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1.
In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schr?dinger equations with electromagnetic fields
for sufficiently large λ, where i is the imaginary unit, for N ≥ 3 and 2 < p < + ∞ for N = 1, 2. a(x) is a real continuous function on is such that A j (x) is a real local H?lder continuous function on for j = 1, 2, ... ,N. We assume that a(x) is nonnegative and has a potential well consisting of k components . We show that for any non-empty subset has a standing wave solution which is trapped in a neighborhood of for λ large.   相似文献   

2.
In this paper we prove that sharp weak-type estimates for the maximal operators associated with a cylindric distance function associated with a convex polygon on when 2/3 < p < 1 and , or when p = 2/3 and . This work was supported (in part) by research funds from Chosun University, 2007.  相似文献   

3.
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.   相似文献   

4.
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T. We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries, yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L 2 sphere. The estimates are given in terms of the γ 2 functional with respect to the ψ 2 metric on F, and hold both in exponential probability and in expectation. Received: November 2005, Revision: May 2006, Accepted: June 2006  相似文献   

5.
We develop a translation-type model for univalent self-maps φ of the unit disc having an interior fixed-point and use the model to classify the φ-invariant measures on . We are particularly interested in maps which can be embedded in continuous semigroups of holomorphic self-maps of . Received: February 2, 2007. Revised: June 18, 2007. Accepted: July 4, 2007.  相似文献   

6.
Let be a finite field with q elements, where q is a prime power. Let G be a subgroup of the general linear group over and be the rational function field over . We seek to understand the structure of the rational invariant subfield . In this paper, we prove that is rational (or, purely transcendental) by giving an explicit set of generators when G is the symplectic group. In particular, the set of generators we gave satisfies the Dickson property.   相似文献   

7.
Summary.  A real-valued function f defined on an open convex set is called (d, t)-convex if it satisfies
for all , where is a given function and t ]0, 1[ is a fixed parameter. The main result of the paper states that if f is locally bounded from above at a point of D and (d, t)-convex then it satisfies the convexity-type inequality (under some assumptions)
for all and s [0, 1], where is defined as the fixed point of a certain contraction. The main result of this paper offers a generalization of the celebrated Bernstein and Doetsch theorem and the recent results by Nikodem and Ng, Páles and the author. This research was supported by the Hungarian Scientific Research Fund (OTKA) Grant T-038072 and K-62316.  相似文献   

8.
The standard correspondence between the normal subgroups of the group G and some ideals of the group algebra FG is described. There is the problem of what we can say (or even prove) about a two-sided ideal of that does not contain any element of the form 1 − g ≠ 0, gG of the standard basis of the augmentation ideal of . The main part of the argument of [2] yields the insight that, for such an ideal I there exists an expansion such that the ideal J of spanned by I contains an element 1 − h, hH \ G. Using the ideas of [2], we construct -thick groups H such that for every ideal J ≠ (0) of there are elements 1 − h ≠ 0 in J. This construction allows many variations. Examples of simple -thick groups were pointed out in [2]. A natural class of (in general non-simple) -full groups are the normal sections of the groups
(Here, Fin(M) is the subgroup of all finitary permutations of M.) Received: July 2007  相似文献   

9.
We show that meromorphic solutions f, g of f 3 + g 3 = 1 in must be constant, if and have the same zeros (counting multiplicities). Received: 12 March 2007  相似文献   

10.
Let be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a -bundle over and that for any fiber F of the bundle projection . The pairs with = 2 are classified, where is the curve genus of . This allows us to improve some previous results. Received: 13 June 2006  相似文献   

11.
A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type. Received: 17 November 2006  相似文献   

12.
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite. Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007.  相似文献   

13.
We study the analytical integrability of the FitzHugh–Nagumo systems in with parameters   相似文献   

14.
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q * Q has an infinite dimensional reducing subspace M with Q * Q| M compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial solutions to the hyperinvariant subspace problem.   相似文献   

15.
It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail. Received March 7, 2006; accepted in final form August 29, 2006.  相似文献   

16.
Let Ω be an open connected subset of for which the imbedding of the Sobolev space W 1,2(Ω) into the space L 2(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset (Ω) of , where is a Lipschitz continuous homeomorphism of Ω onto (Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of . This paper represents an extension of a part of the work performed by P.D. Lamberti in his PhD Thesis at the University of Padova under the guidance of M. Lanza de Cristoforis.  相似文献   

17.
We classify the maximal irreducible periodic subgroups of PGL(q, ), where is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, ) containing the centre ×1 q of GL(q, ), such that G/ ×1 q is a maximal periodic subgroup of PGL(q, ), and if H is another group of this kind then H is GL(q, )-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a maximal irreducible periodic subgroup of PGL(q, ) is self-normalising.   相似文献   

18.
Let E, E* be separable Hilbert spaces. If S is an open subset of , then denotes the space of all functions that are holomorphic in , and bounded and continuous on . In this article we prove the following results:
1.  A theorem concerning the approximation of by a function F that is holomorphic in a neighbourhood of and such that the error Ff is uniformly bounded in the disk .
2.  The corona theorem for when dim(E) < ∞: If there exists a δ > 0 such that for all , , then there exists a such that for all , g(z)f(z) = I.
3.  The problem of complementing to an isomorphism for when {dim(E) < ∞ (Tolokonnikov’s lemma): has a left inverse iff it is a ‘part’ of an invertible element F in .
  相似文献   

19.
In this paper I consider a class of non-standard singular integrals motivated by potential theoretic and probabilistic considerations. The probabilistic applications, which are by far the most interesting part of this circle of ideas, are only outlined in Section 1.5: They give the best approximation of the solution of the classical Dirichlet problem in a Lipschitz domain by the corresponding solution by finite differences. The potential theoretic estimate needed for this gives rise to a natural duality between the L p functions on the boundary ∂Ω and a class of functions A on Ω that was first considered by Dahlberg. The actual duality is given by ∫Ω S f(x)A(x)dx = (f, A) where S f(x) = ∫∂Ω |xy|1−n f(y)dy is the Newtonian potential. We can identify the upper half Lipschitz space with in the obvious way and express for an appropriate kernel K. It is the boundedness properties of the above (for , ) that is the essential part of this work. This relates with more classical (but still “rough”) singular integrals that have been considered by Christ and Journé. Lecture held in the Seminario Matematico e Fisico on March 14, 2005 Received: April 2007  相似文献   

20.
We consider the existence of bound states for the coupled elliptic system
where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum of solutions (λ1, λ2, μ 1, μ 2, β, u 1, u 2) bifurcating from the set of semipositive solutions (where u 1 = 0 or u 2 = 0) and investigate the parameter range covered by . Dedicated to Albrecht Dold and Edward Fadell  相似文献   

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