共查询到20条相似文献,搜索用时 15 毫秒
1.
Der-Shin Chang Yuang-Chin Chiang 《Annals of the Institute of Statistical Mathematics》1980,32(1):275-281
Consider a realization of the process
on the intervalT=[0,1] for functionsf
1(t),f
2(t),...,f
n
(t) inH(R), the reproducing kernel Hilbert space with reproducing kernelR(s,t) onT×T, whereR(s,t)=E[ξ(s)ξt)] is assumed to be continuous and known. Problems of the selection of functions {f
k
(t)}
k=1
n
to be ϕ-optimal design are given, and an unified approach to the solutions ofD-,A-,E- andD
s-optimal design problems are discussed. 相似文献
2.
I. Kiguradze 《Georgian Mathematical Journal》1994,1(5):487-494
The properties of solutions of the equationu″(t) =p
1(t)u(τ1(t)) +p
2(t)u′(τ2(t)) are investigated wherep
i
:a, + ∞[→R (i=1,2) are locally summable functions τ1 :a, + ∞[→R is a measurable function, and τ2 :a, + ∞[→R is a nondecreasing locally absolutely continuous function. Moreover, τ
i
(t) ≥t (i = 1,2),p
1(t)≥0,p
2
2
(t) ≤ (4 - ɛ)τ
2
′
(t)p
1(t), ɛ =const > 0 and
. In particular, it is proved that solutions whose derivatives are square integrable on [α,+∞] form a one-dimensional linear
space and for any such solution to vanish at infinity it is necessary and sufficient that
. 相似文献
3.
We consider a real random walk Sn=X1+...+Xn attracted (without centering) to the normal law: this means that for a suitable norming sequence an we have the weak convergence Sn/an⇒ϕ(x)dx, ϕ(x) being the standard normal density. A local refinement of this convergence is provided by Gnedenko's and Stone's Local Limit
Theorems, in the lattice and nonlattice case respectively. Now let denote the event (S1>0,...,Sn>0) and let Sn+ denote the random variable Sn conditioned on : it is known that Sn+/an ↠ ϕ+(x) dx, where ϕ+(x):=x exp (−x2/2)1(x≥0). What we establish in this paper is an equivalent of Gnedenko's and Stone's Local Limit Theorems for this weak convergence.
We also consider the particular case when X1 has an absolutely continuous law: in this case the uniform convergence of the density of Sn+/an towards ϕ+(x) holds under a standard additional hypothesis, in analogy to the classical case. We finally discuss an application of our
main results to the asymptotic behavior of the joint renewal measure of the ladder variables process. Unlike the classical
proofs of the LLT, we make no use of characteristic functions: our techniques are rather taken from the so–called Fluctuation
Theory for random walks. 相似文献
4.
F. M. Mukhamedov 《Mathematical Notes》2000,67(1):81-86
In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e.,
it is established that the following conditions are equivalent:
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 102–109, January, 2000. 相似文献
i) | P( t )x is weakly convergent tox 0; |
ii) | for any sequence {a n} of nonnegative integrable functions on [1, ∞) such that ∝ 1 ∞ a n(t)dt=1 for anyn and lim n→∞ ∥a n∥∞=0, the integral ∝ 1 ∞ a n(t)P( t )x dt is strongly convergent tox 0 inL 2(M, ϕ), wherex ɛM,P( t ) is a quantum quadratic process,M is a von Neumann algebra, andϕ is an exact normal state onM. |
5.
Let (S)⊄L
2(S′(∔),μ)⊄(S)* be the Gel'fand triple over the white noise space (S′(∔),μ). Let (e
n
,n>-0) be the ONB ofL
2(∔) consisting of the eigenfunctions of the s.a. operator
. In this paper the Euler operator Δ
E
is defined as the sum
, where ∂
i
stands for the differential operatorD
e
i. It is shown that Δ
E
is the infinitesimal generator of the semigroup (T
t
), where (T
t
ϕ)(x)=ϕ(e
t
x) for ϕ∈(S). Similarly to the finite dimensional case, the λ-order homogeneous test functionals are characterized by the Euler equation:
Δ
Eϕ
=λϕ. Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
Supported by the National Natural Science Foundation of China. 相似文献
6.
