共查询到20条相似文献,搜索用时 484 毫秒
1.
P. Bose F. Hurtado H. Meijer S. Ramaswami D. Rappaport V. Sacristán T. Shermer G. Toussaint 《Journal of Mathematical Modelling and Algorithms》2002,1(1):3-16
Given a configuration C of geometric objects in R 2 (called the input configuration), a target configuration T of geometric objects in R 1, and a class S of allowable sectioning lines we consider in this paper many variations on the following problem: ‘Is there a line S∈S such that the section S∩C is equivalent by rigid motion to the target T?’ 相似文献
2.
Let k be a field, and let S,T,S1,T1 be skew-symmetric matrices over k with S,S1 both nonsingular (if k has characteristic 2, a skew-symmetric matrix is a symmetric one with zero diagonal). It is shown that there exists a nonsingular matrix P over k with P'SP = S1, P'TP = T1 (where P' denotes the transpose of P) if and only if S-1T and S-11T1 are similar. It is also shown that a 2m×2m matrix over k can be factored as ST, with S,T skew-symmetric and S nonsingular, if and only if A is similar to a matrix direct sum B⊕B where B is an m×m matrix over k. This is equivalent to saying that all elementary divisors of A occur with even multiplicity. An extension of this result giving necessary and sufficient conditions for a square matrix to be so expressible, without assuming that either S or T is nonsingular, is included. 相似文献
3.
Let T be a free ergodic measure-preserving action of an abelian group G on (X,μ). The crossed product algebra RT=L∞(X,μ)? G has two distinguished masas, the image CT of L∞(X,μ) and the algebra ST generated by the image of G. We conjecture that conjugacy of the singular masas ST(1) and ST(2) for weakly mixing actions T(1) and T(2) of different groups implies that the groups are isomorphic and the actions are conjugate with respect to this isomorphism. Our main result supporting this conjecture is that the conclusion is true under the additional assumption that the isomorphism γ : RT(1)→RT(2) such that γ(ST(1))=ST(2) has the property that the Cartan subalgebras γ(CT(1)) and CT(2) of RT(2) are inner conjugate. We discuss a stronger conjecture about the structure of the automorphism group Aut(RT,ST), and a weaker one about entropy as a conjugacy invariant. We study also the Pukanszky and some related invariants of ST, and show that they have a simple interpretation in terms of the spectral theory of the action T. It follows that essentially all values of the Pukanszky invariant are realized by the masas ST, and there exist non-conjugate singular masas with the same Pukanszky invariant. 相似文献
4.
Seyoung Oh Jae Heon Yun Sei-Young Chung 《Journal of Applied Mathematics and Computing》2003,11(1-2):155-164
The existence and representations of some generalized inverses, includingA T, * (2) ,A T, * (1,2) ,A T, * (2,3) ,A *,S (2) ,A *,S (1,2) andA *,S (2,4) , are showed. As applications, the perturbation theory for the generalized inverseA T,S (2) and the perturbation bound for unique solution of the general restricted systemAx=b (dim (AT)=dimT,b∈AT andx∈T) are studied. Moreover, a characterization and representation of the generalized inverseA T, * Emphasis>(2) is obtained. 相似文献
5.
J. Petean 《Topology and its Applications》2010,157(5):870-873
We show that closed orientable smooth four-manifolds with non-trivial volume flux group and fundamental group of subexponential growth type are finitely covered by a manifold homeomorphic to S3×S1, S2×T2 or a nil-manifold. We also show that if a compact complex surface has non-trivial volume flux group then it has zero minimal volume. 相似文献
6.
《Journal of Pure and Applied Algebra》1987,47(3):283-298
Let I be an ideal in a Noetherian ring R, let (I)a be the integral closure of I, and let S be a multiplicatively closed subset of R. Let T1, T2, and T3 be the topologies given by the filtrations {In RS ∩ R | n ≥ 1}, {In | n ≥ 1}, and {(In)a | n ≥ 1}. We g results due to Schenzel, characterizing when T1 is either equivalent or linearly equivalent to either of T2 or T3. The characterizations involve the sets of essential primes of I, quintessential primes of I, asymptotic primes of I, and quintasymptotic primes of I. 相似文献
7.
