共查询到20条相似文献,搜索用时 109 毫秒
1.
Geoffrey S Watson 《Journal of multivariate analysis》1984,14(1):74-82
The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp κμ′x, where x and the modal vector μ are unit vectors in q. κ (≥0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when κ1,…,κm are known but tend to infinity, and are unknown but equal to κ which tends to infinity. The three null hypotheses are H01:μ = μ0(m=1), H02:μ1 = … =μm, H03:μi?V, i=1,…,m In each case a sequence of alternatives is taken tending to the null hypothesis. 相似文献
2.
Hock Ong 《Linear algebra and its applications》1976,15(2):119-151
Let F be a field, F1 be its multiplicative group, and = {H:H is a subgroup of F1 and there do not exist a, b?F1 such that Ha+b?H}. Let Dn be the dihedral group of degree n, H be a nontrivial group in , and τn(H) = {α = (α1, α2,…, αn):αi?H}. For σ?Dn and α?τn(H), let P(σ, α) be the matrix whose (i,j) entry is αiδiσ(j) (i.e., a generalized permutation matrix), and . Let Mn(F) be the vector space of all n×n matrices over F and P(Dn, H) = {T:T is a linear transformation on Mn (F) to itself and T(P(Dn, H)) = P(Dn, H)}. In this paper we classify all T in P(Dn, H) and determine the structure of the group P(Dn, H) (Theorems 1 to 4). An expository version of the main results is given in Sec. 1, and an example is given at the end of the paper. 相似文献
3.
Let G be the metacyclic group of order pq given by where p is an odd prime, q ≥ 2 a divisor of p ? 1, and where j belongs to the exponent q mod p. Let V denote the group of units of augmentation 1 in the integral group ring G of G. In this paper it is proved that the number of conjugacy classes of elements of order p in V is where ν, μ0, and H are suitably defined numbers. 相似文献
4.
Marvin I. Knopp 《Journal of Number Theory》1980,12(1):2-9
If h, k ∈ Z, k > 0, the Dedekind sum is given by , with , . The Hecke operators Tn for the full modular group SL(2, Z) are applied to log η(τ) to derive the identities (n ∈ Z+) , where (h, k) = 1, k > 0 and σ(n) is the sum of the positive divisors of n. Petersson had earlier proved (1) under the additional assumption k ≡ 0, h ≡ 1 (mod n). Dedekind himself proved (1) when n is prime. 相似文献
5.
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
6.
Bruce Atkinson 《Stochastic Processes and their Applications》1983,15(2):193-201
Let p(t, x, y) be a symmetric transition density with respect to a σ-finite measure m on (E, ), g(x,y)=∫p(t,x,y)dt, and . There exists a Gaussian random field with mean 0 and covariance . Letting we consider necessary and sufficient conditions for the Markov property (MP) on sets B, C: (B), (C) c.i. given (B ∩ C). Of crucial importance is the following, proved by Dynkin: , where μB is the hitting distribution of the process corresponding to p, m with initial law μ. Another important fact is that ?μ=?ν iff μ, ν have the same potential. Putting these together with an additional transience assumption, we present a potential theoretic proof of the following necessary and sufficient condition for (MP) on sets B, C: For every x?E, TB∩C=TB+TC∮ θTB=TC+TB∮θTC a.s. Px where, for D ? , TD is the hitting time of D for the process associated with p, m. This implies a necessary condition proved by Dynkin in a recent preprint for the case where B∪C=E and B, C are finely closed. 相似文献
7.