Gerald Kuba 《Mathematica Slovaca》2009,59(3):349-356
Let ℛ
n
(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛ
n
(t)| of the set ℛ
n
(t) by showing that, as t → ∞, t
2 log t ≪ |ℛ2(t)| ≪ t
2 log t and t
n
≪ |ℛ
n
(t)| ≪ t
n
for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛ
k,n
(t) ⊂ ℛ
n
(t) such that p(X) ∈ ℛ
k,n
(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t
k+1 ≪ |ℛ
k,n
(t)| ≪ t
k+1 and hence |ℛ
n−1,n
(t)| ≫ |ℛ
n
(t)| so that ℛ
n−1,n
(t) is the dominating subclass of ℛ
n
(t) since we can show that |ℛ
n
(t)∖ℛ
n−1,n
(t)| ≪ t
n−1(log t)2.On the contrary, if R
n
s
(t) is the total number of all polynomials in ℛ
n
(t) which split completely into linear factors over ℤ, then t
2(log t)
n−1 ≪ R
n
s
(t) ≪ t
2 (log t)
n−1 (t → ∞) for every fixed n ≥ 2.
相似文献
7.
Michel Talagrand 《Israel Journal of Mathematics》1992,79(2-3):207-224
Consider a setA of symmetricn×n matricesa=(a
i,j)
i,j≤n
. Consider an independent sequence (g
i)
i≤n
of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN
2(A, α) (resp.N
t(A, α)) the smallest number of balls of radiusα for thel
2 norm ofR
n
2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN
2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logN
t≤K(δ)M.
Work partially supported by an N.S.F. grant. 相似文献
8.
B. Uhrin 《Geometriae Dedicata》1995,57(3):249-258
Given a totally ordered setT containing at leastn+1 elements (say a subset ofR
1), the graph of the functiona:TR
n is called a Chebyshev curve (inR
n) if the determinant of the matrix (a(t
1),a(t
2), ...,a(t
n)) is either positive whenevert
1<t
2<...<t
n or negative whenevert
1<t
2<...<t
n. For finiteT a characterization of these curves (sequences) has been given by the author.In this paper the result is extended to non-finiteT. The characterization proved here is an improved (reformulated) version of that given by the author for infiniteT. 相似文献
9.
The additive subgroup generated by a polynomial 总被引:3,自引:0,他引:3
C. -L. Chuang 《Israel Journal of Mathematics》1987,59(1):98-106
SupposeR is a prime ring with the centerZ and the extended centroidC. Letp(x
1, …,x
n) be a polynomial overC in noncommuting variablesx
1, …,x
n. LetI be a nonzero ideal ofR andA be the additive subgroup ofRC generated by {p(a
1, …,a
n):a
1, …,a
n ∈I}. Then eitherp(x
1, …,x
n) is central valued orA contains a noncentral Lie ideal ofR except in the only one case whereR is the ring of all 2 × 2 matrices over GF(2), the integers mod 2. 相似文献
10.
Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q
1(t)q
2(t)2 ... q
m
(t)m, where each q
i
(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of q
j
(t). We give an algorithm to construct the polynomials q
i
(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
|λi| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic
polynomial has integral coefficients.
This work was done during a visit of the second named author to UNAM. 相似文献
11.
Gil Kalai 《Discrete and Computational Geometry》1992,8(1):363-372
Let Δ(d, n) be the maximum diameter of the graph of ad-dimensional polyhedronP withn-facets. It was conjectured by Hirsch in 1957 that Δ(d, n) depends linearly onn andd. However, all known upper bounds for Δ(d, n) were exponential ind. We prove a quasi-polynomial bound Δ(d, n)≤n
2 logd+3.
LetP be ad-dimensional polyhedron withn facets, let ϕ be a linear objective function which is bounded onP and letv be a vertex ofP. We prove that in the graph ofP there exists a monotone path leading fromv to a vertex with maximal ϕ-value whose length is at most
.
This research was supported in part by a BSF grant, by a GIF grant, and by ONR-N00014-91-C0026. 相似文献
12.
V. M. Petrogradsky 《Monatshefte für Mathematik》2006,149(3):243-249
Let R be a finitely generated associative algebra with unity over a finite field
. Denote by a
n
(R) the number of left ideals J ⊂ R such that dim R/J = n for all n ≥ 1. We explicitly compute and find asymptotics of the left ideal growth for the free associative algebra A
d
of rank d with unity over
, where d ≥ 1. This function yields a bound a
n
(R) ≤ a
n
(A
d
),
, where R is an arbitrary algebra generated by d elements. Denote by m
n
(R) the number of maximal left ideals J ⊂ R such that dim R/J = n, for n ≥ 1. Let d ≥ 2, we prove that m
n
(A
d
) ≈ a
n
(A
d
) as n → ∞. 相似文献
13.
Letf(t) = ∑a
k
e
ikt
be infinitely differentiable on R, |f(t)|<1. It is known that under these assumptions ‖n‖ converges to a finite limitl asn → ∞ (l
2 = sec(arga),a = (f′(0))2 -f″(0)). We obtain here more precise results: (i) an asymptotic series (in powers ofn
-1/2) for the Fourier coefficientsa
nk
off
n
, which holds uniformly ink asn → ∞; (ii) an asymptotic series (this time only powers ofn
-1 are present!) for ‖f
n
‖; (iii) the fact that ifi
j
f
(j)(0) is real forj = 1,2,..., 2h + 2 then ‖f
n
‖ = l + o(n
-h
),n → ∞. More generally, we obtain analogous finite asymptotic expansions whenf is assumed to be differentiable only finitely many times. 相似文献
14.