三矩阵乘积的(T,S,2)-逆的反序律 总被引:1,自引:1,他引:0
矩阵A的(T,S,2)-逆是指适合XAX=X,R(X)=T和N(X)=S的矩阵X,以矩阵的秩为工具,本文研究了三矩阵乘积的(T,S,2)-逆的反序律,给出了(ABC)(T4,S4)(2)=C(T3,S3)(2)B(T2,S2)(2)A(T1,S1)(2)的充要条件。 相似文献
8.
In this note, we present some results on maximality of the difference of two monotone operators. It is shown that, for two multifunctions S and T from X to X *, maximal monotonicity of S and monotonicity of both T and S?T imply maximal monotonicity of S?T. 相似文献
9.
Dennis E. White 《Discrete Mathematics》1976,15(1):85-105
It is observed that if Δ is a system of orbit representatives for the action of a finite group G on a G-stable subset L of a finite set S and if F is a field of characteristic zero, then FS is an algebra of dimension |S|. Furthermore, if S = RD, the set of functions from a finite set D to a finite set R, then FS has a multilinear structure. A general problem is stated: Given linear operators T1 and T2, construct vectors v1, … vt?FS such that T2IΔ = T1(v1 + … + vt) where lΔ is the indicator or characteristic function of Δ. (Note that this construction gives, in some sense, a solution to the problem of isomorph rejection.) For appropriate choices of T1 and T2, two approaches to this construction problem are considered. These are the principle of inclusion-exclusion and backtrack computer programming. In particular, these approaches are discussed when S = RD and the vectors to be constructed are pure or homogeneous tensors. 相似文献
10.
Dhruba R. Adhikari 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4622-4641
Let X be an infinite dimensional real reflexive Banach space with dual space X∗ and G⊂X, open and bounded. Assume that X and X∗ are locally uniformly convex. Let T:X⊃D(T)→2X∗ be maximal monotone and strongly quasibounded, S:X⊃D(S)→X∗ maximal monotone, and C:X⊃D(C)→X∗ strongly quasibounded w.r.t. S and such that it satisfies a generalized (S+)-condition w.r.t. S. Assume that D(S)=L⊂D(T)∩D(C), where L is a dense subspace of X, and 0∈T(0),S(0)=0. A new topological degree theory is introduced for the sum T+S+C, with degree mapping d(T+S+C,G,0). The reason for this development is the creation of a useful tool for the study of a class of time-dependent problems involving three operators. This degree theory is based on a degree theory that was recently developed by Kartsatos and Skrypnik just for the single-valued sum S+C, as above. 相似文献
11.
Gleason [A.M. Gleason, The definition of a quadratic form, Amer. Math. Monthly 73 (1966) 1049-1066] determined all functionals Q on K-vector spaces satisfying the parallelogram law Q(x+y)+Q(x-y)=2Q(x)+2Q(y) and the homogeneity Q(λx)=λ2Q(x). Associated with Q is a unique symmetric bi-additive form S such that Q(x)=S(x,x) and 4S(x,y)=Q(x+y)-Q(x-y). Homogeneity of Q corresponds to that of S: S(λx,λy)=λ2S(x,y). The associated S is not necessarily bi-linear.Let V be a vector space over a field K, char(K)≠2,3. A tri-additive form T on V is a map of V3 into K that is additive in each of its three variables. T is homogeneous of degree 3 if T(λx,λy,λz)=λ3T(x,y,z) for all .We determine the structure of tri-additive forms that are homogeneous of degree 3. One of the keys to this investigation is to find the general solution of the functional equation
F(t)+t3G(1/t)=0, 相似文献
12.
The assignment problem may be stated as follows: Given finite sets of points S and T, with|S| ? |T|, and given a “metric” which assigns a distance d(x, y) to each pair (x, y) such that x ∈ T and y ∈ S find a 1?1 function Q: T→ S which minimizes Σx∈Td(x, Q(x)) We consider the two special cases in which the points lie (1) on a line segment and (2) on a circle, and the metric is the distance along the line segment or circle, respectively. In each case, we show that the optimal assignment Q can be computed in a number of steps (additions and comparisons) proportional to the number of points. The problem arose in connection with the efficient rearrangement of desks located in offices along a corridor which encircles one floor of a building. 相似文献
13.
