共查询到20条相似文献,搜索用时 46 毫秒
1.
If A∈T(m, N), the real-valued N-linear functions on Em, and σ∈SN, the symmetric group on {…,N}, then we define the permutation operator Pσ: T(m, N) → T(m, N) such that Pσ(A)(x1,x2,…,xN = A(xσ(1),xσ(2),…, xσ(N)). Suppose Σqi=1ni = N, where the ni are positive integers. In this paper we present a condition on σ that is sufficient to guarantee that 〈Pσ(A1?A2???Aq),A1?A2?? ? Aq〉 ? 0 for Ai∈S(m, ni), where S(m, ni) denotes the subspace of T(m, ni) consisting of all the fully symmetric members of T(m, ni). Also we present a broad generalization of the Neuberger identity which is sometimes useful in answering questions of the type described below. Suppose G and H are subgroups of SN. We let TG(m, N) denote all A∈T(m, N) such that Pσ(A) = A for all σ∈G. We define the symmetrizer G: T(m, N)→TG(m,N) such that . Suppose H is a subgroup of G and A∈TH(m, N). Clearly We are interested in the reverse type of comparison. In particular, if D is a suitably chosen subset of TH(m,N), then can we explicitly present a constant C>0 such that for all A∈D? 相似文献
2.
Н. Е. лУшпАИ 《Analysis Mathematica》1979,5(1):67-88
On the classW r L p (1≦p≦∞;r=1, 2,…) of 1-periodic functions ?(x) having an absolutely continuous (r? l)st derivative such that $$\parallel f^{(r)} \parallel _{L_p } \leqq 1 (\parallel f^{(r)} \parallel _{L_\infty } = vrai \sup |f^{(r)} (x)|)$$ vrai sup ¦?(r)(x)¦) an optimal quadrature formula of the form (0 ≦? ≦r?1, 0 ≦x 0 < x1 <…< xm ≦ 1) is found in the cases ?=r?2 and ?=r? 3 (r=3, 5, …). An exact error bound is established for this formula. The statements proved forW r L p allowed us also to obtain, under certain restrictions posed on the coefficientsp kl, and the nodesx 0 andx m, optimal quadrature formulae for the classes $$W_0^r L_p = \{ f:f \in W^r L_p , f^{(i)} (0) = 0 (i = 0,1,...,r - 2)\} $$ and $$W_0^r L_p = \{ f:f \in \tilde W^r L_p , f^{(i)} (0) = f^{(i)} (1) = 0 (i = 0,1,...,r - 2)\} $$ for the same values ofp andr as above. 相似文献
3.
M. H. Lim 《Linear and Multilinear Algebra》2013,61(4):333-354
Let G be a subgroup of the symmetric group Sm and V be an n-dimensional unitary space where nm. Let V(G) be the symmetry class of tensors over V associated with G and the identity character. Let D(G) be the set of all decomposable elements of V(G) and O(G) be its subset consisting of all nonzero decomposable tensors x 1 ?…? xm such that {x 1,…,xm } is an orthogonal set. In this paper we study the structure of linear mappings on V(G) that preserve one of the following subsets: (i)O(G), (ii) D(G)\(O(G)?{0}). 相似文献
4.
Chaobang Gao 《Results in Mathematics》2003,44(1-2):86-96
Let x: M → A n+1 be the graph of some strongly convex function x n+1= ?( x1,…,xn) defined on a domain Ω ? A n in a real affine space. We consider the relative metric G, defined by $ G=\sum{\partial^{2}f\over\partial x_{i}\partial x_{j}}dx_{i}dx_{j}$ .In this paper, we calculate the second variation of the area integral with respect to the relative metric G. We prove that the parabolic affine hyperspheres are stable. 相似文献
5.
W. Kratz 《Rendiconti del Circolo Matematico di Palermo》1987,36(3):457-473
The following limit theorem on Hamiltonian systems (resp. corresponding Riccati matrix equations) is shown: Given(N, N)-matrices,A, B, C andn ∈ {1,…, N} with the following properties:A and kemelB(x) are constant, rank(I, A, …, A n?1) B(x)≠N,B(x)∈C n(R), andB(x)(A T)j-1 C(x)∈C n-j(R) forj=1, …, n. Then \(\mathop {\lim }\limits_{x \to x_0 } \eta _1^T \left( x \right)V\left( x \right)U^{ - 1} \left( x \right)\eta _2 \left( x \right) = d_1^T \left( {x_0 } \right)U\left( {x_0 } \right)d_2 \) forx 0∈R, whenever the matricesU(x), V(x) are a conjoined basis of the differential systemU′=AU + BV, V′=CU?A TV, and whenever ηi(x)∈R N satisfy ηi(x 0)=U(x 0)d i ∈ imageU(x 0) η′i-Aηni(x) ∈ imageB(x),B(x)(η′i(x)-Aηi(x)) ∈C n-1 R fori=1,2. 相似文献
6.
