共查询到20条相似文献,搜索用时 46 毫秒
1.
Y. -K. Choi 《Acta Mathematica Hungarica》2009,123(4):331-355
This paper establishes the general moduli of continuity for l
∞-valued Gaussian random fields {X(t):= (X
1(t),X
2(t), h.), t ∈ [0, ∞)
N
} indexed by the N-dimensional parameter t:= (t
1,…,t
N
), under the explicit condition yielding that the covariance function of distinct increments of X
k
(t) for fixed k ≧ 1 is positive or nonpositive.
Supported by KOSEF-R01-2008-000-11418-0. 相似文献
2.
Sofiya Ostrovska 《Proceedings Mathematical Sciences》2007,117(4):485-493
Let φ be a power series with positive Taylor coefficients {a
k
}
k=0∞ and non-zero radius of convergence r ≤ ∞. Let ξ
x
, 0 ≤ x < r be a random variable whose values α
k
, k = 0, 1, …, are independent of x and taken with probabilities a
k
x
k
/φ(x), k = 0, 1, ….
The positive linear operator (A
φ
f)(x):= E[f(ξ
x
)] is studied. It is proved that if E(ξ
x
) = x, E(ξ
x
2) = qx
2 + bx + c, q, b, c ∈ R, q > 0, then A
φ
reduces to the Szász-Mirakyan operator in the case q = 1, to the limit q-Bernstein operator in the case 0 < q < 1, and to a modification of the Lupaş operator in the case q > 1. 相似文献
3.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
4.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
We find also other upper bounds onh
0 (X, F).
(a) | M≊L ⊗r; |
(b) | M is the subsheaf of ω X⊗(L*)⊗t, t:=g−d+r−1, spanned by H0(X, ωX⊗(L*)⊗t); |
(c) | there is a rank 1 torsion free sheaf F on X with 1≦h 0(X, F)≦k−2 such that M≊L⊗s⊗F. Moreover, if we fix an integer m with 2≦m≦k−2 and assume r#(s+1)k−(ns+n+1) per every 2≦n≦m, we have h0 (X, F)≦k−m−1. |
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献Si ricavano anche altre maggiorazioni suh 0,(X, F).
(a) M≊L ⊗r; (b) M è il sottofascio di ω X⊗(L*)⊗t, t:=g−d+r−1 generato da H0 (X, ωX⊗(L*)⊗t); (c) esiste un fascio senza torsione di rango un F su X con 1≦h 0 (X, F) <=k−2 tale che M ≊L ⊗8 ⊗ F. Inoltre, se si fissa un intero m con 2≦m≦k−2 e si suppone r#(s+1) k−(ns+n+1) per ogni 2≦n≦m, si ottiene h 0 (X, F)≦k−m−1.
5.
A. K. Varma 《Israel Journal of Mathematics》1972,12(4):337-341
Letx
kn=2θk/n,k=0,1 …n−1 (n odd positive integer). LetR
n(x) be the unique trigonometric polynomial of order 2n satisfying the interpolatory conditions:R
n(xkn)=f(xkn),R
n
(j)(xkn)=0,j=1,2,4,k=0,1…,n−1. We setw
2(t,f) as the second modulus of continuity off(x). Then we prove that |R
n(x)-f(x)|=0(nw2(1/nf)). We also examine the question of lower estimate of ‖R
n-f‖. This generalizes an earlier work of the author. 相似文献
6.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
7.
E. G. Goluzina 《Journal of Mathematical Sciences》2006,137(3):4774-4779
The paper studies the region of values Dm,1(T) of the system {ƒ(z1), ƒ(z2), …, ƒ(zm), ƒ(r)}, m e 1, where zj (j = 1, 2, …,m) are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0 (j = 1, 2, …,m), and r, 0 < r < 1, is fixed, in the class T of functions ƒ(z) = z+a2z2+ ⋯ regular in the disk U and satisfying in the latter the condition Im ƒ(z) Imz > 0 for Im z ≠ 0. An algebraic characterization of the set Dm,1(T) in terms of nonnegative-definite Hermitian forms is given, and all the boundary functions are described. As an implication,
the region of values of ƒ(zm) in the subclass of functions from the class T with prescribed values ƒ(zk) (k = 1, 2, …,m − 1) and ƒ(r) is determined. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 24–33. Original article submitted June 13, 2005. 相似文献
8.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
9.
Michele Capon 《Israel Journal of Mathematics》1982,42(1-2):87-98
In this article we show thatL
p(L
r) is primary forp andr in ]1,+∞[. If (h
k)
k≧1 denote the Haar basis, we begin with a study of the sequence (h
k ⊗h
i) and, in particular, the space generated by a subsequence of this sequence. In the first part we study the base ofL
p(L
r) and in the second part we show that this space is primary. 相似文献
10.
K. N. Venkataraman K. Suresh Chandra 《Annals of the Institute of Statistical Mathematics》1984,36(1):101-118
Summary LetX(t) be a linear autoregressively generated explosive time series, with autoregressive coefficientsb
1,…,bq, and a constant termb
0, and an error term
; a0=1. Where ε(t),t≧1 are independent, Eε(t)=0, and Eε
2(t)=σ2 is positive and finite. In this paper two categories of
-consisent and asymptotically singularly normal estimators are proposed for (b
1,…,bq, b0) thus settling an open problem since the publication of the paper (Venkataraman [5]). Based on these estimators several additional
limit theorems based on estimated error residuals are proved. The parameter-free limit theorems of Spectral and Quenouille
types of this paper serve as asymptotic goodness of fit tests for the model generatingX(t). 相似文献
11.