《Topology and its Applications》1986,22(2):109-122
We write 2x for the hyperspace of all non-empty compact sets in a complete metric linear space X topologized by the Hausdorff metric. Using the notation (X) = {A ϵ 2X: A is finite}, lf2 = {x} = (xi) ϵ l2: xi = 0 for almost all i}, and lσ2 = {x = (x i) ϵ l2:σ∞i=1 (ixi)2 < ∞}, we have the following theorem:A family ⊂(X) is homeomorphic to lf2 if is σ-fd-compact, the closure of in 2x is not locally compact and if whenever A, B ∈ , λ ∈ [0, 1] and C ⊂ λA + (1 - λ)B with card C⩽ max{card A, card B} then C ϵ .Moreover, for any Gδ-AR-set of with ⊃ we have (, )≅(l2, lƒ2).Similar conditions for hyperspaces to be homeomorphic to lσ2 are also established. 相似文献
8.
Medha Dhurandhar 《Journal of Combinatorial Theory, Series B》1984,37(3):210-220
Here quadratic and cubic σ-polynomials are characterized, or, equivalently, chromatic polynomials of the graphs of order p, whose chromatic number is p ? 2 or p ? 3, are characterized. Also Robert Korfhage's conjecture that if σ2 + bσ + a is a σ-polynomial then is verified. In general, if σ(G) = Σ0naiσi is a σ-polynomial of a graph G, then an?2 is determined. 相似文献
9.
Let ′ be either the space ′1 of distributions of exponential growth or the space ′ of tempered distributions, and let ′C(′:′) be the space of convolution operators in ′. In each case ′ is the dual of a space of C∞-functions which are in ′C(′:′). We establish necessary and sufficient conditions on the Fourier transform of ? of S ? ′C(′:′) in order that every distribution u? ′C(′:′) with S1u? be in . If ′ = ′1, the condition is equivalent to S×H′1=H′1. 相似文献
10.
11.
The authors have studied in [5] alternative real variable models based on the function , for certain integer or mixed-interger programming problems. Mainly, we have shown that there exists a vector α > 0 such that the solution to the problem min , is a solution to the problem min σxσ+, Ax = b, x ? 0, where σxσ+ denotes the cardinal of x, i.e. the number of strictly positive components of x, thus obtaining a new model for solving in real numbers a Generalized Lattice Point Problem (Cabot, [3]).The function d(x) has been introduced by use as a general tool for solving integer or mixed-integer problems due to its property of having almost everywhere almost discrete values. In the meantime we noticed that this function may represent a membership function of a fuzzy set.In this paper, we study in detail the features of this membership function and show that Cabot's results [3] may be derived in this more general setting using the complementary function .At the same time, in the paper there are some production scheduling models within the framework of fuzzy-sets theory. To this end, a nonconvex production model is presented and it is shown that the value of the objective function for a production programming model whose deman and/or resource vector components are parametrized, may be considered as a grade of membership of the solution of the parametrized model to the feasible set of the nonparametrized production programming model.Consequently, we get a nonconvex production programming model whose convex envelope is linear with coefficients which are in an inverse proportior to the magnitude of the nonparametrized demand or resource vector components. This result agrees with the intuitive idea that a high level of demand or resource allows a greater interval of variation in the production process than a lower level of demand or resource. 相似文献
12.
Two timing, an ad hoc method for studying periodic evolution equations, can be given a rigorous justification when the problem is in standard form, u = ?f(t, u). First solve , where M is the mean value operator and v is any initial value. Then w(σ, v) is periodic in σ but does not satisfy the original equation. Now, force a solution u(t), using nonlinear variation of constants, in the form w(σ, v(τ)), where σ = t is the fast time and τ = ?t is the slow time. With the resulting differential equation for v, one reads off from its nonconstant solutions thè approximate transient behavior of u(t) for times of order ??1. On the other hand, the equilibrium points (constant solutions) v0 correspond to steady state (periodic solutions) of the original system. Interesting applications, such as to one-dimensional wave equations with cubic damping, can be given. 相似文献
13.
14.
Robert Gold 《Journal of Number Theory》1976,8(4):420-423
Let ((?m)) and ((3m)) be a pair of quadratic fields, m > 0, and let λ?, μ?; λ+, μ+ be the respective Iwasawa invariants of the basic 3-extensions of these fields. A generalization of a result of Scholz shows that λ? ≥ λ+ and if μ? = 0, then μ+ = 0. 相似文献
15.