Maurice Tchuente 《Mathematical Social Sciences》1985,9(1):77-82
We are interested in the minimum time T(S) necessary for computing a family S = { < Si, Sj >: ? Si, Sj?Rp, (i, j) ?E } of inner products of order p, on a systolic array of order p × 2. We first prove that the determination of T(S) is equivalent to the partition problem and is thus NP-complete. Then we show that the designing of an algorithm which runs in time T(S) + 1 is equivalent to the problem of finding an undirected bipartite eulerian multigraph with the smallest number of edges, which contains a given undirected bipartite graph, and can therefore be solved in polynomial time. 相似文献
14.
LetG be a finite group, andS a subset ofG \ |1| withS =S ?1. We useX = Cay(G,S) to denote the Cayley graph ofG with respect toS. We callS a Cl-subset ofG, if for any isomorphism Cay(G,S) ≈ Cay(G,T) there is an α∈ Aut(G) such thatS α =T. Assume that m is a positive integer.G is called anm-Cl-group if every subsetS ofG withS =S ?1 and | S | ≤m is Cl. In this paper we prove that the alternating groupA 5 is a 4-Cl-group, which was a conjecture posed by Li and Praeger. 相似文献
15.
W.W. Comfort 《Topology and its Applications》2010,157(5):839-856
The recent literature offers examples, specific and hand-crafted, of Tychonoff spaces (in ZFC) which respond negatively to these questions, due respectively to Ceder and Pearson (1967) [3] and to Comfort and García-Ferreira (2001) [5]: (1) Is every ω-resolvable space maximally resolvable? (2) Is every maximally resolvable space extraresolvable? Now using the method of KID expansion, the authors show that every suitably restricted Tychonoff topological space (X,T) admits a larger Tychonoff topology (that is, an “expansion”) witnessing such failure. Specifically the authors show in ZFC that if (X,T) is a maximally resolvable Tychonoff space with S(X,T)?Δ(X,T)=κ, then (X,T) has Tychonoff expansions U=Ui (1?i?5), with Δ(X,Ui)=Δ(X,T) and S(X,Ui)?Δ(X,Ui), such that (X,Ui) is: (i=1) ω-resolvable but not maximally resolvable; (i=2) [if κ′ is regular, with S(X,T)?κ′?κ] τ-resolvable for all τ<κ′, but not κ′-resolvable; (i=3) maximally resolvable, but not extraresolvable; (i=4) extraresolvable, but not maximally resolvable; (i=5) maximally resolvable and extraresolvable, but not strongly extraresolvable. 相似文献
16.
In this paper, we give two explicit examples of unbounded linear maximal monotone operators. The first unbounded linear maximal monotone operator S on ?2 is skew. We show its domain is a proper subset of the domain of its adjoint S∗, and −S∗ is not maximal monotone. This gives a negative answer to a recent question posed by Svaiter. The second unbounded linear maximal monotone operator is the inverse Volterra operator T on L2[0,1]. We compare the domain of T with the domain of its adjoint T∗ and show that the skew part of T admits two distinct linear maximal monotone skew extensions. These unbounded linear maximal monotone operators show that the constraint qualification for the maximality of the sum of maximal monotone operators cannot be significantly weakened, and they are simpler than the example given by Phelps-Simons. Interesting consequences on Fitzpatrick functions for sums of two maximal monotone operators are also given. 相似文献
17.
Oladele Fajuyigbe 《Israel Journal of Mathematics》1979,34(1-2):12-20
For a given simplicial periodic transformationT of the compact orientable surfaceS, subject to certain constraints onT, a simplicial embedding ofS in the 3-dimensional sphereS
3 is defined and an orthogonal periodic transformationt ofS
3 such thatt/f(S) is equivalent toT is also defined. 相似文献
18.
19.
Huiling Li 《Journal of Combinatorial Theory, Series A》2009,116(1):1-11
Suppose that an almost simple group G acts line transitively on a finite linear space S. Let Gx be a point stabilizer in G and suppose that G has socle T, a simple group of Lie type. In this paper we show that if T∩Gx is a parabolic subgroup of T, then G is flag transitive on S. 相似文献
20.
G. Stengle 《Journal of Pure and Applied Algebra》2011,215(9):2257-2261
Let A⊂R be rings containing the rationals. In R let S be a multiplicatively closed subset such that 1∈S and 0∉S, T a preorder of R (a proper subsemiring containing the squares) such that S⊂T and I an A-submodule of R. Define ρ(I) (or ρS,T(I)) to be
ρ(I)={a∈R|sa2m+t∈I2m for some m∈N,s∈S and t∈T}. 相似文献