Bin Han 《Advances in Computational Mathematics》2006,24(1-4):375-403
In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space Wpk(ℝs) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented.
Rate of convergence of vector cascade algorithms in a Sobolev space Wpk(ℝs) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the Lp (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function
vector. As a consequence, we show that if a compactly supported function vector φ∈Lp(ℝs) (φ∈C(ℝs) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz
space Lip(ν,Lp(ℝs)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167)
in the univariate setting to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C20, 41A25, 39B12.
Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant
G121210654. 相似文献
12.
An upper bound estimate in the law of the iterated logarithm for Σf(n
k ω) where nk+1∫nk≧ 1 + ck
-α (α≧0) is investigated. In the case α<1/2, an upper bound had been given by Takahashi [15], and the sharpness of the bound
was proved in our previous paper [8]. In this paper it is proved that the upper bound is still valid in case α≧1/2 if some
additional condition on {n
k} is assumed. As an application, the law of the iterated logarithm is proved when {n
k} is the arrangement in increasing order of the set B(τ)={1
i
1...qτ
i
τ|i1,...,iτ∈N
0}, where τ≧ 2, N
0=NU{0}, and q
1,...,q
τ are integers greater than 1 and relatively prime to each others.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
V. S. Atabekyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(2):112-122
In the present paper for arbitrary automorphism φ of the free Bunside group B(m, n) and for any odd number n ≥ 1003 a sufficient condition for existence of non-φ-admissible normal subgroup of B(m, n) was found. In particular, if automorphism φ is normal, then for any basis {a
1, a
2, …, a
m
} of the group B(m, n) there is an integer k such that for each i the elements a
i
and φ(a
i)
k
are conjugates. 相似文献
14.
W. G. Bridges 《Israel Journal of Mathematics》1972,12(4):369-372
Bounds on the number of row sums in ann×n, non-singular (0,1)-matrixA sarisfyingA
tA=diag (k
1-λ1,…,k
n-λn),k
j>λj>0,λ1=…=λe,λe+1=…=λn are obtained which extend previous results for such matrices. 相似文献
15.
LetG=H
p
(H
k
n
) be the (2n+1)-dimensional Heisenberg group over local fieldK. In this paper we prove some theorems about convolution operators onH
p
(G) and vector-valued Hardy spaces. As an example, the distribution
for some φ∈S(G), ξ φ=0 is a ramified 0-type kernel. These results can be applied to characterizeH
p
(G) spaces by square functions. 相似文献
16.
Noga Alon 《Israel Journal of Mathematics》1986,53(1):97-120
All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphsG, H, letN(G, H) denote the number of subgraphs ofG isomorphic toH. Define also, forl≧0,N(l, H)=maxN(G, H), where the maximum is taken over all graphsG withl edges. We determineN(l, H) precisely for alll≧0 whenH is a disjoint union of two stars, and also whenH is a disjoint union ofr≧3 stars, each of sizes ors+1, wheres≧r. We also determineN(l, H) for sufficiently largel whenH is a disjoint union ofr stars, of sizess
1≧s
2≧…≧s
r>r, provided (s
1−s
r)2<s
1+s
r−2r. We further show that ifH is a graph withk edges, then the ratioN(l, H)/l
k tends to a finite limit asl→∞. This limit is non-zero iffH is a disjoint union of stars. 相似文献
17.
We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P
1, …, P
k
∈ Z[m] in one unknown m with P
1(0) = … = P
k
(0) = 0, and given any ε > 0, we show that there are infinitely many integers x and m, with
1 \leqslant m \leqslant xe1 \leqslant m \leqslant x^\varepsilon, such that x + P
1(m), …, x + P
k
(m) are simultaneously prime. The arguments are based on those in [18], which treated the linear case P
j
= (j − 1)m and ε = 1; the main new features are a localization of the shift parameters (and the attendant Gowers norm objects) to both coarse
and fine scales, the use of PET induction to linearize the polynomial averaging, and some elementary estimates for the number
of points over finite fields in certain algebraic varieties. 相似文献
18.
LetR be a ring and J its radical. DefineJ
1=∩Jn, J2=∩J
1
n
,…,… Jk=∩J
k−1
n
.... It is shown that in a ringR satisfying a polynomial identity and the ascending chain condition on ideals,J
k
=0 for some appropriatek.
The work of the first author was supported by an NSF grant at the University of Chicago. The work of the second author was
supported by an NSF grant at the University of California, San Diego. 相似文献
19.
A refinable function φ(x):ℝn→ℝ or, more generally, a refinable function vector Φ(x)=[φ1(x),...,φr(x)]T is an L1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding
integer matrix. A refinable function vector is called orthogonal if {φj(x−α):α∈ℤn, 1≤j≤r form an orthogonal set of functions in L2(ℝn). Compactly supported orthogonal refinable functions and function vectors can be used to construct orthonormal wavelet and
multiwavelet bases of L2(ℝn). In this paper we give a comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported
refinable functions and refinable function vectors. 相似文献
20.
A. Hajnal 《Combinatorica》1985,5(2):137-139
We prove (in ZFC) that for every infinite cardinal ϰ there are two graphsG
0,G
1 with χ(G
0)=χ(G
1)=ϰ+ and χ(G
0×G
1)=ϰ. We also prove a result from the other direction. If χ(G
0)≧≧ℵ0 and χ(G
1)=k<ω, then χ(G
0×G
1)=k. 相似文献