共查询到20条相似文献,搜索用时 15 毫秒
1.
A classification theory is developed for pairs of simple closed curves (A,B) in the sphere S2, assuming that A∩B has finitely many components. Such a pair of simple closed curves is called an SCC-pair, and two SCC-pairs (A,B) and (A′,B′) are equivalent if there is a homeomorphism from S2 to itself sending A to A′ and B to B′. The simple cases where A and B coincide or A and B are disjoint are easily handled. The component code is defined to provide a classification of all of the other possibilities. The component code is not uniquely determined for a given SCC-pair, but it is straightforward that it is an invariant; i.e., that if (A,B) and (A′,B′) are equivalent and C is a component code for (A,B), then C is a component code for (A′,B′) as well. It is proved that the component code is a classifying invariant in the sense that if two SCC-pairs have a component code in common, then the SCC-pairs are equivalent. Furthermore code transformations on component codes are defined so that if one component code is known for a particular SCC-pair, then all other component codes for the SCC-pair can be determined via code transformations. This provides a notion of equivalence for component codes; specifically, two component codes are equivalent if there is a code transformation mapping one to the other. The main result of the paper asserts that if C and C′ are component codes for SCC-pairs (A,B) and (A′,B′), respectively, then (A,B) and (A′,B′) are equivalent if and only if C and C′ are equivalent. Finally, a generalization of the Schoenflies theorem to SCC-pairs is presented. 相似文献
2.
Considering a single dyadic orthonormal wavelet ψ in L 2(?), it is still an open problem whether the support of $\widehat{\psi}$ always contains a wavelet set. As far as we know, the only result in this direction is that if the Fourier support of a wavelet function is “small” then it is either a wavelet set or a union of two wavelet sets. Without assuming that a set S is the Fourier support of a wavelet, we obtain some necessary conditions and some sufficient conditions for a “small” set S to contain a wavelet set. The main results, which are in terms of the relationship between two explicitly constructed subsets A and B of S and two subsets T 2 and D 2 of S intersecting itself exactly twice translationally and dilationally respectively, are (1) if $A\cup B\not\subseteq T_{2}\cap D_{2}$ then S does not contain a wavelet set; and (2) if A∪B?T 2∩D 2 then every wavelet subset of S must be in S?(A∪B) and if S?(A∪B) satisfies a “weak” condition then there exists a wavelet subset of S?(A∪B). In particular, if the set S?(A∪B) is of the right size then it must be a wavelet set. 相似文献
3.
Osamu Hatori 《Journal of Mathematical Analysis and Applications》2011,376(1):84-93
We prove that an isometry T between open subgroups of the invertible groups of unital Banach algebras A and B is extended to a real-linear isometry up to translation between these Banach algebras. While a unital isometry between unital semisimple commutative Banach algebras need not be multiplicative, we prove in this paper that if A is commutative and A or B are semisimple, then (T(eA))−1T is extended to an isometric real algebra isomorphism from A onto B. In particular, A−1 is isometric as a metric space to B−1 if and only if they are isometrically isomorphic to each other as metrizable groups if and only if A is isometrically isomorphic to B as a real Banach algebra; it is compared by the example of ?elazko concerning on non-isomorphic Banach algebras with the homeomorphically isomorphic invertible groups. Isometries between open subgroups of the invertible groups of unital closed standard operator algebras on Banach spaces are investigated and their general forms are given. 相似文献
4.
Piotr Minc 《Topology and its Applications》2006,153(10):1622-1629
We say that point x∈R2 is sheltered by a continuum S⊂R2 if x does not belong to the unbounded component of R2\S. Suppose that points a and b are the endpoints of each of three arcs A0, A1 and A2 contained in R2. We prove that there is an arc B⊂A0∪A1∪A2 with its endpoints a and b such that each point of B is sheltered by the union of each two of the arcs A0, A1 and A2. 相似文献
5.
V. M. Petrichkovich 《Ukrainian Mathematical Journal》1997,49(6):963-965
We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent. 相似文献
6.
The matrix equation is studied, under the assumption that (A, B1) is controllable, but allowing nonhermitian S. An inequality is given relating the dimensions of the eigenspaces of A and of the null space of S. In particular, if B has rank 1 and S is nonsingular, then S is hermitian, and the inertias of A and S are equal. Other inertial results are obtained, the role of the controllability of (A1, B1S1) is studied, and a class of D-stable matrices is determined. 相似文献
7.
