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1.
2.
The chaos caused by a strong-mixing preserving transformation is discussed and it is shown that for a topological spaceX satisfying the second axiom of countability and for an outer measurem onX satisfying the conditions: (i) every non-empty open set ofX ism-measurable with positivem-measure; (ii) the restriction ofm on Borel σ-algebra ℬ(X) ofX is a probability measure, and (iii) for everyYX there exists a Borel setB⊂ℬ(X) such thatBY andm(B) =m(Y), iff:XX is a strong-mixing measure-preserving transformation of the probability space (X, ℬ(X),m), and if {m}, is a strictly increasing sequence of positive integers, then there exists a subsetCX withm (C) = 1, finitely chaotic with respect to the sequence {m i}, i.e. for any finite subsetA ofC and for any mapF:AX there is a subsequencer i such that limi→∞ f r i(a) =F(a) for anyaA. There are some applications to maps of one dimension. the National Natural Science Foundation of China.  相似文献   

3.
We derive explicit equations for the maximal function fields F over 𝔽 q 2n given by F = 𝔽 q 2n (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field 𝔽 q 2n , and where A(Y) is q-additive and deg(f) = q n  + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over 𝔽 q 2n (i.e., the extension H/F is Galois).  相似文献   

4.
The present paper continues the work begun by Anstee, Griggs and Sali on small forbidden configurations. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. Let F be a k×l (0,1)-matrix (the forbidden configuration). Small refers to the size of k and in this paper k = 3. Assume A is an m×n simple matrix which has no submatrix which is a row and column permutation of F. We define forb(m,F) as the best possible upper bound on n, for such a matrix A, which depends on m and F. We complete the classification for all 3-rowed (0,1)-matrices of forb (m,F) as either Θ(m), Θ(m2) or Θ(m3) (with constants depending on F). * Research is supported in part by NSERC. † Research was done while the second author visited the University of British Columbia supported by NSERC of first author. Research was partially supported by Hungarian National Research Fund (OTKA) numbers T034702 and T037846.  相似文献   

5.
Let F m × n be the set of all m × n matrices over the field F = C or R Denote by Un (F) the group of all n × n unitary or orthogonal matrices according as F = C or F-R. A norm N() on F m ×n, is unitarily invariant if N(UAV) = N(A): for all AF m×n UU m (F). and VUn (F). We characterize those linear operators T F m × n F m × n which satisfy N (T(A)) = N(A)for all AF m × n

for a given unitarily invariant norm N(). It is shown that the problem is equivalent to characterizing those operators which preserve certain subsets in F m × n To develop the theory we prove some results concerning unitary operators on F m × n which are of independent interest.  相似文献   

6.
A 3-(n,4,1) packing design consists of an n-element set X and a collection of 4-element subsets of X, called blocks, such that every 3-element subset of X is contained in at most one block. The packing number of quadruples d(3,4,n) denotes the number of blocks in a maximum 3-(n,4,1) packing design, which is also the maximum number A(n,4,4) of codewords in a code of length n, constant weight 4, and minimum Hamming distance 4. In this paper the last packing number A(n,4,4) for n≡ 5(mod 6) is shown to be equal to Johnson bound with 21 undecided values n=6k+5, k∈{m: m is odd , 3≤ m≤ 35, m≠ 17,21}∪ {45,47,75,77,79,159}. AMS Classification:05B40, 94B25  相似文献   

7.
A social choice function C defined on the m-element subsets of a set X for n voters assigns a non-empty subset C(A,R) of A to each pair (A,R) in which ¦A¦ = m,A X, and R is an n-tuple of voter preference orders on X. When n > 2, 3 m < ¦X¦, and C satisfies natural conditions of independence, symmetry among voters and alternatives, and collective rationality, it is proved that C is completely indecisive in the sense that C(A,R) = A for all (A,R). This non-binary result complements a binary (m = 2) result proved by Hanson. It suggests that there is a fundamental incompatibility between collective rationality and conditions designed to assure equitable treatment of voters and of alternatives.  相似文献   

8.
A polynomial Q = Q(X 1, …, X n ) of degree m in independent identically distributed random variables with distribution function F is an unbiased estimator of a functional q(α 1(F), …, α m (F)), where q(u 1, …, u m ) is a polynomial in u 1, …, u m and α j (F) is the jth moment of F (assuming the necessary moment of F exists). It is shown that the relation E(Q | X 1 + … + X n) = 0 holds if and only if q(α 1(θ), …, α m (θ)) ≡ 0, where α j (θ) is the jth moment of the natural exponential family generated by F. This result, based on the fact that X 1 + … + X n is a complete sufficient statistic for a parameter θ in a sample from a natural exponential family of distributions F θ(x) = ∫−∞ x e θu−k(θ) dF(u), explains why the distributions appearing as solutions of regression problems are the same as solutions of problems for natural exponential families though, at the first glance, the latter seem unrelated to the former.  相似文献   

