共查询到20条相似文献,搜索用时 93 毫秒
1.
Consider a semilinear eigenvalue problem where λ ∈ R , the linear operator is defined in a real Hilbert space H and : H → H is generaly a nonlinear perturbation. We can define a coincidence degree of the pair ( ) under some conditions weaker than the ones when the classical coincidence degree was defined. Our final purpose is to extend the results to the case of the operators from the Banach space X into its dual X*, using the representation theorem due to Browder and Ton. We use these results to study resonance problems in mechanics of continua, such as the buckling in finite elastostatics and the steady state flow of incompressible fluids. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
In this paper we provide a new arithmetic characterization of the levels of the og‐time hierarchy (LH). We define arithmetic classes and that correspond to ‐LOGTIME and ‐LOGTIME, respectively. We break and into natural hierarchies of subclasses and . We then define bounded arithmetic deduction systems ′ whose ‐definable functions are precisely B( ‐LOGTIME). We show these theories are quite strong in that (1) LIOpen proves for any fixed m that , (2) TAC, a theory that is slightly stronger than ′ whose (LH)‐definable functions are LH, proves LH is not equal to ‐TIME(s) for any m> 0, where 2s ∈L, s(n) ∈ ω(log n), and (3) TAC proves LH ≠ for all k and m. We then show that the theory TAC cannot prove the collapse of the polynomial hierarchy. Thus any such proof, if it exists, must be argued in a stronger systems than ours. 相似文献
3.
Ross G. Pinsky 《Random Structures and Algorithms》2006,29(3):277-295
Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1,…,n}. We show that Var(Z) = o((EZ)2) as n → ∞ if and only if . In particular then, the weak law of large numbers holds for Z if ; that is, We also show the following approximation result for the uniform measure Un on Sn. Define the probability measure μ on Sn by where U denotes the uniform measure on the subset of permutations that contain the increasing subsequence {x1,x2,…,x}. Then the weak law of large numbers holds for Z if and only if where ∣∣˙∣∣ denotes the total variation norm. In particular then, (*) holds if . In order to evaluate the asymptotic behavior of the second moment, we need to analyze occupation times of certain conditioned two‐dimensional random walks. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
4.
Let k be an arbitrary field, X1,….,Xn indeterminates over k and F1…, F3 ε ∈ k[X1…,Xn] polynomials of maximal degree $ d: = \mathop {\max }\limits_{1 \le i \le a} \deg $ (Fi). We give an elementary proof of the following effective Nullstellensatz: Assume that F1,…,F have no common zero in the algebraic closure of k. Then there exist polynomials P1…, P3 ε ∈ k[X1…,Xn] such that $ 1: = \mathop \Sigma \limits_{1 \le i \le a} $ PiFi and This result has many applications in Computer Algebra. To exemplify this, we give an effective quantitative and algorithmic version of the Quillen-Suslin Theorem baaed on our effective Nullstellensatz. 相似文献
5.
In this paper we prove a Tauberian type theorem for the space L ( H n ). This theorem gives sufficient conditions for a L ( H n ) submodule J ? L ( H n ) to make up all of L ( H n ). As a consequence of this theorem, we are able to improve previous results on the Pompeiu problem with moments on the Heisenberg group for the space L∞( H n ). In connection with the Pompeiu problem, given the vanishing of integrals ∫ z m L g f ( z , 0) dσ ( z ) = 0 for all g ∈ H n and i = 1, 2 for appropriate radii r1 and r2, we now have the (improved) conclusion f ≡ 0, where = · · · and form the standard basis for T(0,1)( H n ). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Risto Kaila 《Mathematical Logic Quarterly》2002,48(2):301-320
We prove convergence laws for logics of the form , where is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics , where is a collection of generalized quantifiers and k ∈ ℕ+, under arbitrary probability measures of finite structures. 相似文献
7.
