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Table of Content
30 December 1992, Volume 7 Issue 4
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Boundedness of the Littlewood-Paley Operator,the Function g(f),on BMO(T)
Qiu Sigang
1992, 7(4): 1-8.
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Little wood-Paley operator,the function g（f）, is considered as an operator on BMO（T）. It is proved that if f E BMO （T）, then g（f）∈BMO （T） and there is a constant C that is independent of f such that ‖g（f）‖* ≤C‖f‖*. Moreover,we have got the further results.
Operator Matrix Forms of Positive Operators
Du Hongke
1992, 7(4): 9-12.
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If a 3-tuple （A:H
1
→H
1
,B:H
2
→H1,C:H
2
→H
2
） of operators on Hilbert spaces is given,we proved that the operator ... is the generalized inverse of A. In general,A+ is a closed operator,but since ... is bounded yet.
A Pole Assignment Design Method of Process Control System for Tubular Heat Exchanger
Zhou Qingquan
1992, 7(4): 13-19.
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This paper has first studied the simplified model of tubular heat exchanger which is widely used in the industry and other field. On the basis of reference 2,a new pole assignment design method of process control system with derivative control action is found. For the above system, the method and the formation which calculate the feedback matrix K and gain matrix L is given,and the simulation of the system is made.
Existence of Periodic Solutions About One Class Differential Equation
Li Lin
1992, 7(4): 20-25.
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We discuss the existence and the number of periodic solutions of differential equation dx/dt=A
1
（t）x+A
2
（t）x
2
+A
3
（t）x
3
/a
0
（t）+a
1
（t）x+a
2
（t）x
2
（1）where A
i
（t）, a
j
（t） （i=1,2,3;j=0,1,2） are continuous periodic functions. The results of this paper extend the work of paper [1].
An Algorithm for Finding All Isolated Zeros of Polynomial Systems
Liu Zhuojun
1992, 7(4): 26-34.
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Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems. In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations). By solving Lorenz equations, it is shown that our algorithm is efficient and powerful.
Utility Representations of Preferences on General Choice Spaces
1992, 7(4): 35-39.
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The purpose of this paper is to reconsider the utility representation problem of preferences. Several representation theorems are obtained on general choice spaces. Preferences having continuous utility functions are characterized by their continuities and countable satiation. It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a continuous utility function is that the preference is continuous and countably satiable. For monotone preferences,we obtain that any space has continuous utility representations.
Generalized Inverses of Matrices over Rings
Han Ruizhu, Chen Jianlong
1992, 7(4): 40-47.
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Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.
On the Pal's Problem
Xie Tingfan
1992, 7(4): 48-50.
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The correct answer of Pal's interpolation polynomial problem has been given in this paper ,especially, the explict form of this polynomial has been obtained.
Some Properties of Two Kinds of Multifunctions
Cao Jiling
1992, 7(4): 51-55.
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Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.
A Sufficient Condition for Interolation by Functions in AP（φ）（1<P<∞）
Xiao Jie, Zhao Dahong
1992, 7(4): 56-62.
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Let φ be a normal function on [0,1) and A'（φ）(1P（|·|）/（1-|·|2）.A sufficient condition for interpolation by functions in AP（φ） is obtained by controlling norms of linear operators.
On a Trigonometric Inequality of Vinogradov
Xiong Qingliang, Yu Kongting
1992, 7(4): 63-67.
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In this paper, we improve an inequality of Vinogradov by analysis method.
The Law of the Iterated Logarithm for the Sums of φ-Mixing Sequences with Duple Suffixes
Yang Shanchao
1992, 7(4): 68-71.
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Hu Shuhe[l]gets a sufficient conditign on the law of the iterated logarithm for the sums of q- mixing sequences with duple suffixes.This paper greatly improves his condition.
On Positive Eigenvalues and Positive Fixed Points of Multivalued Condensing Mappings
Zhao Zengqin
1992, 7(4): 72-75.
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In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.
Finite Type Non-Minimal Submanifolds
Song Hongzao, Wu Baoqiang
1992, 7(4): 76-83.
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The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E3m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E3m are also proved.
Some Equivalent Conditions for the Differentiability of Continuous Gauge Functions on Banach Space
Nan Chaoxun
1992, 7(4): 84-88.
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In this paper,some equivalent conditions for differentiability of condtinuous gauge function are given.
Sasakian Submanifolds of Kaehlerian Manifolds(Ⅱ)
Sun Zhenzu, Hu Zejun
1992, 7(4): 89-94.
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In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian manifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ohtained.
An Extension of the Mitrinovi c-Djokovi e Inequality
Wang Zhen, Chen Ji
1992, 7(4): 95-99.
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A certain generalization of the Mitrinovi c-Djokovi c inequality is proved by means of elementary calculus.
Coefficient of Partial Correlation and Its Calculation
Duan Quancai, Zhang Baofa
1992, 7(4): 100-105.
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This thesis offers the general concept of coefficient of partial correlation. Starting with regression analysis, the paper, by using samples, infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.
Researches of DC-Problem Under the Model S in which the Numbers of Defective Coins are not Fixed
Ding Chenjie, Liu Wenan
1992, 7(4): 106-110.
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In this paper,we research general Defective Cion Problem under the model S,i.e,the number d of Defective cions is not fixed. For d=O,1,or 2. we get some good results.
