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1.
We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function
where ζ0, ζ1, … are independent standard complex-valued Gaussian variables) can be regarded as a random perturbation of a lattice in the
plane. The distribution of the distances between the zeroes and the corresponding lattice points is shift-invariant and has
a Gaussian-type decay of the tails.
Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities. 相似文献
2.
V. V. Vysotsky 《Journal of Mathematical Sciences》2007,147(4):6873-6883
Let Si be a random walk with standard exponential increments. The sum ∑
i=1
k
Si is called the k-step area of the walk. The random variable
∑
i=1
k
Si plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of
this variable and prove that
for 0 ≤ t ≤ 1. We also show that
, where the Ui,n are order statistics of n i.i.d. random variables uniformly distributed on [0, 1]. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 48–67. 相似文献
3.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
4.
Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p,
q1, q2, ..., qm be distinct primes, ni be the exponent of p modulo qi, and n be the exponent of p modulo
. Then G = Pλ〈x〉, where P is a group and
; Zi; here, Zi and P/Z(P) are elementary Abelian groups of respective orders
and pn, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Zi, and
. We state necessary and sufficient conditions for such groups to exist.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. 相似文献
5.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
6.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
7.
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L
2(ℝ
s
). Suppose ψ = (ψ1,..., ψ
r
)
T
and are two compactly supported vectors of functions in the Sobolev space (H
μ(ℝ
s
))
r
for some μ > 0. We provide a characterization for the sequences {ψ
jk
l
: l = 1,...,r, j ε ℤ, k ε ℤ
s
} and to form two Riesz sequences for L
2(ℝ
s
), where ψ
jk
l
= m
j/2ψ
l
(M
j
·−k) and , M is an s × s integer matrix such that lim
n→∞
M
−n
= 0 and m = |detM|. Furthermore, let ϕ = (ϕ1,...,ϕ
r
)
T
and be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, and M, where a and are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr
)
T
and , ν = 1,..., m − 1 such that two sequences {ψ
jk
νl
: ν = 1,..., m − 1, l = 1,...,r, j ε ℤ, k ε ℤ
s
} and { : ν=1,...,m−1,ℓ=1,...,r, j ∈ ℤ, k ∈ ℤ
s
} form two Riesz multiwavelet bases for L
2(ℝ
s
). The bracket product [f, g] of two vectors of functions f, g in (L
2(ℝ
s
))
r
is an indispensable tool for our characterization.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123) 相似文献
8.
We present several series and product representations for γ, π, and other mathematical constants. One of our results states
that, for all real numbers μ s>0, we have
where S(m) = ∑
k=1∞ 1/2
k
+m.
相似文献
9.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献
10.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
11.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
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
12.
Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
13.
E.M.E.ZAYED 《应用数学学报(英文版)》2004,20(2):215-230
The asymptotic expansion of the heat kernel Θ(t)=sum from ∞to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R~n(n=2 or 3) is studied for short-time t for a generalbounded domain Ωwith a smooth boundary (?)Ω.In this paper,we consider the case of a finite number of theDirichlet conditions φ=0 on Γ_i (i=1,...,J) and the Neumann conditions (?)=0 on Γ_i (i=J 1,...,k) andthe Robin conditions ((?) γ_i)φ=0 on Γ_i (i=k 1,...,m) where γ_i are piecewise smooth positive impedancefunctions,such that (?)Ωconsists of a finite number of piecewise smooth components Γ_i(i=1,...,m) where(?)Ω=(?)Γ_i.We construct the required asymptotics in the form of a power series over t.The senior coefficients inthis series are specified as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a“special ideal gas”,i.e.,the set of non-interacting particles set up in abox with Dirichlet,Neumann and Robin boundary conditions for the appropriate wave function.Calculationof the thermodynamic quantities for the ideal gas such as the internal energy,pressure and specific heat revealsthat these quantities alone are incapable of distinguishing between two different shapes of the domain.Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function;nevertheless,its formal theoretical motivation is of some interest. 相似文献
14.
