Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R~n

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ△ｕ＋ｆ（ｕ）＝０（１．１）ｕ（ｘ）→０ａｓ｜ｘ｜→∞（１．２）ｉｎＲｎｗｅｒｅｃｏｎｓｉｄｅｒｅｄｗｉｄｅｌｙ（ｓｅｅ［１］－［７］）．Ｉｎｔｈｅｎｉｃｅｐａｐｅｒｓ［１］ａｎｄ［２］，ｉｔｗａｓｐｒｏｖｅｄｔｈａｔａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｏｆ（１．１）ｍｕｓｔｂｅｒａｄｉａｌｉｎｃａｓｅｆ（ｕ）∈Ｃ１＋δ（δ＞０）．Ｔｈｅｒｅｆｏｒｅ，ａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉ…     

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９０８，Ｅ．Ｌａｎｄａｕｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｗｅｌｌｋｎｏｗｎｓｅｑｕｅｎｃｅｏｆｏｐｅｒａｔｏｒｓ［１］Ｌｎ［ｆ（ｔ）；ｘ］＝Ｋｎ∫１－１ｆ（ｔ）［１－（ｔ－ｘ）２］ｎｄｔ，　　　　（１．１）ｗｈｅｒｅ　　　　　Ｋｎ＝［∫１｛－１（１－ｔ２）ｎｄｔ］－１～ｎπ　　（ｎ→∞）．（１．１）ｗａｓｕｓｅｄｉｎｔｈｅｐｒｏｏｆｏｆｔｈｅＷｅｉｅｒｓｔｒａｓｓＴｈｅｏｒｅｍ．Ｓｉｎｃｅｔｈｅｎ，ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｐｒｏｐ－ｅｒｔ…     

Travelling Wave Solutions for Generalized Fisher Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１，２］，ＡｒｏｎｓｏｎａｎｄＷｅｉｎｂｅｒｇｅｒｈａｖｅｓｔｕｄｉｅｄｓｙｓｔｅｍａｔｉｃｌｙｔｈｅｓｃａｌａｒｎｏｎｌｉｎｅａｒｄｉｆｆｕ－ｓｉｏｎｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｖａｒｉａｂｌｅｕｔ＝ｕｘｘ＋φ（ｕ），（１．１）ｗｈｅｒｅｕ＝ｕ（ｘ，ｔ）ａｎｄφ（ｕ）ｉｓａｎｏｎｌｉｎｅａｒｆｕｎｃｔｉｏｎ．Ｅｑｕａｔｉｏｎ（１．１）ａｒｉｓｅｓｉｎｓｅｖｅｒａｌａｐｐｌｉｃａ－ｔｉｏｎｓ；Ｓｅｅ［１，２］ａｎｄ［３］ｆｏｒｉｎｆｏｒｍａｔｉｏｎａ…     

关于可分解算子的扰动的不变子空间(英文)

在文献［１］中,Ｊ．Ｅｓｃｈｍｅｉｅｒ和Ｂ．Ｐｒｕｎａｒｕ证明了（复）Ｂａｎａｃｈ空间上的每个具有Ｂｉｓｈｏｐ性质（β）和浓厚谱的有界线性算子有非平凡的不变子空间．在文献［２］中,Ｈ．Ｍｏｈｅｂｉ和Ｍ．Ｒａｄｊａｂａｌｉｐｏｕｒ在减弱算子的Ｂｉｓｈｏｐ性质（β）和加强谱的浓厚性条件的情况下得到了另外几个不变子空间定理．本文给出了一个更进一步的不变子空间定理（见定理１）．     

Stability of a Chem ostatModelfor a Single Specieswith Delayed NutrientRecycling——Case ofWeak KernelFunction

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｍｍｏｎｃｈｅｍｏｓｔａｔｍｏｄｅｌｈａｓｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｍａｎｙｍａｔｈｅｍａｔｉａｎｓ（ｓｅｅ［１］）．Ｃｈｅｍｏｓｔａｔｍｏｄｅｌｓｉｎｃｏｒｐｏｒａｔｉｎｇｄｉｓｃｒｅｔｅｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｉｎ［２］ａｎｄ［３］．Ｉｎ［４］ａｎｄ［５］，ｃｈｅｍｏｓｔａｔｍｏｄｅｌｓｗｉｔｈｃｏｎｔｉｎｕｏｕｓｔｉｍｅｄｅｌａｙｉｎｎｕｔｒｉｅｎｔｒｅｃｙｃｌｉｎｇｗｅｒｅｃｏｎｓｉｄ－ｅｒｅｄ．Ｉｎｔｈｉ…     

