Heegaard分解的重新分块

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＭｂｅａｃｏｍｐａｃｔ 3 ｍａｎｉｆｏｌｄ .ＩｆｔｈｅｒｅｉｓａｐｒｏｐｅｒｌｙｅｍｂｅｄｄｅｄｃｌｏｓｅｄｓｕｒｆａｃｅＳｉｎＭｗｈｉｃｈｓｅｐａｒａｔｅｓＭｉｎｔｏｔｗｏｃｏｍｐｒｅｓｓｉｏｎｂｏｄｉｅｓＨ1ａｎｄＨ2 ,ｔｈｅｎＭｃａｎｂｅｗｒｉｔｔｅｎａｓＭ =Ｈ1∪ＳＨ2 .ＴｈｉｓｓｔｒｕｃｔｕｒｅｏｎＭｉｓｃａｌｌｅｄａＨｅｅｇａａｒｄｓｐｌｉｔｔｉｎｇｏｆＭａｎｄＳｉｓａｓｐｌｉｔｔｉｎｇｓｕｒｆａｃｅ .Ｈ1∪ＳＨ2 ｉｓｓａｉｄｔｏｂｅｒｅｄｕｃｉｂｌｅ…     

On Minimal Surfaces in Space Forms Whose Gauss Imageshave Constant Curvature

ＯｎＭｉｎｉｍａｌＳｕｒｆａｃｅｓｉｎＳｐａｃｅＦｏｒｍｓＷｈｏｓｅＧａｕｓｓＩｍａｇｅｓｈａｖｅＣｏｎｓｔａｎｔＣｕｒｖａｔｕｒｅ￥ＭａｋｏｔｏＳＡＫＡＫＩ（ＤｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＦａｃｕｌｔｙｏｆＳｃｉｅｎｃｅ，Ｈｉｒｏｓ...     

Fixed Point Theorems for Nonlinear Semigroups of Lipschitzian Mappings in Uniformly Convex Spaces

ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｓｆｏｒＮｏｎｌｉｎｅａｒＳｅｍｉｇｒｏｕｐｓｏｆＬｉｐｓｃｈｉｔｚｉａｎＭａｐｐｉｎｇｓｉｎＵｎｉｆｏｒｍｌｙＣｏｎｖｅｘＳｐａｃｅｓ￥ＺｅｎｇＬｉｕｃｈｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｈ...     

Necessary and Sufficient Conditions for the Strong Consistency of Mnltiple Regression Coefficients Undera Restrictive Condition

ＮｅｃｅｓｓａｒｙａｎｄＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎｓｆｏｒｔｈｅＳｔｒｏｎｇＣｏｎｓｉｓｔｅｎｃｙｏｆＭｎｌｔｉｐｌｅＲｅｇｒｅｓｓｉｏｎＣｏｅｆｆｉｃｉｅｎｔｓＵｎｄｅｒａＲｅｓｔｒｉｃｔｉｖｅＣｏｎｄｉｔｉｏｎＪｉｎＭｉｎｇｚｈｏｎｇ...     

Modified Tricomi Problem for a Nonlinear System of Second Order Equations of Mixed Type

ＭｏｄｉｆｉｅｄＴｒｉｃｏｍｉＰｒｏｂｌｅｍｆｏｒａＮｏｎｌｉｎｅａｒＳｙｓｔｅｍｏｆＳｅｃｏｎｄＯｒｄｅｒＥｑｕａｔｉｏｎｓｏｆＭｉｘｅｄＴｙｐｅＳｕｎＨｅｓｈｅｎｇ（孙和生）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａ...     

DynamicsinaSystemofCoupledOscillators

ＤｙｎａｍｉｃｓｉｎａＳｙｓｔｅｍｏｆＣｏｕｐｌｅｄＯｓｃｉｌｌａｔｏｒｓＭｉｎＱＩＡＮ＆ＳｈｕＺＨＵ￣２（ＳｃｈｏｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，ＰｅｋｉｎｇＵｎｉｖ．，Ｂｅｉｊｉｎｇ１００８７１）Ａｂｓｔｒａｃｔ：Ｔｈｉｓａｒｔ...     

MAXIMUM TREES OF SUBSETS

ＭＡＸＩＭＵＭＴＲＥＥＳＯＦＳＵＢＳＥＴＳＷｕＳｈｉｑｕａｎ（巫世权）（Ｉｎｓｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＣｈｉｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，ＰＯＢｏｘ２７３４，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＬｅｔＸｂｅａｆ...     

An Interpretation of the Poincare Morphism for Compact Toric Varieties

ＡｎＩｎｔｅｒｐｒｅｔａｔｉｏｎｏｆｔｈｅＰｏｉｎｃａｒéＭｏｒｐｈｉｓｍｆｏｒＣｏｍｐａｃｔＴｏｒｉｃＶａｒｉｅｔｉｅｓ￥Ｊｅａｎ－ＰａｕｌＢＲＡＳＳＥＬＥＴ（ＣＩＲＭ－Ｍａｒｓｅｉｌｌｅ－ＦｒａｎｃｅＳｉＧｍＡＣＮＲＳ，ＣＩＲＭＬｕｍｉｎｙＣａｓ...     