Camil Muscalu 《纯数学与应用数学通讯》1999,52(10):1213-1230
In this paper we prove the following theorem (for notation and definitions, see the paragraphs below): “Let Ω ⊆ ℝn be a domain, m ∈ ℕ, and λ, q > 0. Then, there exists r (= r(λ, q)) > 1 such that for every 0 < p < q, whenever are weak solutions of a strongly elliptic system with m equations of ellipticity λ satisfying ∈ 𝒫r a.e. and Ω′ ⊆ Ω subdomain, the following inequalities hold: where C (= C(n,m,λ,q,p,Ω,Ω′)) is a positive constant.” © 1999 John Wiley & Sons, Inc. 相似文献
8.
Massimo Gobbino 《Mathematical Methods in the Applied Sciences》1999,22(5):375-388
We investigate the evolution problem where H is a Hilbert space, A is a self‐adjoint linear non‐negative operator on H with domain D(A), and is a continuous function. We prove that if , and , then there exists at least one global solution, which is unique if either m never vanishes, or m is locally Lipschitz continuous. Moreover, we prove that if for all , then this problem is well posed in H. On the contrary, if for some it happens that for all , then this problem has no solution if with β small enough. We apply these results to degenerate parabolic PDEs with non‐local non‐linearities. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
9.
We construct a smooth function g* : IR ? IR with such that the equation has a slowly oscillating periodic solution y, and a slowly oscillating solution z* whose phase curve is homoclinic with respect to the orbit o of y in the space C = C0([1,0],IR). For an associated Poincaré map we obtain a transversal homoclinic loop. The proof of transversality employs a criterion which uses oscillation properties of solutions of variational equations. The main result is that the trajectories (ψn)∞-∞ of the Poincaré map in a neighbourhood of the homoclinic loop form a hyperbolic set on which the motion is chaotic. 相似文献
10.
Carmen Fernndez 《Mathematische Nachrichten》2000,216(1):61-71
Let (ω)(ℝ) denote the non–quasianalytic class of Beurling type on ℝ. For μ, ν ∈ ′(ω)(ℝ) we give necessary conditions for the inclusion Tν( (ω)(ℝ)) ⊂ Tμ( (ω)(ℝ)), thus extending previous work of Malgrange and Ehrenpreis . 相似文献
11.
Itai Benjamini Simi Haber Michael Krivelevich Eyal Lubetzky 《Random Structures and Algorithms》2008,32(1):101-114
The isoperimetric constant of a graph G on n vertices, i(G), is the minimum of , taken over all nonempty subsets S ⊂ V (G) of size at most n/2, where ∂S denotes the set of edges with precisely one end in S. A random graph process on n vertices, , is a sequence of graphs, where is the edgeless graph on n vertices, and is the result of adding an edge to , uniformly distributed over all the missing edges. The authors show that in almost every graph process equals the minimal degree of as long as the minimal degree is o(log n). Furthermore, it is shown that this result is essentially best possible, by demonstrating that along the period in which the minimum degree is typically Θ(log n), the ratio between the isoperimetric constant and the minimum degree falls from 1 to , its final value. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008 相似文献
12.
Henrik Winkler 《Mathematische Nachrichten》2000,220(1):115-141
Two–dimensional canonical systems are boundary value problems of the form with y1(0) = 0 and Weyl's limit point case at L. The 2 × 2 matrix valued function H is real, symmetric and nonnegative, . The correspondence between canonical systems and their Titchmarsh–Weyl coefficients Q is a bijection between the class of all matrix functions H with tr H(x) = 1 a.e. on [0, L) and the class of the Nevanlinna functions ℕ augmented by the function Q ≡ 8. Each Titchmarsh–Weyl coefficient Q ∈ ℕ can be represented by means of a measure σ, the so–called spectral measure of the canonical system. In this note matrix functions H are specified whose corresponding spectral measures σ satisfy conditions of the form or . Herewith we generalize corresponding results of M.G. Krein and I. S. Kac for so–called vibrating strings. 相似文献
13.