Extension of Proper _-holom orphic Mappings

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｆＤ１，Ｄ２ａｒｅｔｗｏｓｍｏｏｔｈｂｏｕｎｄｅｄｐｓｅｕｄｏｃｏｎｖｅｘｄｏｍａｉｎｓｉｎＣｎ，Ｄ１ｓａｔｉｓｆｉｅｓｔｈｅｃｏｎｄｉｔｉｏｎＲ（ｓｅｅ［１］），ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔａｎｙｂｉｈｏｌｏｍｏｒｐｈｉｃｍａｐｐｉｎｇｆ：Ｄ１→Ｄ２ｅｘｔｅｎｄｓｓｍｏｏｔｈｌｙｔｏｔｈｅｂｏｕｎｄａｒｙ．Ｔｈｉｓｒｅｓｕｌｔｈａｓｂｅｅｎｇｅｎｅｒａｌｉｚｅｄｔｏｔｈｅｃａｓｅｓｏｆｐｒｏｐｅｒｈｏｌｏｍｏｒｐｈｉｃｍａｐｐｉｎｇｓ（［２］）．Ｉｎｔｈ…     

The Degree Theory of a New Operator

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｄｅｇｒｅｅｔｈｅｏｒｙｆｏｒａｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｈａｓｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｅｑｕａｔｉｏｎｓ（ｓｅｅ［１］，［２］，［３］）．Ｈｏｗｅｖｅｒ，ｓｏｍｅｏｐｅｒａ－ｔｏｒｓａｒｅｎｏｔｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｓ．Ｉｔｉｓａｎｅｗｐｒｏｂｌｅｍｔｈａｔｗｅｅｓｔａｂｌｉｓｈａｄｅｇｒｅｅｔｈｅｏｒｙｆｏ…     

Banach空间中广义正交分解定理与广义正交可补子空间

本文首先将 Ｈｉｌｂｅｒｔ空间中的Ｒｉｅｓｚ正交分解定理推广到 Ｂａｎａｃｈ空间,得到 Ｂａｎａｃｈ空间广义正交分解定理．然后,利用此定理讨论由Ｊａｍｅｓ Ｒ．Ｃ．［１］引入的Ｂａｎａｃｈ空间中正交概念及 Ｎａｓｈｅｄ Ｍ．Ｚ．［２］引入的 Ｂａｎａｃｈ空间中（广义）正交可补子空间,得到判别子空间广义正交可补的充分必要条件,并由此给出Ｈｉｌｂｅｒｔ空间的一个新特征．     

A Duality Theorem Associated with the Smash Product of Graded Ring and G-set

ＬｅｔＲｂｅａＧ－ｇｒａｄｅｄｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙ１；ｔｈａｔｉｓＲｇ∈ＧＲｇａｎｄＲｇＲｈＲｇｈｆｏｒａｌｌｇ，ｈ∈Ｇ．ＴｈｅａｓｓｏｃｉａｔｉｖｅｒｉｎｇＲ＃ＧｄｅｎｏｔｅｓｔｈｅｓｍａｓｈｐｒｏｄｕｃｔｆｏｒｔｈｅｇｒｏｕｐＧａｎｄｔｈｅｇｒａｄｅｄｒｉｎｇＲ（ｓｅｅ［３］ｏｒ［４］）．Ｉｎ［１］，ＣｏｈｅｎａｎｄＭｏｎｔｇｏｍｅｒｙｐｒｏｖｅｄｔｈｅｄｕａｌｉｔｙＴｈｅｏｒｅｍｓｆｏｒａｃｔｉｏｎｓａｎｄｃｏａｃｔｉｏｎｓｆｏｒｆｉｎｉｔｅｇｒｏｕｐＧ．Ｉｎ［２］，ａｆ…     

A Property of MRA of Multiplicity r with an Arbitrary Dilation Matrix

ＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｍｅｔｈｏｄｔｏｃｏｎｓｔｒｕｃｔｗａｖｅｌｅｔｉｓｍｕｌｔｉｒｅｓｏｌｕｔｉｏｎａｎａｌｙｓｉｓｗｈｉｃｈｗａｓｇｉｖｅｎｆｉｒｓｔｂｙＳ．Ｍａｌｌａｔ（［１］,［２］）ｉｎ１９８９．Ｉｎ１９９４,Ｔ．Ｎ．Ｔ．ＧｏｏｄｍａｎａｎｄＳ．Ｌ．Ｌｅｅ（［３］）ｇｅｎｅｒａｌｉｚｅｄｃｏｎｃｅｐｔｏｆｍｕｌｔｉｒｅｓｏｌｕｔｉｏｎａｎａｌｙｓｉｓｔｏｔｈｅｃａｓｅｏｆｍｕｌｔｉｐｈｃｉｔｙｒ（ｒ１）ｓｕｃｈｔｈａｔｍｕｌｔｉｗａｖｅｌｅｔｓｃａｎｂｅｃｏｎｓｔ…     

Decomposition algorithms for locating minimal cuts in a network

This paper provides decomposition algorithms for locating minimal cuts in a large directed network. The main theorem provides several cases for the algorithms. In the worst case, it is shown that the efficiency of one of the proposed algorithms is of the same order as a no-decomposition algorithm. As in linear programming, the obvious advantage of the proposed decomposition procedure is its ability to potentially handle larger problems than a no-decomposition algorithm.     