R.S. Singh 《Journal of multivariate analysis》1976,6(1):111-122
On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a σ-finite measure dominated by the Lebesgue measure on Rm, p = (p1,…,pm), pj ≥ 0, fixed integers, and for x = (x1,…,xm) in Rm, f(p)(x) = ?p1+…+pm f(x)/(?p1x1 … ?pmxm). Asymptotic unbiasedness as well as both almost sure and mean square consistencies of fn(p) are examined. Further, a necessary and sufficient condition for uniform asymptotic unbisedness or for uniform mean square consistency of fn(p) is given. Finally, applications of estimators of this note to certain statistical problems are pointed out. 相似文献
7.
Yiu Tung Poon 《Linear and Multilinear Algebra》2013,61(1-3):221-223
Let A 1,…,Am be nxn hermitian matrices. Definine W(A 1,…,Am )={(xA1x ?,…xAmx ?):x?C n ,xx ?=1}. We will show that every point in the convex hull of W(A 1,…,Am ) can be represented as a convex combination of not more than k(m,n) points in W(A 1,…,Am ) where k(m,n)=min{n,[√m]+δ n 2 m+1}. 相似文献
8.
E. Ballico 《Results in Mathematics》2004,46(3-4):223-226
Fix integers x > 0, m1 ≥ … ≥ m x > 0 and P1,…,Px ∈ P2 such that no 3 of them are collinear. Let C ? P2 a “ general ” degree d plane curve with an ordinary point with multiplicity m i at each P i and y further singularities which are ordinary nodes. Fix any A ? Sing(C){P1,…, Px} and any integer m > 0. Here we study the postulation of the fat points m A ? ∪Q∈AmQ. 相似文献
9.
The Dirichlet integral provides a formula for the volume over the k-dimensional simplex ω={x1,…,xk: xi?0, i=1,…,k, s?∑k1xi?T}. This integral was extended by Liouville. The present paper provides a matrix analog where now the region becomes , where now each Vi is a p×p symmetric matrix and A?B means that A?B is positive semidefinite. 相似文献
10.
J.P. May 《Journal of Pure and Applied Algebra》1982,26(1):1-69
Let G be a finitely presented group given by its pre-abelian presentation <X1,…,Xm; Xe11ζ1,…,Xemmζ,ζm+1,…>, where ei≥0 for i = 1,…, m and ζj?G′ for j≥1. Let N be the subgroup of G generated by the normal subgroups [xeii, G] for i = 1,…, m. Then Dn+2(G)≡γn+2(G) (modNG′) for all n≥0, where G” is the second commutator subgroup of G,γn+2(G) is the (n+2)th term of the lower central series of G and Dn+2(G) = G∩(1+△n+2(G)) is the (n+2)th dimension subgroup of G. 相似文献
11.
Z. J. Jabłoński 《Acta Mathematica Hungarica》2008,120(1-2):21-28
Given a family $ \{ A_m^x \} _{\mathop {m \in \mathbb{Z}_ + ^d }\limits_{x \in X} } $ (X is a non-empty set) of bounded linear operators between the complex inner product space $ \mathcal{D} $ and the complex Hilbert space ? we characterize the existence of completely hyperexpansive d-tuples T = (T 1, … , T d ) on ? such that A m x = T m A 0 x for all m ? ? + d and x ? X. 相似文献
12.
Ronald Evans 《Journal of Number Theory》1977,9(1):61-62
Let P(X) be a homogeneous polynomial in X = (x, y), Q(X) a positive definite integral binary quadratic form, and G the group of integral automorphs of Q(X). Let A(m) = {N ∈ × : Q(N) = m}. It is shown that if ΣN∈A(m)P(N) = 0 for each m = 1, 2, 3,… then ΣU∈GP(UX) ≡ 0. 相似文献
13.
Helmut Bender 《Israel Journal of Mathematics》1975,22(3-4):208-213
A solvableA-signalizer functor? assigns to any non-identity elementx of the abelian 2-subgroupA of the finite groupG anA-invariant solvable 2′-subgroupθ(C G(x)) ofC G(x) such thatθ(C G(x)) ∩C G(y) ??(C G(y)) for allx, y ∈ A #.θ is called complete ifG has a solvableA-invariant 2′-subgroupK=θ(G) such thatC k(x)=θ(C G(x)) for everyx ∈ A#. This note contains an alternate proof of the completeness theorem below. 相似文献
14.