Harry Kesten 《Stochastic Processes and their Applications》1978,7(1):9-47
We consider a branching diffusion {Zt}t?0 in which particles move during their life time according to a Brownian motion with drift -μ and variance coefficient σ2, and in which each particle which enters the negative half line is instantaneously removed from the population. If particles die with probability c dt+o(dt) in [t,t+dt] and if the mean number of offspring per particle is m>1, then Zt dies out w.p.l. if . If μ<μ0, then itZt grows exponentially with positive probability. Our main concern here is with the critical case where μ=μ0. Even though in this case, we find that is only exp, and conditionally on {ZT>0} there are with high probability much fewer particles alive at time T than . 相似文献
16.
Given a unitary operator T in a Hilbert space H = (H, 〈·, ·〉) convergence results for two sequences of ( two-point Padé approximants to the function f(z) = 〈(I ? zT)?1u0, u0〉, (u0 ∈ H, ∥ u0∥ = 1, z regular for T) are given. An elementary proof is also given of the well-known operator version of the trigonometric moment problem, not using the solution of the classical trigonometric moment problem. 相似文献
17.
Stephen M. Paneitz 《Journal of Functional Analysis》1981,41(3):315-326
Let Sp() be the symplectic group for a complex Hibert space . Its Lie algebra sp() contains an open invariant convex cone C0; each element of C0 commutes with a unique sympletic complex structure. The Cayley transform : X∈ sp()→(I + X)1∈ Sp() is analyzed and compared with the exponential mapping. As an application we consider equations of the form is strongly continuous, and show that if ∝?∞∞ ∥A(t)∥ dt < 2 and ∝? t8∞A(t) dt?C0, the (scattering) operator , where St′(t) is the solution such that St′(t′) = I, is in the range of restricted to C0. It follows that S leaves invariant a unique complex structure; in particular, it is conjugate in Sp() to a unitary operator. 相似文献
18.
Robyn Curtis 《Comptes Rendus Mathematique》2002,334(1):31-35
We define the Hecke von Neumann algebra associated with a group G, a subgroup H and a unitary representation σ of H. We show that when σ is finite dimensional, can be seen as a corner algebra of the tensor product of the group von Neumann algebra of a locally compact group and a matrix algebra. To cite this article: R. Curtis, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 31–35 相似文献
19.
An anti-Hadamard matrix may be loosely defined as a real (0, 1) matrix which is invertible, but only just. Let A be an invertible (0, 1) matrix with eigenvalues λi, singular values σi, and inverse B = (bij). We are interested in the four closely related problems of finding λ(n) = minA, i|λi|, σ(n) = minA, iσi, χ(n) = maxA, i, j |bij|, and μ(n) = maxAΣijb2ij. Then A is an anti-Hadamard matrix if it attains μ(n). We show that λ(n), σ(n) are between and c√n (2.274)?n, where c is a constant, , and . We also consider these problems when A is restricted to be a Toeplitz, triangular, circulant, or (+1, ?1) matrix. Besides the obvious application—to finding the most ill-conditioned (0, 1) matrices—there are connections with weighing designs, number theory, and geometry. 相似文献
20.
Matania Ben-Artzi 《Journal of Differential Equations》1980,38(1):41-50
Let H = ?Δ + V, where the potential V is spherically symmetric and can be decomposed as a sum of a short-range and a long-range term, V(r) = VS(r) + VL(r). Assume that for some r0, VL(r) ?C2k(r0, ∞) and that there exist μ > 0, δ > 0, such that . Assume further that min(2kμ, (2k ? 1)δ + μ) > 1. Under this weak decay condition on VL(r) it is shown in this paper that the positive spectrum of H is absolutely continuous and that the absolutely continuous part of H is unitarily equivalent to ?Δ, provided that the singularity of V at 0 is properly restricted. In particular, some oscillation of VL(r) at infinity is allowed. 相似文献