The Hauptsatz for Stratified Comprehension: A Semantic Proof

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality. Mathematics Subject Classification: 03B15, 03F05.     

几种新的截集及其应用

本文从“邻域”和“重域”的观点出发引入了三种新的截集：下截集，下重截集和上重截集。我们给出这些截集的性质及相应的分解定理，表现定理和扩展原理，作为应用，我们讨论了两方面的内容；一是利用落影表现理论，将一个模糊集看作“重云”的落影，然后用下生截集和落影表现理论来定义模糊集的运算，得到了与“２”一致的结果。     

Cut‐elimination Theorems for Some Infinitary Modal Logics

In this article, a cut‐free system TLM_ω1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames.The system TLM_ω1 is a kind of Gentzen style sequent calculus, but a sequent of TLM_ω1 is defined as a finite tree of sequents in a standard sense. We prove the cut‐elimination theorem for TLM_ω1 via its Kripke completeness.     

一类新的KKM定理及其应用*

本文得到一类新的KKM定理,统一和改进了[2,3,0,7,11]中的结果。作为应用,我们得到了几个匹配定理、重合定理、不动点定理、极大极小不等式定理及截口定理。     

A bound on the total size of a cut cover

A cycle cover (cut cover) of a graph G is a collection of cycles (cuts) of G that covers every edge of G at least once. The total size of a cycle cover (cut cover) is the sum of the number of edges of the cycles (cuts) in the cover.We discuss several results for cycle covers and the corresponding results for cut covers. Our main result is that every connected graph on n vertices and e edges has a cut cover of total size at most 2e-n+1 with equality precisely when every block of the graph is an odd cycle or a complete graph (other than K₄ or K₈). This corresponds to the result of Fan [J. Combin. Theory Ser. B 74 (1998) 353-367] that every graph without cut-edges has a cycle cover of total size at most e+n-1.     

Metrics and undirected cuts

Suppose thatG is an undirected graph whose edges have nonnegative integer-valued lengthsl(e), and that {s ₁,t ₁},?, {s _m ,t _m } are pairs of its vertices. Can one assign nonnegative weights to the cuts ofG such that, for each edgee, the total weight of cuts containinge does not exceedl(e) and, for eachi, the total weight of cuts ‘separating’s _i andt _i is equal to the distance (with respect tol) betweens _i andt _i ? Using linear programming duality, it follows from Papernov's multicommodity flow theorem that the answer is affirmative if the graph induced by the pairs {s ₁,t ₁},?, {s _m ,t _m } is one of the following: (i) the complete graph with four vertices, (ii) the circuit with five vertices, (iii) a union of two stars. We prove that if, in addition, each circuit inG has an even length (with respect tol) then there exists a suitable weighting of the cuts with the weights integer-valued; moreover, an algorithm of complexity O(n ³) (n is the number of vertices ofG) is developed for solving such a problem. Also a class of metrics decomposable into a nonnegative linear combination of cut-metrics is described, and it is shown that the separation problem for cut cones isNP-hard.     

An n-dimensional version of Steinhaus' chessboard theorem

The main result of this paper is an n-dimensional version of the Steinhaus' chessboard theorem. Our theorem implies the Poincaré theorem as well as its parametric extension. But it is known that the Poincaré theorem is equivalent to the Brouwer Fixed-Point theorem.     

Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel

In this paper we establish an existence of solution theorem and an existence of bifurcation point theorem for Hammerstein integral equation whose kernel is supposed neither symmetric nor positive defined. To prove our result, we use the Tychonoff fixed point theorem. In particular, our bifurcation result is directly comparable with an analogous one recently established by F. Faraci.     

Desargues Theorem, Dynamics, and Hyperplane Arrangements

The Desargues theorem is a basic theorem in classical projective geometry. In this paper we generalize Desargues theorem in the direction of dynamical systems. Our result comprises an infinite family of configurations, having unbounded complexity. The proof of the result involves constructing special kinds of hyperplane arrangements and then projecting subsets of them into the plane.