Alexander K. Kelmans 《Journal of Graph Theory》2000,35(3):206-221
Let G be a graph and p ϵ (0, 1). Let A(G, p) denote the probability that if each edge of G is selected at random with probability p then the resulting spanning subgraph of G is connected. Then A(G, p) is a polynomial in p. We prove that for every integer k ≥ 1 and every k‐tuple (m1, m2, … ,mk) of positive integers there exist infinitely many pairs of graphs G1 and G2 of the same size such that the polynomial A(G1, p) − A(G2, p) has exactly k roots x1 < x2 < ··· < xk in (0, 1) such that the multiplicity of xi is mi. We also prove the same result for the two‐terminal reliability polynomial, defined as the probability that the random subgraph as above includes a path connecting two specified vertices. These results are based on so‐called A‐ and T‐multiplying constructions that are interesting in themselves. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 206–221, 2000 相似文献
15.
L. Socha 《Journal of Optimization Theory and Applications》1981,33(3):393-399
Let a quasilinear control system having the state space \(\bar X \subseteq R^n \) be governed by the vector differential equation $$\dot x = G(u(t))x,$$ wherex(0) =x 0 andU is the family of all bounded measurable functions from [0,T] intoU, a compact and convex subset ofR m.LetG:U ?R be a bounded measurable nonlinear function, such thatG(U) is compact and convex.G ?1 can be convex onG(U) or concave. The main results of the paper establish the existence of a controlu ∈U which minimizes the cost functional $$I(u) = \int_0^T {L(u(t))x(t)dt,} $$ whereL(·) is convex. A practical example of application for chemical reactions is worked out in detail. 相似文献
16.
If p is a polynomial with all roots inside the unit disc and C its companion matrix, then the Lyapunov equation has a unique solution for every positive semidefinite matrix P. We characterize sets of vectors x0,…,xn?1 and y0,…,yn?1 such that X = G(x0,…,xn?1)= G(y0,…, yn?1)-1. Geometrical connections between such bases and contractions with one- dimensional defect spaces are established. 相似文献
17.
Viktor S. Rykhlov 《Results in Mathematics》1999,36(3-4):342-353
In this paper a system of differential equations y′ ? A(·,λ)y = 0 is considered on the finite interval [a,b] where λ ∈ C, A(·, λ):= λ A1+ A 0 +λ ?1A?1(·,λ) and A 1,A 0, A ? 1 are n × n matrix-functions. The main assumptions: A 1 is absolutely continuous on the interval [a, b], A 0 and A - 1(·,λ) are summable on the same interval when ¦λ¦ is sufficiently large; the roots φ1(x),…,φn (x) of the characteristic equation det (φ E — A 1) = 0 are different for all x ∈ [a,b] and do not vanish; there exists some unlimited set Ω ? C on which the inequalities Re(λφ1(x)) ≤ … ≤ Re (λφn(x)) are fulfilled for all x ∈ [a,b] and for some numeration of the functions φj(x). The asymptotic formula of the exponential type for a fundamental matrix of solutions of the system is obtained for sufficiently large ¦λ¦. The remainder term of this formula has a new type dependence on properties of the coefficients A 1 (x), A o (x) and A - 1 (x). 相似文献
18.
Ming-Huat Lim 《Linear and Multilinear Algebra》2013,61(4):481-496
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?1 ∈ A and some distinct elements a, b ∈ A. 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
19.
Maurice J Dupré 《Journal of Functional Analysis》1974,15(3):244-278
A Hilbert bundle (p, B, X) is a type of fibre space p:B → X 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(n)]/[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
20.
Edward A. Bertram 《Israel Journal of Mathematics》1984,47(4):335-344
In 1955 R. Brauer and K. A. Fowler showed that ifG is a group of even order >2, and the order |Z(G)| of the center ofG is odd, then there exists a strongly real) elementx∈G−Z whose centralizer satisfies|C
G(x)|>|G|1/3. In Theorem 1 we show that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C
G(x)|>[G:G′∩Z]1/2 (and thus|C
G(x)|>|G|1/3). We also note that if non-abelianG is either metabelian, nilpotent or (more generally) supersolvable, or anA-group, or any Frobenius group, then|C
G(x)|>|G|1/2 for somex∈G−Z. In Theorem 2 we prove that every non-abelian groupG of orderp
mqn (p, q primes) contains a proper centralizer of order >|G|1/2. Finally, in Theorem 3 we show that theaverage
|C(x)|, x∈G, is ≧c|G|
1/3 for metabelian groups, wherec is constant and the exponent 1/3 is best possible. 相似文献