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1.
M.S. Bernabei 《Probability Theory and Related Fields》2001,119(3):410-432
The Central Limit Theorem for a model of discrete-time random walks on the lattice ℤν in a fluctuating random environment was proved for almost-all realizations of the space-time nvironment, for all ν > 1 in
[BMP1] and for all ν≥ 1 in [BBMP]. In [BMP1] it was proved that the random correction to the average of the random walk for
ν≥ 3 is finite. In the present paper we consider the cases ν = 1,2 and prove the Central Limit Theorem as T→∞ for the random correction to the first two cumulants. The rescaling factor for theaverage is for ν = 1 and (ln T), for ν=2; for the covariance it is , ν = 1,2.
Received: 25 November 1999 / Revised version: 7 June 2000 / Published online: 15 February 2001 相似文献
2.
We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the \mathfrak p{\mathfrak {p}}-adic and adelic Galois representations associated to M. The method makes essential use of the Harder–Narasimhan filtration for locally free coherent sheaves on an algebraic curve. 相似文献
3.
Manohar Aggrawal Poonam SinghMahesh Kumar Panda 《Statistics & probability letters》2011,81(2):259-266
Chan et al. (1998a) obtained A-optimal designs for an additive quadratic mixture model for q≥3 mixture components. In this paper, we obtain the A-optimal designs for an additive cubic model for q≥3 mixture components using the class of symmetric weighted centroid designs based on barycentres of various depths. We observe that barycentres of depths 0 and 2 are possible support points for an A-optimal design. We have also given the optimal weights of A-optimal designs for 3≤q≤17. 相似文献
4.
Hartmut Pecher 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(6):1851-1877
The Cauchy problem for the Gross-Pitaevskii equation in three space dimensions is shown to have an unconditionally unique global solution for data of the form 1 + H s for 5/6 < s < 1, which do not have necessarily finite energy. The proof uses the I-method which is complicated by the fact that no L 2-conservation law holds. This shows that earlier results of Bethuel-Saut for data of the form 1 + H 1 and Gérard for finite energy data remain true for this class of rough data. 相似文献
5.
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ||·||div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes. 相似文献
6.
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces Hs, for s negative but close to 0. For smooth solutions there is an a priori upper bound for the Hs norm of the solution, in terms of the Hs norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrary initial data in Hs. 相似文献
7.
We consider a specific continuous-spin Gibbs distribution μt=0 for a double-well potential that allows for ferromagnetic ordering. We study the time-evolution of this initial measure under
independent diffusions.
For `high temperature' initial measures we prove that the time-evoved measure μt is Gibbsian for all t. For `low temperature' initial measures we prove that μt stays Gibbsian for small enough times t, but loses its Gibbsian character for large enough t. In contrast to the analogous situation for discrete-spin Gibbs measures, there is no recovery of the Gibbs property for
large t in the presence of a non-vanishing external magnetic field. All of our results hold for any dimension d≥2. This example suggests more generally that time-evolved continuous-spin models tend to be non-Gibbsian more easily than
their discrete-spin counterparts.
Research carried out at EURANDOM and supported by Deutsche Forschungsgemeinschaft 相似文献
8.
The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic
α
-stable process with parameter m on ℝ
d
space. This process has an infinitesimal generator of the form mI–(m
2/α
I–Δ)
α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing
was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide
two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates
known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting
Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space.
The main result states that the Green function is comparable with the Green function for the Brownian motion if the points
are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points
the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough.
Research supported by KBN Grants. 相似文献
9.
Alex Samorodnitsky 《Journal of Combinatorial Theory, Series A》2008,115(2):279-292
A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in lp is attained either for the identity matrix I or for a constant multiple of the all-1 matrix J.The conjecture is known to be true for p=1 (I) and for p?2 (J).We prove the conjecture for a subinterval of (1,2), and show the conjectured upper bound to be true within a subexponential factor (in the dimension) for all 1<p<2. In fact, for p bounded away from 1, the conjectured upper bound is true within a constant factor. 相似文献
10.
Suppose denote the ergodic averages for the natural numbers . Let denote the corresponding maximal function and let for . We show that for if there exists such that then there exists such that . Similar weak (1,1) inequalities follow for V
q
when you know them for M too also with q > 1. We also show this fails completely if q= 1. We also show that for certain polynomial like and random sequences , if
and
is of exponential growth then
for a certain positive constant C.
(Received 11 February 1998; in revised form 10 December 1998) 相似文献
11.
T. Radul 《Topology and its Applications》2007,154(8):1794-1798
R. Pol has shown that for every countable ordinal number α there exists a universal space for separable metrizable spaces X with trindX?α. W. Olszewski has shown that for every countable limit ordinal number λ there is no universal space for separable metrizable space with trIndX?λ. T. Radul and M. Zarichnyi have proved that for every countable limit ordinal number there is no universal space for separable metrizable spaces with dimWX?α where dimW is a transfinite extension of covering dimension introduced by P. Borst. We prove the same result for another transfinite extension dimC of the covering dimension.As an application, we show that there is no absorbing sets (in the sense of Bestvina and Mogilski) for the classes of spaces X with dimCX?α belonging to some absolute Borel class. 相似文献
12.
