О несколвких принципиальных вопросах задач о цоБственных значениях отосительно систем Дифференциальных уравнений. I

Summary In the course of the numerical solution of Eigenvalue-problems connected with linear differential equations, the so-called encompassing theorems are of great importantce. We generalize in this paper the most important results of the theory, especially the encompassing-theorems, to the case of systems of differential equations. We expound further a method of perturbation which can be well applied also in the practice for the solution of Eigenvalue-problems connected with the systems. The problem acrose in connection with the fixation of the number of critical self-oscillation of turbine shovels.

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I believe it,but I don’t see it

Since its discovery by Cantor in the 1870s, the one-to-one, onto function from the unit interval to the unit square has been a subject of continual interest. A corresponding function from the square to the interval, however, has rarely been considered, in spite of its unusual characteristics. This Classroom Note demonstrates how to create such a function, highlighting the counterintuitive nature of its continuities, discontinuities and slopes. This will likely be the first function whose graph students of multivariable calculus cannot visualize, and the particular results presented will surprise them. Nevertheless, guided by their instructor, using methods they have used in more standard contexts and helped by some brief hints in the text, they will be able to prove these results. While some familiarity with transfinite numbers and set concepts will enhance the experience, this is not strictly necessary. A goal is to give serious students a sense of participation in the investigation of such a function, knowing that they are not simply repeating work that others have done many times before.     

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A cured model is a useful approach for analysing failure time data in which some subjects could eventually experience and others never experience the event of interest. All subjects in the test belong to one of the two groups: the susceptible group and the non-susceptible group. There has been considerable progress in the development of semi-parametric models for regression analysis of time-to-event data. However, most of the current work focuses on right-censored data, especially when the population contains a non-ignorable cured subgroup. In this paper, we propose a semi-parametric cure model for current status data. In general, treatments are developed to both increase the patients' chances of being cured and prolong the survival time among non-cured patients. A logistic regression model is proposed for whether the subject is in the susceptible group. An accelerated failure time regression model is proposed for the event time when the subject is in the non-susceptible group. An EM algorithm is used to maximize the log-likelihood of the observed data. Simulation results show that the proposed method can get efficient estimations.     

SomePropertiesofSolutionsforaNonlinearDifusionSystem（I）

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＮｏｎｌｉｎｅａｒＤｉｆｕｓｉｏｎＳｙｓｔｅｍ（Ｉ）＊）ＷｕＺｈｕｏｑｕｎ（伍卓群）ａｎｄＹｉｎＪｉｎｇｘｕｅ（尹景学）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒ...     

Was sierpinski right? I

Aroused by Todorcevic’s breakthrough we prove here some complementary consistency results, mainly . We also get some generalization of his theorem to, e.g.,λ↛ forλ regular notω-Mahlo. The author thanks the NSF and N.S.E.R.C. for partially supporting the research. Preliminary versions of §3 and §2 were circulated in November ’84 and February ’85, respectively.     

τ-Categories I: Ladders

In this series of papers, we introduce τ-categories, which are additive categories with some kind of Auslander–Reiten sequences. We apply them to study the category of lattices over orders. In this first paper, we study minimal projective resolutions in functor categories over τ-categories. Then we give a structure theorem of completely graded τ-categories using mesh categories. Presented by K. Roggenkamp Mathematics Subject Classifications (2000) primary 16G30; secondary 16E65, 16G70, 18E05. Osamu Iyama: Current address: Department of Mathematics, University of Hyogo, Himeji, 671-2201, Japan. e-mail: iyama@sci.u-hyogo.ac.jp.     

三I算法的鲁棒性

基于三I算法的模糊推理不仅在语义上而且在语构上均有合理的解释。在模糊推理三I算法中,研究输入的微小变化所引起输出变化幅度尤为重要。本文首先给出了基于QL蕴涵的三I算法的表达式,进一步借助模糊连接词的鲁棒性,系统地研究了基于几种常见的蕴涵的三I算法的鲁棒性。     

I半π正则环

Let R be a ring and I an ideal of R.A ring R is called I-semi-π-regular if R/I isπ-regular and idempotents of R can be strongly lifted modulo I.Charac- terizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.     

ÜberStifelsche magische Quadrate I

Ohne Zusammenfassung Alexander Ostrowski zum 25. September 1953     

I型可选增道路

讨论了平面I型可选增道路的存在性,并对其性质进行了研究,得出了I型可选增道路的一些重要性质.     

I.I.D.序列最大部分和的精确渐近性

借助于截尾技术和强逼近原理,本文研究了独立同分布(i.i.d.)序列最大部分和的精确渐近性,给出了更加一般的结果.     

关于拓扑对策中的I2(κ)(∈)I(κ)问题

证明了如果空间类K为D-空间类或闭遗传不可约空间类,则I（K）包含K.这一结果对于K为D空间类和闭遗传不可约空间类,肯定地回答了I（K）是否包含I^2（K）问题.     

I.I.D.随机变量序列矩完全收敛的精确渐近性

{X,Xn;n≥1}为独立同分布的随机变量序列, EX=0,01 p/2满足E|X|r<∞,且E|X|3<∞,那么其中Z服从均值为0,方差为σ2的正态分布.     

数学与农业（I）

本文旨在阐述我国水稻遗传学家和水稻育种学家用数理统计中的多元回归、方差、协方差、主成份分析、聚类分析、多项式回归…等方法，对提高水稻单位面积产量的数量性状及性状间的相互影响的诸因素，对稻米外观品质，碾磨品质，营养价值，蒸煮食用品质同遗传基因的关系进行了讨论．     

Belman不等式(I)

本文考察不等式：ｔｒ（ＡＢ）^ｍ≤ｔｒ（Ａ^ｍＢ^ｍ），ｍ＝１，２，３，…，其中Ａ，Ｂ为Ｋ阶方阵．证明了当Ａ正定Ｂ对称幂等条件下上述不等式成立．还考察了Ａ，Ｂ为非负矩阵时的情形