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1.
In this paper, we establish some limit theorems on the increments of an l^p-valued multiparameter Gaussian process under weaker conditions than those of Csoergoe-Shao theorems published in Ann. Probab. (1993).  相似文献   

2.
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ 1, ..., ϕ r ) T is unknown, g is a given vector of compactly supported functions on ℝ s , a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ n , n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ 0. We characterize the L p -convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation. This project is supported by the NSF of China under Grant No. 10071071  相似文献   

3.
We present a method for computing pth roots using a polynomial basis over finite fields of odd characteristic p, p ≥ 5, by taking advantage of a binomial reduction polynomial. For a finite field extension of our method requires p − 1 scalar multiplications of elements in by elements in . In addition, our method requires at most additions in the extension field. In certain cases, these additions are not required. If z is a root of the irreducible reduction polynomial, then the number of terms in the polynomial basis expansion of z 1/p , defined as the Hamming weight of z 1/p or , is directly related to the computational cost of the pth root computation. Using trinomials in characteristic 3, Ahmadi et al. (Discrete Appl Math 155:260–270, 2007) give is greater than 1 in nearly all cases. Using a binomial reduction polynomial over odd characteristic p, p ≥ 5, we find always.   相似文献   

4.
In general, given a finite group G, a prime p and a p-subgroup R of G, the sylowizers of R in G are not conjugate. In this paper we afford some conditions to achieve the conjugation of the sylowizers of R in a p-soluble group G, among others
1.  p = 2 and the Sylow 2-subgroups of G are dihedral or quaternion.
2.  The Sylow p-subgroups of G have order at most p 3.
3.  p is odd, R is abelian and every element of order p in C G (R) lies in R.
This research has been supported by Grants: MTM2004-06067-C02-01 and MTM 2004-08219-C02-01, MEC (Spain) and FEDER (European Union).  相似文献   

5.
We determine the L p discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the L p discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on L p discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the Hammersley point set and show that there always exist permutations such that the L p discrepancy of the generalized Hammersley point set is of best possible order. For the L 2 discrepancy such permutations are given explicitly. F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”.  相似文献   

6.
In this paper we study the L p -discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which is also known as Roth net) with N points has L p -discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has L p -discrepancy (p an even integer) of order which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L 2-discrepancy of digitally shifted Hammersley point sets which show that the value of the L 2-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position of these. This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305.  相似文献   

7.
It is proved that association schemes with bipartite basis graphs are exactly 2-schemes. This result follows from a characterization of p-schemes for an arbitrary prime p in terms of basis digraphs. Second author work was partially supported by RFFI Grants 07-01-00485, 08-01-00379 and 08-01-00640. First author was visiting the Euler Institute of Mathematics, St. Petersburg, Russia during the time a part of this paper was written and he thanks the Euler Institute for its hospitality  相似文献   

8.
L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1R 1 and ∈ L loc p (R n ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L p (K) with any accuracy for any compact set K in R n , if and only if g(x) is not an even polynomial. Partly supported by the National Natural Science Foundation of China (10471017)  相似文献   

9.
We present an equivalence theorem, which includes all known characterizations of the class B p , i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p * , B * and RB p , and prove and apply a “gluing lemma” of independent interest.  相似文献   

10.
In this paper, we get W 1,p (R n )-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and Tananka’s results. Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural Science Foundation of China.  相似文献   

11.
For a big number of varieties of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups in the class does not coincide with the variety of all o-approximable lattice-ordered groups. Supported by FP “Universities of Russia” grant No. UR.04.01.001. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 20–27, January–February, 2006.  相似文献   

12.
In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.  相似文献   

13.
In this paper we obtain local L p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)  相似文献   

14.
We prove firstly the classification theorem for p-harmonic morphisms between Euclidean domains. Secondly, we show that if is a p-harmonic morphism (p ≥ 2) from a complete Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive scalar curvature such that the L q -energy is finite, then is constant, which improve the corresponding result due to G. Choi, G. Yun in (Geometriae Dedicata 101 (2003), 53–59).   相似文献   

15.
Let be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian and we prove that the limit of when is 2/d(M), where d(M) is the diameter of M. Moreover, if is an oriented compact hypersurface of the Euclidean space or , we prove an upper bound of in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of then: . Mathematics Subject Classifications (2000): 53A07, 53C21.  相似文献   

16.
In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+|u| p−2 u=0 in Ω with | u| p−2 u ν =f on Ω. Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and CONICET (Argentina) PIP 5478/1438. J. Fernández Bonder is a member of CONICET. Leandro M. Del Pezzo is a fellow of CONICET.  相似文献   

17.
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u * belongs to L  ∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)). This work was partially supported by MCyT BMF 2002-04613-CO3-02.  相似文献   

18.
We derive a lower bound of L p norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X 1,..., X n with under the boundedness condition ℙ{|X i | ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑ r⩾1 r 2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005.  相似文献   

19.
In this paper, we consider the generation and propagation of interfaces for p-Laplacian equations with the derivative of a bi-stable potential.  相似文献   

20.
The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over as well as over the prime field , are established. Q-ary 1-perfect codes of length n=(qm − 1)/(q − 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established.Communicated by: I.F. Blake  相似文献   

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