P. Erdös 《Israel Journal of Mathematics》1963,1(3):156-160
Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n
2/4]+1) contains a circuit ofl edges for every 3 ≦l<c
2
n, also that everyG(n; [n
2/4]+1) contains ak
e(u
n, un) withu
n=[c
1 logn] (for the definition ofk
e(u
n, un) see the introduction). Finally fort>t
0 everyG(n; [tn
3/2]) contains a circuit of 2l edges for 2≦l<c
3
t
2.
This work was done while the author received support from the National Science Foundation, N.S.F. G.88. 相似文献
15.
Explosive solutions of elliptic equations with absorption and nonlinear gradient term 总被引:2,自引:0,他引:2
Marius Ghergu Constantin Niculescu Vicenţiu Rădulescu 《Proceedings Mathematical Sciences》2002,112(3):441-451
Letf be a non-decreasing C1-function such that
andF(t)/f
2
a(t)→ 0 ast → ∞, whereF(t)=∫
0
t
f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|
a
=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded. 相似文献
16.
József Beck 《Combinatorica》1981,1(4):319-325
Letg be a coloring of the set {1, ...,N} = [1,N] in red and blue. For each arithmetic progressionA in [1,N], consider the absolute value of the difference of the numbers of red and of blue members ofA. LetR(g) be the maximum of this number over all arithmetic progression (thediscrepancy ofg). Set
over all two-coloringsg. A remarkable result of K. F. Roth gives*R(N)≫N
1/4. On the other hand, Roth observed thatR(N)≪N
1/3+ɛ and suggested that this bound was nearly sharp. A. Sárk?zy disproved this by provingR(N)≪N
1/3+ɛ. We prove thatR(N)=N
1/4+o(1) thus showing that Roth’s original lower bound was essentially best possible.
Our result is more general. We introduce the notion ofdiscrepancy of hypergraphs and derive an upper bound from which the above result follows. 相似文献
17.
Let {S
n
} be a random walk on ℤ
d
and let R
n
be the number of different points among 0, S
1,…, S
n
−1. We prove here that if d≥ 2, then ψ(x) := lim
n
→∞(−:1/n) logP{R
n
≥nx} exists for x≥ 0 and establish some convexity and monotonicity properties of ψ(x). The one-dimensional case will be treated in a separate paper.
We also prove a similar result for the Wiener sausage (with drift). Let B(t) be a d-dimensional Brownian motion with constant drift, and for a bounded set A⊂ℝ
d
let Λ
t
= Λ
t
(A) be the d-dimensional Lebesgue measure of the `sausage' ∪0≤
s
≤
t
(B(s) + A). Then φ(x) := lim
t→∞:
(−1/t) log P{Λ
t
≥tx exists for x≥ 0 and has similar properties as ψ.
Received: 20 April 2000 / Revised version: 1 September 2000 / Published online: 26 April 2001 相似文献
18.
S. A. Amitsur 《Israel Journal of Mathematics》1984,47(1):1-22
Bounds and asymptotic formulas are given for the size of the irreducible representations of the symmetric groups. These are
applied to obtain information on the identities and codimension sequencec
n(R) of a PI-algebraR, of a PI-algebraR of characteristic zero, e.g., the “ultimate” width of the hook in which the diagrams of the cocharacters ofR lies is <=(lim
c
n (R)1/n
)
2
, and lim cn(R)1/n≦ 2(lim cn(R)1/n)2 for rings with no right (or left) total annihilators. 相似文献
19.
Turán's problem is to determine the maximum numberT(n,k,t) oft-element subsets of ann-set without a complete sub-hypergraph onk vertices, i.e., allt-subsets of ak-set. It is proved that fora≥1 fixed andt sufficiently largeT(n, t+a,t)>(1-a(a+4+o(1))logt/(
a
t
)(
t
n
holds 相似文献
20.
Edgar Reich 《Israel Journal of Mathematics》1977,28(1-2):91-97
Letf(t, z)=z+tω(1/z) be schlicht for ⋎z⋎>1, ω(z) = Σ
n
= 0/∞
a
n
z
n
,t>0. The paper considers first-order estimates for the dilatation of extremal quasiconformal extensions off ast→0.
This work was initiated during the Special Year in Complex Analysis at the Technion, and was supported in parts by the Samuel
Neaman Fund, the Forschungsinstitut für Mathematik, ETH, Zürich, and the National Science Foundation. 相似文献