Yago DiezAuthor Vitae J. Antoni SellarèsAuthor Vitae 《Discrete Applied Mathematics》2011,159(6):433-449
We propose a process for determining approximated matches, in terms of the bottleneck distance, under color preserving rigid motions, between two colored point sets A,B∈R2, |A|≤|B|. We solve the matching problem by generating all representative motions that bring A close to a subset B′ of set B and then using a graph matching algorithm. We also present an approximate matching algorithm with improved computational time. In order to get better running times for both algorithms we present a lossless filtering preprocessing step. By using it, we determine some candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B′ of S. Then, we solve the matching problem between A and every candidate zone. Experimental results using both synthetic and real data are reported to prove the effectiveness of the proposed approach. 相似文献
8.
A criterion for the classification of Bott towers is presented, i.e., two Bott towers B *(A) and B *(A′) are isomorphic if and only if the matrices A and A′ are equivalent. The equivalence relation is defined by two operations on matrices. And it is based on the observation that any Bott tower B *(A) is uniquely determined by its structure matrix A, which is a strictly upper triangular integer matrix. The classification of Bott towers is closely related to the cohomological rigidity problem for both Bott towers and Bott manifolds. 相似文献
9.
Two square matrices A and B over a ring R are semisimilar, written AB, if YAX=B and XBY=A for some (possibly rectangular) matrices X, Y over R. We show that if A and B have the same dimension, and if the ring is a division ring , then AB if and only if A2 is similar to B2 and rank(Ak)=rank(Bk), k=1,2,… 相似文献
10.
Yik-Hoi Au-Yeung 《Linear algebra and its applications》1973,7(4):347-350
In this note the author gives a simple proof of the following fact: Let r and s be two positive rational numbers such that r ? s and let A and B be two n × n non-negative definite Hermitian matrices such that Ar ? Br. Then AS ? Bs. 相似文献
11.
For a matrix decomposable as A=sI?B, where B?0, it is well known that A?1?0 if and only if the spectral radius ρ(B)>s. An extension of this result to the singular case ρ(B)=s is made by replacing A?1 by [A+t(I?AAD)]?1, where AD is the Drazin generalized inverse. 相似文献
12.
The real Lyapunov order in the set of real n×n matrices is a relation defined as follows: A?B if, for every real symmetric matrix S, SB+BtS is positive semidefinite whenever SA+AtS is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity. 相似文献
13.
Frank P. Weber 《Mathematical Logic Quarterly》1995,41(2):143-160
The main results of the present paper are the following theorems: 1. There is no e ∈ ω such that for any A, B ? ω, SA = W is simple in A, and if A′ ?T B′, then SA =* SB. 2 There is an e ∈ ω such that for any A, B ? ω, MA = We is incomplete maximal in A, and if A =* B, then MA ?T MB. 相似文献
14.
George B Purdy 《Journal of Combinatorial Theory, Series B》1979,26(1):75-77
A graph G is two-point universal if, given any two vertices A and B, there is a vertex jointed to both, a vertex joined to neither, a vertex joined to A but not B, and a vertex joined to B but not A. Erdös asked whether there is an infinite family of such graphs of some genus γ. In this note, we show that the number of vertices of a two-point universal graph of genus γ satisfies n ≤ 216(2γ + 1)2 so that there are most finitely many of each genus. 相似文献
15.
Imre Leader 《Journal of Combinatorial Theory, Series A》2007,114(5):825-839
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the same colour class in S, which satisfies Ax=0. We also say that S is PR for A. Many of the classical theorems of Ramsey Theory, such as van der Waerden's theorem and Schur's theorem, may naturally be interpreted as statements about partition regularity. Those matrices which are partition regular over the positive integers were completely characterised by Rado in 1933.Given matrices A and B, we say that A Rado-dominates B if any set which is PR for A is also PR for B. One trivial way for this to happen is if every solution to Ax=0 actually contains a solution to By=0. Bergelson, Hindman and Leader conjectured that this is the only way in which one matrix can Rado-dominate another. In this paper, we prove this conjecture for the first interesting case, namely for 1×3 matrices. We also show that, surprisingly, the conjecture is not true in general. 相似文献
16.