A family of permutations of [n] = {1,2,…,n} is (ε,k)‐min‐wise independent if for every nonempty subset X of at most k elements of [n], and for any x ∈ X, the probability that in a random element π of , π(x) is the minimum element of π(X), deviates from 1/∣X∣ by at most ε/∣X∣. This notion can be defined for the uniform case, when the elements of are picked according to a uniform distribution, or for the more general, biased case, in which the elements of are chosen according to a given distribution D. It is known that this notion is a useful tool for indexing replicated documents on the web. We show that even in the more general, biased case, for all admissible k and ε and all large n, the size of must satisfy as well as This improves the best known previous estimates even for the uniform case. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 相似文献
14.
A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree
Michael Drmota Alex Iksanov Martin Moehle Uwe Roesler 《Random Structures and Algorithms》2009,34(3):319-336
Let Xn be the number of cuts needed to isolate the root in a random recursive tree with n vertices. We provide a weak convergence result for Xn. The basic observation for its proof is that the probability distributions of are recursively defined by , where Dn is a discrete random variable with ? , which is independent of . This distributional recursion was not studied previously in the sense of weak convergence. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献
15.
De‐Jun Feng 《Mathematische Nachrichten》2002,241(1):65-72
For each 0 < s < 1, define where , denote respectively the s‐dimensional packing measure and Hausdorff measure, and the infimum is taken over all the sets E ⊂ R with . In this paper we give a nontrivial estimation of c(s), namely, for each 0 < s < 1, where . As an application, we obtain a lower density theorem for Hausdorff measures. 相似文献
16.
We consider the half‐linear boundary value problem where and the weight function q is assumed to change sign. We prove the existence of two sequences , of eigenvalues and derive asymptotic estimates for as . 相似文献
17.
Nina Chernyavskaya 《Mathematische Nachrichten》2002,243(1):5-18
We consider a boundary value problem where f(x) ∈ Lp(R), p ∈ [1,∞] (L∞(R) ≔ C(R) and 0 ≤ q(x) ∈ Lloc1( R). Boundary value problem (0.1) is called correctly solvable in the given space Lp(R) if for any f(x) ∈ Lp(R) there is a unique solution y(x) ∞ Lp(R) and the following inequality holds with absolute constant c(p) ∈ (0,∞). We find criteria for correct solvability of the problem (0.1) in Lp(R). 相似文献
18.
In this article we give the definition of the class ??1 and prove: (1) ??1(v) ≠ ? for v ∈ ?? = ??1 ∪ ??2 ∪ ??3 where (2) there exists 2 ? {2q2; q2 ± q, q2;q2 ± q} supplementary difference sets for q2 ∈ ??; (3) there exists an Hadamard matrix of order 4v for v ∈ ??; (4) if t is an order of T-matrices, there exists an Hadamard matrix of order 4tv for v ∈ ??. © 1994 John Wiley & Sons, Inc. 相似文献
19.
If Tφ is a hyponormal Toeplitz operator with polynomial symbol φ = ḡ + f (f, g ∈ H∞ (𝕋 )) such that g divides f, and if ψ := then where μ is the leading coefficient of ψ and 𝒵(ψ) denotes the set of zeros of ψ. In this paper we present a necessary and sufficient condition for Tφ to be hyponormal when φ enjoys an extremal case in the above inequality, that is, equality holds in the above inequality. 相似文献
20.
If Rt is the position of the rightmost particle at time t in a one dimensional branching brownian motion, whore α is the inverse of the mean life time and m is the mean of the reproduction law. If Zt denotes the random point measure of particles living at time t, we get in the critical area {c = c0} The function u(t, x) = P(Rt > x) is studied as a solution of the K-P-P equation for some function f. Conditioned on non-extinction of the spatial tree in the c0-direction, a limit distribution is obtained and characterized. 相似文献