Phase-lockinginaConnectedSystemofNonlinearlyCoupledOscillators

Ｐｈａｓｅ－ｌｏｃｋｉｎｇｉｎａＣｏｎｎｅｃｔｅｄＳｙｓｔｅｍｏｆＮｏｎｌｉｎｅａｒｌｙＣｏｕｐｌｅｄＯｓｃｉｌｌａｔｏｒｓＭｉｎＱＩＡＮ，ＳｈｕＺＨＵ￣２（ＳｃｈｏｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，ＰｅｋｉｎｇＵｎｉｖ．，Ｂｅｋｊｉ...     

C-cosine Operator Functions and the Second Order Abstract Cauchy Problem

Ｃ－ｃｏｓｉｎｅＯｐｅｒａｔｏｒＦｕｎｃｔｉｏｎｓａｎｄｔｈｅＳｅｃｏｎｄＯｒｄｅｒ　ＡｂｓｔｒａｃｔＣａｕｃｈｙＰｒｏｂｌｅｍＷａｎｇＨａｉｙａｎ（王海燕）（ＤｅｐａｒｔｍｅｔｎｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ，Ｓｏｕｔｈｅａｓｔ...     

Bipolar fuzzy relation equations systems based on the product t‐norm

Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation simultaneously can give very useful information for certain frameworks where the human reasoning plays a key role. Hence, the resolution of bipolar fuzzy relation equations systems is a research topic of great interest. This paper focuses on the study of bipolar fuzzy relation equations systems based on the max‐product t‐norm composition. Specifically, the solvability and the algebraic structure of the set of solutions of these bipolar equations systems will be studied, including the case in which such systems are composed of equations whose independent term be equal to 0. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max‐product fuzzy relation equations.     

Reconstruction families of possibilistic structure systems

A method is presented for characterizing the family of overall systems reconstructable from a given possibilistic structure system. The technique is elaborated in terms of fuzzy relation equations.It is demonstrated that the reconstruction family of a given structure system is equivalent to the set of solutions of a special type of fuzzy relation equation. The solution set is partially ordered, and contains both minimal solutions and a unique maximum solution. When these elements are identified, all members of the reconstruction family are determined.Another characteristic of the reconstruction family is its reconstruction uncertainty, a measure of which is also developed in this paper. This measure is used to define an identifiability quotient that expresses the degree of confidence with which we may identify a single overall system given a particular structure system.     

基于∨-·运算的Fuzzy矩阵方程的摄动问题

定义基于∨ - .运算的 Fuzzy矩阵 A的同解简化矩阵 ,利用 A的同解简化矩阵 A(1) 给出基于∨ - .运算的 Fuzzy矩阵方程的矩阵解法 ,并研究这类 Fuzzy矩阵方程的摄动问题。     

On the unique solvability of fuzzy relational equations

The solution set of a consistent system of fuzzy relational equations with max-min composition can be characterized by one maximum solution and a finite number of minimal solutions. A polynomial-time method of O(mn) complexity is proposed to determine whether such a system has a unique minimal solution and/or a unique solution, where m, n are the dimensions of the input data. The proposed method can be extended to examining a system of fuzzy relational equations with max-T composition where T is a continuous triangular norm.     

Banach空间非线性混合型微分－积分方程的解

本文利用一些新的比较结果研究了Ｂａｎａｃｈ空间中非线性混合型微分积分方程初值问题的最大解和最小解，唯一解以及解的迭代逼近，统一和推广了最近的许多结果。     

Banach空间非线性混合型微分－积分方程的解

本文利用一些新的比较结果研究了Ｂａｎａｃｈ空间中非线性混合型微分积分方程初值问题的最大解和最小解，唯一解以及解的迭代逼近，统一和推广了最近的许多结果。     

求解具有max-t-norm合成算子的模糊关系不等式

研究一类具有max-t-norm合成算子的模糊关系不等式,该问题是模糊关系方程以及区间值模糊关系方程的推广.通过分析其解集的特点,提出一个基于筛选原则求解该类问题的算法,并给出数值算例说明该算法的有效性.     

Differential Equations With Fuzzy Parameters

This paper is concerned with systems of ordinary differential equations with fuzzy parameters. Applying the Zadeh extension principle to the equations, we introduce the notions of fuzzy solutions and of componentwise fuzzy solutions. The fuzzy extension of the solution operator is shown to provide the unique fuzzy solution as well as the maximal componentwise fuzzy solution. A numerical algorithm based on monotonicity properties of membership functions is presented, together with a proof of convergence. In an interplay of interval analysis and possibility theory, these methods allow to process subjective information on the possible fluctuations of parameters in models involving ordinary differential equations. This is demonstrated in two engineering applications: a queueing model for earthwork and a model of oscillations of bell-towers.     

Some properties of minimal solutions for a fuzzy relation equation

Some properties of the solution set and minimal solutions of a fuzzy relation equation are considered. In this paper, we show the necessary and sufficient condition for existence of a minimal solution of a finite fuzzy relation equation defined on infinite index sets.     

Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max–min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm that is not Archimedean is the “minimum”.