共查询到20条相似文献,搜索用时 834 毫秒
1.
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
2.
A. V. Ustinov 《Journal of Mathematical Sciences》2006,137(2):4722-4738
Statistical properties of continued fractions for numbers a/b, where a and b lie in the sector a, b ≥ 1, a2 + b2 ≤ R2, are studied. The main result is an asymptotic formula with two meaning terms for the quantity
where sx(a/b) = |{j ε {1, …, s}: [0; tj, …, ts] ≤ x}| is the Gaussian statistic for the fraction a/b = [t0; t1, …, ts]. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 186–211. 相似文献
3.
Ilya V. Boikov 《分析论及其应用》1996,12(3):59-67
Local splines are presented for the approximation of functions of one and many variables, which are analytic in the domains
, where Ui(zi) is a unit disk in the complex plane Ci,i=1,2,…,l, l=1,2, …. Results are given for functions whose r-order derivatives belong to the Hardy's class Hp,1≤p≤∞. It is shown that the approximation converge to the function at the rate
for functions of one variable and An−(r−1/p)/(l−1) for functions of l variables, where n is the number of points of local splines and A and C are positive constants.
This work was supported by Russian Foundation of Fundumental Inverstigations 相似文献
4.
Nicholas A. Loehr Gregory S. Warrington Herbert S. Wilf 《Israel Journal of Mathematics》2004,143(1):141-156
We study the polynomial
, where ω is a primitivepth root of unity. This polynomial arises in CR geometry [1]. We show that it is the determinant of thep×p circulant matrix whose first row is (1, −x,0,…,0,−y,0,…,0), the −y being in positionq+1. Therefore, the coefficients of this polynomial Φ are integers that count certain classes of permutations. We show that
all of the permutations that contribute to a fixed monomialx
rys in Φ have the same sign, and we determine that sign. We prove that a monomialx
rys appears in Φ if and only ifp dividesr+sq. Finally, we show that the size of the largest coefficient of the monomials in Φ grows exponentially withp, by proving that the permanent of the circulant whose first row is (1, 1, 0, …, 0, 1, 0, …, 0) is the sum of the absolute
values of the monomials in the polynomial Φ.
Supported by NSF Postdoctoral research grants. 相似文献
5.
E. G. Goluzina 《Journal of Mathematical Sciences》2008,150(3):2005-2012
The paper studies the regions of values of the systems {f(z1), f(r1), f(r2),…, f(rn)} and {f(r1), f(r2),…, f (rn)}, where n 2; z1 is an arbitrary fixed point of the disk U = {z: |z| < 1} with Im z1 ≠ 0; rj are fixed numbers, 0 < rj < 1, j = 1, 2,…, n; f ∈ T, and the class T consists of the functions f(z), f(0) = 0, f′(0) = 1, regular in the disk U and
satisfying the condition Im f(z) · Imz > 0 for Im z ≠ 0. As an implication, the region of values of f(z1) in the subclass of functions f ∈ T with prescribed values f(rj) (j = 1, 2,…, n) is determined. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 5–16. 相似文献
6.
Amitai Regev 《Israel Journal of Mathematics》1999,113(1):15-28
The numbers
% MathType!End!2!1!, λ ⊢n appear in the enumeration of various objects, as well as coefficients inS
nrepresentations associated with products of higher commutators. We study their asymptotics asn→∞ and show that if (λ1, λ2, …)≈(α
1,α
2, …)n, if (λ′1, λ′2, …)≈(β
1,β
2, …)n and ifγ=1− Σ
k⩽1(α
k⩽1+β
k⩽1), then
% MathType!End!2!1!.
Work partially supported by N.S.F. Grant No. DMS 94-01197. 相似文献
7.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
8.
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
9.
Sh. R. Shakirov 《Theoretical and Mathematical Physics》2010,163(3):804-812
We study the homogeneous non-Gaussian integral $
J_{n|r} (S) = \int {e^{ - S(x_1 , \ldots ,x_n )} } d^n x
$
J_{n|r} (S) = \int {e^{ - S(x_1 , \ldots ,x_n )} } d^n x
, where S(x1,…,xn) is a symmetric form of degree r in n variables. This integral is naturally invariant under SL(n) transformations and therefore
depends only on the invariants of the form. For example, in the case of quadratic forms, it is equal to the (−1/2)th power of the determinant of the form. For higher-degree forms, the integral can be calculated in some cases using the
so-called Ward identities, which are second-order linear differential equations. We describe the method for calculating the
integral and present detailed calculations in the case where n = 2 and r = 5. It is interesting that the answer is a hypergeometric function of the invariants of the form. 相似文献
10.