J.W. Cohen 《Stochastic Processes and their Applications》1976,4(3):297-316
A cost function is studied for an M/G/1 queueing model for which the service rate of the virtual waiting time process Ut for Ut<K differs from that for Ut > K. The costs considered are costs for maintaining the service rate, costs for switching the service rate and costs proportional to the inventory Ut. The relevant cost factors for the system operating below level K differ from those when Ut > K. The cost function which is considered only for the stationary situation of the Ut-process expresses the average cost per unit time. The problem is to find that K for which the cost function reaches a minimum. Criteria for the possibly optimal cases are found; they have an interesting intuitive interpretation, and require the knowledge of only the first moment of the service time distribution. 相似文献
13.
We study univariate integration with the Gaussian weight for a positive variance α. This is done for the reproducing kernel Hilbert space with the Gaussian kernel for a positive shape parameter γ. We study Gauss-Hermite quadratures, although this choice of quadratures may be questionable since polynomials do not belong
to this space of functions. Nevertheless, we provide the explicit formula for the error of the Gauss-Hermite quadrature using
n function values. In particular, for 2αγ
2<1 we have an exponential rate of convergence, and for 2αγ
2=1 we have no convergence, whereas for 2αγ
2>1 we have an exponential divergence. 相似文献
14.
Bruce M. Landman 《Graphs and Combinatorics》1998,14(2):131-142
A quasi-progression of diameter n is a finite sequence for which there exists a positive integer L such that for . Let be the least positive integer such that every 2-coloring of will contain a monochromatic k-term quasi-progression of diameter n. We give a lower bound for in terms of k and i that holds for all . Upper bounds are obtained for in all cases for which . In particular, we show that . Exact formulae are found for and . We include a table of computer-generated values of , and make several conjectures.
Received: September 22, 1995 / Revised: February 28, 1997 相似文献
15.
H. Zguitti 《Journal of Mathematical Analysis and Applications》2006,316(1):373-381
We prove that if either T or T∗ has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every f∈H(σ(T)). An application is given for algebraically paranormal operators. 相似文献
16.
《Discrete Applied Mathematics》2001,108(1-2):85-103
A tree t-spanner of a graph G is a spanning subtree T of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs, the problem of deciding the existence of a tree t-spanner can be solved in polynomial time for t=2, while it is NP-hard for any t⩾4; the case t=3 is open, but has been conjectured to be hard. In this paper, we consider tree spanners in planar graphs. We show that even for planar unweighted graphs, it is NP-hard to determine the minimum t for which a tree t-spanner exists. On the other hand, we give a polynomial algorithm for any fixed t that decides for planar unweighted graphs with bounded face length whether there is a tree t-spanner. Furthermore, we prove that it can be decided in polynomial time whether a planar unweighted graph has a tree t-spanner for t=3. 相似文献
17.
Summary In a recent paper [11], two of the authors investigated a fast reduction method for solving difference equations which approximate certain boundary value problems for Poisson's equation. In this second paper, we prove the numerical stability of the reduction method, and also report on further developments of the method. For the general case, the provided bounds for the numerical errors behave roughly like the condition numberO(n
2) of the linear system; for more realistic model problems estimates of order less thanO(n) are obtained (n
–1=h=mesh width). The number of operations required for the reduction method isO(n
2
), for the usual five-point difference formula, as well as for the common nine-point formula with discretization error of orderh
4. 相似文献
18.
Michael Molloy 《Random Structures and Algorithms》2005,27(1):124-135
We describe a technique for determining the thresholds for the appearance of cores in random structures. We use it to determine (i) the threshold for the appearance of a k‐core in a random r‐uniform hypergraph for all r, k ≥ 2, r + k > 4, and (ii) the threshold for the pure literal rule to find a satisfying assignment for a random instance of r‐SAT, r ≥ 3. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
19.
Alexander V. Arhangel'skii 《Topology and its Applications》2010,157(16):2542-1389
We consider a topological game GΠ involving two players α and β and show that, for a paratopological group, the absence of a winning strategy for player β implies the group is a topological one. We provide a large class of topological spaces X for which the absence of a winning strategy for player β is equivalent to the requirement that X is a Baire space. This allows to extend the class of paratopological or semitopological groups for which one can prove that they are, actually, topological groups.Conditions of the type “existence of a winning strategy for the player α” or “absence of a winning strategy for the player β” are frequently used in mathematics. Though convenient and satisfactory for theoretical considerations, such conditions do not reveal much about the internal structure of the topological space where they hold. We show that the existence of a winning strategy for any of the players in all games of Banach-Mazur type can be expressed in terms of “saturated sieves” of open sets. 相似文献
20.
Formulas for the number of primitive representations of any integer n as a sum of k squares are given, for 2 ≤ k ≤ 8, and for certain values of n, for 9 ≤ k ≤ 12. The formulas have a similar structure and are striking for their simplicity.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—11E25; Secondary—05A15, 33E05. 相似文献