9.
A Hilbert bundle (p, B, X) is a type of fibre space p:BX such that each fibre p?1(x) is a Hilbert space. However, p?1(x) may vary in dimension as x varies in X. We generalize the classical homotopy classification theory of vector bundles to a “homotopy” classification of certain Hilbert bundles. An (m, n)-bundle over the pair (X, A) is a Hilbert bundle (p, B, X) such that the dimension of p?1(x) is m for x in A and n otherwise. The main result here is that if A is a compact set lying in the “edge” of the metric space X (e.g. if X is a topological manifold and A is a compact subset of the boundary of X), then the problem of classifying (m, n)-bundles over (X, A) reduces to a problem in the classical theory of vector bundles. In particular, we show there is a one-to-one correspondence between the members of the orbit set, [A, Gm(Cn)]/[X, U(n)] ¦ A, and the isomorphism classes of (m, n)-bundles over (X, A) which are trivial over X, A.  相似文献   

10.
For a metric continuum X, let Fn(X)={AX:A is nonempty and has at most n points}. In this paper we show a continuum X such that F2(X) has the fixed point property while X does not have it.  相似文献   

11.
Adam Nyman 《代数通讯》2013,41(7):2208-2234
Let k ? K be an extension of fields, and let A ? M n (K) be a k-algebra. We study parameter spaces of m-dimensional subspaces of K n which are invariant under A. The space A (m, n), whose R-rational points are A-invariant, free rank m summands of R n , is well known. We construct a distinct parameter space, A (m, n), which is a fiber product of a Grassmannian and the projectivization of a vector space. We then study the intersection A (m, n) ∩  A (m, n), which we denote by A (m, n). Under suitable hypotheses on A, we construct affine open subschemes of A (m, n) and A (m, n) which cover their K-rational points. We conclude by using A (m, n), A (m, n), and A (m, n) to construct parameter spaces of 2-sided subspaces of 2-sided vector spaces.  相似文献   

12.
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b n : π n (X)→H n (H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π n (X)→E n (X), F n (X)→(EF) n (X), F n (X)→H n (X;π 0 F) and F n (X)→H n+t (X;π t F) for other cohomology theories E *(−) and F *(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in terms of the order of the Postnikov invariants of the spectrum F.  相似文献   

13.
Let c = c(m,n,j,k) be the largest integer such that every matrix with m rows and n columns whose entries belong to a set of cardinal c has a constant submatrix with j rows and k columns. Some results in the case j = 2 are given.  相似文献   

14.
We show that a maximal curve over Fq2 given by an equation A(X)=F(Y), where A(X)∈Fq2[X] is additive and separable and where F(Y)∈Fq2[Y] has degree m prime to the characteristic p, is such that all roots of A(X) belong to Fq2. In the particular case where F(Y)=Ym, we show that the degree m is a divisor of q+1.  相似文献   

15.
It is shown that ifA andB are non-empty subsets of {0, 1} n (for somenεN) then |A+B|≧(|A||B|)α where α=(1/2) log2 3 here and in what follows. In particular if |A|=2 n-1 then |A+A|≧3 n-1 which anwers a question of Brown and Moran. It is also shown that if |A| = 2 n-1 then |A+A|=3 n-1 if and only if the points ofA lie on a hyperplane inn-dimensions. Necessary and sufficient conditions are also given for |A +B|=(|A||B|)α. The above results imply the following improvement of a result of Talagrand [7]: ifX andY are compact subsets ofK (the Cantor set) withm(X),m(Y)>0 then λ(X+Y)≧2(m(X)m(Y))α wherem is the usual measure onK and λ is Lebesgue measure. This also answers a question of Moran (in more precise terms) showing thatm is not concentrated on any proper Raikov system.  相似文献   

16.
Abstract

Let A be a commutative ring with identity, let X, Y be indeterminates and let F(X,Y), G(X, Y) ∈ A[X, Y] be homogeneous. Then the pair F(X, Y), G(X, Y) is said to be radical preserving with respect to A if Rad((F(x, y), G(x, y))R) = Rad((x,y)R) for each A-algebra R and each pair of elements x, y in R. It is shown that infinite sequences of pairwise radical preserving polynomials can be obtained by homogenizing cyclotomic polynomials, and that under suitable conditions on a ?-graded ring A these can be used to produce an infinite set of homogeneous prime ideals between two given homogeneous prime ideals P ? Q of A such that ht(Q/P) = 2.  相似文献   

17.
It is proved that under certain conditions the group K n (X) of a smooth projective variety X over a field F is a natural direct summand of K n (A) for some separable F-algebra A. As an application we study the K-groups of toric models and toric varieties. A presentation in terms of generators and relations of the groupK 0(T) for an algebraic torus T is given.  相似文献   

18.
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ...  相似文献   

19.
Let A be a non-empty set and m be a positive integer. Let ≡ be the equivalence relation defined on A m such that (x 1, …, x m ) ≡ (y 1, …, y m ) if there exists a permutation σ on {1, …, m} such that y σ(i) = x i for all i. Let A (m) denote the set of all equivalence classes determined by ≡. Two elements X and Y in A (m) are said to be adjacent if (x 1, …, x m?1, a) ∈ X and (x 1, …, x m?1, b) ∈ Y for some x 1, …, x m?1A and some distinct elements a, bA. We study the structure of functions from A (m) to B (n) that send adjacent elements to adjacent elements when A has at least n + 2 elements and its application to linear preservers of non-zero decomposable symmetric tensors.  相似文献   

20.
Let A, X and Y be n-by-n complex matrices such that A is positive semi-definite and X, Y are contractions. We prove that if f is an increasing convex function on [0, ∞) such that f(0) ≤ 0, then the eigenvalues of f(|X*AY|) are dominated by those of X*f(A)XY* f(A)Y. Several related results are considered.  相似文献   

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