Frank Uhlig 《Linear algebra and its applications》1973,7(4):281-289
The simultaneous diagonalization of two real symmetric (r.s.) matrices has long been of interest. This subject is generalized here to the following problem (this question was raised by Dr. Olga Taussky-Todd, my thesis advisor at the California Institute of Technology): What is the first simultaneous block diagonal structure of a nonsingular pair of r.s. matrices ? For example, given a nonsingular pair of r.s. matrices S and T, which simultaneous block diagonalizations X′SX = diag(A1, , Ak), X′TX = diag(B1,, Bk) with dim Ai = dim Bi and X nonsingular are possible for 1 ? k ? n; and how well defined is a simultaneous block diagonalization for which k, the number of blocks, is maximal? Here a pair of r.s. matrices S and T is called nonsingular if S is nonsingular.If the number of blocks k is maximal, then one can speak of the finest simultaneous block diagonalization of S and T, since then the sizes of the blocks Ai are uniquely determined (up to permutations) by any set of generators of the pencil P(S, T) = {aS + bT|a, tb ε R} via the real Jordan normal form of S?1T. The proof uses the canonical pair form theorem for nonsingular pairs of r.s. matrices. The maximal number k and the block sizes dim Ai are also determined by the factorization over C of ? (λ, μ) = det(λS + μT) for λ, μ ε R. 相似文献
17.
Agnes Hui Chan 《Discrete Mathematics》1981,37(1):29-33
Let be a class of subsets of a finite set X. Elements of are called blocks. Let υ, t, λ and k be nonnegative integers such that υ?k?t?0. A pair (X, ) is called a (υ, k, λ) t-design, denoted by Sλ(t, k, υ), if (1) |X| = υ, (2) every t-subset of X is contained in exactly λ blocks and (3) for every block A in , |A| = k. A Möbius plane M is an S1(3, q+1, q2+1) where q is a positive integer. Let ∞ be a fixed point in M. If ∞ is deleted from M, together with all the blocks containing ∞, then we obtain a point-residual design M*. It can be easily checked that M* is an Sq(2, q+1, q2). Any Sq(2, q+1, q2) is called a pseudo-point-residual design of order q, abbreviated by PPRD(q). Let A and B be two blocks in a PPRD(q)M*. A and B are said to be tangent to each other at z if and only if A∩B={z}. M* is said to have the Tangency Property if for any block A in M*, and points x and y such that x?A and y?A, there exists at most one block containing y and tangent to A at x. This paper proves that any PPRD(q)M* is uniquely embeddable into a Möbius plane if and only if M* satisfies the Tangency Property. 相似文献
18.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2009,359(2):631-636
A Banach space operator T∈B(X) satisfies Browder's theorem if the complement of the Weyl spectrum σw(T) of T in σ(T) equals the set of Riesz points of T; T is polaroid if the isolated points of σ(T) are poles (no restriction on rank) of the resolvent of T. Let Φ(T) denote the set of Fredholm points of T. Browder's theorem transfers from A,B∈B(X) to S=LARB (resp., S=A⊗B) if and only if A and B∗ (resp., A and B) have SVEP at points μ∈Φ(A) and ν∈Φ(B) for which λ=μν∉σw(S). If A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to LARB; again, restricting ourselves to the completion of X⊗Y in the projective topology, if A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to A⊗B. 相似文献
19.
Alexandru Tupan 《Linear algebra and its applications》2008,428(1):254-258
Let k be a field of characteristic ≠2 with an involution σ. A matrix A is split if there is a change of variables Q such that (Qσ)TAQ consists of two complementary diagonal blocks. We classify all matrices that do not split. As a consequence we obtain a new proof for the following result. Given a square matrix A there is a matrix S such that (Sσ)TAS=AT and SσS=I. 相似文献
20.
Zhong Kui Liu 《数学学报(英文版)》2002,18(2):245-252
Let A, B be associative rings with identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and finitely generated. For any bimodule
A
M
B
, we show that the bimodule [[
AS,≤
]][M
S
,≤][[
BS, ≤
]] defines a Morita duality if and only if
A
M
B
defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[A
S
,≤]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule
A
M
B
such that B is right noetherian.
Received April 13, 1999, Accepted December 12, 1999 相似文献