Summary We are given a random walk S
1, S
2, ... on ℤν, ν≧1, and a strongly correlated stationary random field ξ(x), xεℤν, which is independent of the random walk. We consider the field as observed by a random walker and study partial sums of
the form
. It is assumed that the law corresponding to the random walk belongs to the domain of attraction of a non-degenerate stable
law of index β, 0<β≦2. We further suppose that the field ξ satisfies the non-central limit theorem of Dobrushin and Major with a scaling factor
. Under the assumption αk<β it is shown that
converges weakly as n→∞ to a self-similar process {Δ
t
, t≧0} with stationary increments, and Δ
t
can be represented as a multiple Wiener-It? integral of a random function. This extends the noncentral limit theorem of Dobrushin
and Major and yields a new example of a self-similar process with stationary increments. 相似文献
15.
Emin Özçag 《Proceedings Mathematical Sciences》1999,109(1):87-94
The distributionF(x
+, −r) Inx+ andF(x
−, −s) corresponding to the functionsx
+
−r lnx+ andx
−
−s respectively are defined by the equations
(1) and
(2) whereH(x) denotes the Heaviside function. In this paper, using the concept of the neutrix limit due to J G van der Corput [1], we evaluate
the non-commutative neutrix product of distributionsF(x
+, −r) lnx+ andF(x
−, −s). The formulae for the neutrix productsF(x
+, −r) lnx
+ ox
−
−s, x+
−r lnx+ ox
−
−s andx
−
−s o F(x+, −r) lnx+ are also given forr, s = 1, 2, ... 相似文献
16.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
17.
Xian Yin Zhou 《Acta Mathematica Hungarica》2002,96(3):187-220
Let {X
n
d
}n≥0be a uniform symmetric random walk on Zd, and Π(d) (a,b)={X
n
d
∈ Zd : a ≤ n ≤ b}. Suppose f(n) is an integer-valued function on n and increases to infinity as n↑∞, and let
Estimates on the probability of the event
are obtained for
. As an application, a necessary and sufficient condition to ensure
is derived for
. These extend some results obtained by Erdős and Taylor about the self-intersections of the simple random walk on Zd.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
V. G. Zhuravlev 《Journal of Mathematical Sciences》2006,137(2):4658-4672
For the two-dimensional torus
, we construct the Rauzy tilings d0 ⊃ d1 ⊃ … ⊃ dm ⊃ …, where each tiling dm+1 is obtained by subdividing the tiles of dm. The following results are proved. Any tiling dm is invariant with respect to the torus shift S(x) = x+
mod ℤ2, where ζ−1 > 1 is the Pisot number satisfying the equation x3− x2−x-1 = 0. The induced map
is an exchange transformation of Bmd ⊂
, where d = d0 and
. The map S(m) is a shift of the torus
, which is affinely isomorphic to the original shift S. This means that the tilings dm are infinitely differentiable. If ZN(X) denotes the number of points in the orbit S1(0), S2(0), …, SN(0) belonging to the domain Bmd, then, for all m, the remainder rN(Bmd) = ZN(Bmd) − N ζm satisfies the bounds −1.7 < rN(Bmd) < 0.5. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 83–106. 相似文献
19.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
20.
An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed
convex proper cone inR
n and −Γ′ be the antipodes of the dual cone of Γ. Let
be a partial differential operator with constant coefficients inR
n, whereQ(ζ)≠0 onR
n−iΓ′ andP
i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R
n−iΓ′;P
j(ζ)=0, gradP
j(ζ)≠0} contains some real point on which gradP
j≠0 and gradP
j∉Γ∪(−Γ). LetC be an open cone inR
n−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in
{ξ∈R
n;P(ξ)=0}. Ifu∈ℒ′∩L
loc
2
(R
n−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition
implies that the support ofu is contained in Γ. 相似文献