC) and SDS-PAGE, stem Bromelain and Endocut-02 were selected. Studies on hydrolysis of four different poultry by-products at 40 °C, evaluated by protein yield, SEC, and SDS-PAGE, indicate that the proteases’ selectivity difference can be utilized in tailor-making hydrolysates, enriched in either meat- and collagen-derived peptides or gelatin. Three modes of stem Bromelain and Endocut-02 combinations during hydrolysis of MDCR were performed and compared with single protease hydrolysis. All modes of the protease combinations resulted in a similar approximately 15% increase in product yield, with products exhibiting similar SEC and SDS-PAGE profiles. This shows that irrespective of the modes of combination, the use of more than one enzyme in hydrolysis of collagen-rich material can provide means to increase the total protein yield and ultimately contribute to increased value creation of poultry by-products.     

Nonparametric inference on the difference of location parameters of correlated variables from fragmentary samples

Summary In this paper, two types of robust estimators and approximate confidence intervals for the difference of location parameters of correlated random variables are proposed and investigated when some observations are missing. It is shown that the suggested estimators are consistent and asymptotically normally distributed. In addition, the proposed approximate confidence intervals are also shown to enjoy some nice asymptotic properties.     

证券投资组合的风险与收益

本文利用概率统计原理对证券的投资组合能减轻所遇的风险作了讨论 ,并介绍了如何选择投资组合可使所遇风险达到最小     

导管架海洋平台自振特性的简化计算方法

本文提出一个方程中考虑剪切、弯曲、转动惯量效应,而其它如塔架形状变化,平台面转动惯量及台面集中质量变化等其它影响因素均以修正系数方法确定,给出平台基本频率的简化算法。     

Weak laws of large numbers for cooperative gamblers

Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables. The class of applicable distributions, herein described, extends beyond that for sample means, but even for sample means our theory offers new results concerning the characterization of explicit norming sequences. The general form of the latter characterization for linear combinations also yields a surprising new result in the theory of slow variation. Work was supported in part by the Hungarian Scientific Research Fund, Grant T048360, and carried out within the Analysis and Stochastics Research Group of the Hungarian Academy of Sciences.     

A Biokinetic Model to Describe Consequences of Inhibition/Stimulation in <Emphasis Type="Italic">DNA</Emphasis>-Proofreading and -Repair,Part 4

Summary. In previous papers a strongly simplified physical-mathematical (biokinetic) model has been presented, which dealt with the factors influencing the timely development of DNA mismatches dependent cells (malignant cells) in their kinetic competition to the development of normal somatic cells (i.e. cells with correct genetic information). The kinetic results have been studied by comparing them with experimental results reported in the literature upon inhibiting the organisms own enzymatic DNA-proofreading and repair machinery. In spite of the fact that the model uses fully the chances of kinetics, which allows to describe even rather complicated systems with many regulation circuits and feed back loops in a rather simple, summarizing way, it has been demonstrated that the model does not only well describe the experimentally found significant increases of mutants in cases when the DNA repair system has been inhibited, but it can also reflect cancer-development and the efficacy of classical cancer therapies like surgery or chemotherapy as well.In applying the predictions of the model as to the opposite of an inhibition of the DNA repair system, i.e., in testing the results, if the organisms own repair systems were stimulated, the model shows that there could be a chance for a new, adjuvant cancer-therapy if this concept was combined with biochemical facts and clinical findings which are reported in the literature.In continuation of this concept, the predictions of the model have been compared with findings upon cancer-therapies by apoptosis-triggerers like tamoxifen. Further, according to the fact that there exists literature by which it is demonstrated by clinical facts that it is not necessary to use living cells (e.g. from umbilical cords blood or bone-marrow) to achieve surprising therapeutic successes in cancer therapy, but also cell-free human-placenta-extracts (HPEs) can be similarily effective, it has been tried in a first preliminary analytical effort to characterize effector-substances contained therein.Received January 27, 2003; accepted (revised) March 25, 2003 Published online August 18, 2003