Let X, X1 , X2 , . . . be i.i.d. random variables, and set Sn = X1 +···+Xn , Mn = maxk≤n |Sk|, n ≥1. Let an = o( (n)(1/2)/logn). By using the strong approximation, we prove that, if EX = 0, VarX = σ2 0 and E|X| 2+ε ∞ for some ε 0, then for any r 1, lim ε1/(r-1)(1/2) [ε-2-(r-1)]∞∑n=1 nr-2 P{Mn ≤εσ (π2n/(8log n))(1/2) + an } = 4/π . We also show that the widest a n is o( n(1/2)/logn). 相似文献
11.
If w1,…,w
N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ1,…, λN on the unit circle and positive numbers Μ1,…,Μ
N such that
is the zero sequence of the function 1 —
. The points λ1,…, λN and numbers Μ1,…,ΜN are unique (except for reorderings). 相似文献
12.
We give an example of two distinct stationary processes {X
n} and {X′
n} on {0, 1} for whichP[X0=1|X−1=a−1,X−2=a−2, …]=P[X′0=1|X′−1=a−1,X′−2=a−2, …] for all {a
i},i=−1, −2, …, even though these probabilities are bounded away from 0 and 1, and are continuous in {a
i}.
Supported in part by NSF Grant DMS 89-01545.
Supported in part by the US Army Research Office. 相似文献
13.
A. V. Zheleznyak 《Vestnik St. Petersburg University: Mathematics》2009,42(4):269-274
In the middle of the 20th century Hardy obtained a condition which must be imposed on a formal power series f(x) with positive coefficients in order that the series f
−1(x) = $
\sum\limits_{n = 0}^\infty {b_n x^n }
$
\sum\limits_{n = 0}^\infty {b_n x^n }
b
n
x
n
be such that b
0 > 0 and b
n
≤ 0, n ≥ 1. In this paper we find conditions which must be imposed on a multidimensional series f(x
1, x
2, …, x
m
) with positive coefficients in order that the series f
−1(x
1, x
2, …, x
m
) = $
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
$
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
satisfies the property b
0, …, 0 > 0, $
bi_1 ,i_2 , \ldots ,i_m
$
bi_1 ,i_2 , \ldots ,i_m
≤ 0, i
12 + i
22 + … + i
m
2 > 0, which is similar to the one-dimensional case. 相似文献
14.
Markus Brodmann 《manuscripta mathematica》1992,76(1):181-192
Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x1, …, xd∈m with respect to M and let
. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ
R/I
d-1
whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H
m
i
(M), (i=0, …, d−1). 相似文献
15.
N. S. Romanovskii 《Algebra and Logic》1999,38(3):193-201
Denote byB a class of solvable groups having a finite normal series with torsion-free Abelian factors, and by % MathType!MTEF!2!1!+-%
feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb%
L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam% aaeaqbaaGcbaWefv3ySLgzgjxyRrxDYbqehuuDJXwAKbIrYf2A0vNC%
aGGbaiqb-fa8czaaraaaaa!475E!\[\bar \mathfrak{B}\] a class of groups every finitely generated subgroup of which is approximated
by {ie193-3}. We prove that if {ie193-4} is a free product with relations of groups A1,…,An in the class {ie193-5}, where n>m and all relations are taken from the Cartesian subgroups, then there exist distinct indices
i1,…,in-m such that gp(Ai1,…,Ain-m)=Ai1 *…* Ain-m. A similar fact is established for solvable products with relations.
Supported by RFFR grant No. 99-01-00567.
Translated fromAlgebra i Logika, Vol. 38, No. 3, pp. 354–367, May–June, 1999. 相似文献
16.
Liu Yongping 《分析论及其应用》1991,7(3):27-34
In this paper, we study the so-called entire (0,m1,m2,…mq)-interpolation on equidistant nodes for q=2r-1 case, obtain that it has unique solution B
rσ
2
,σ>0. if and only if E-O=−1, where E and O denote the number of even and odd integers in the {m1,…,mq} respectively, and give the explicit formulae of this kind of interpolation functions if they exist.
The Project Supported by National Natural Science Foundation of China 相似文献
17.
Let f∈C
[−1,1]
″
(r≥1) and Rn(f,α,β,x) be the generalized Pál interpolation polynomials satisfying the conditions Rn(f,α,β,xk)=f(xk),Rn
′(f,α,β,xk)=f′(xk)(k=1,2,…,n), where {xk} are the roots of n-th Jacobi polynomial Pn(α,β,x),α,β>−1 and {x
k
″
} are the roots of (1−x2)Pn″(α,β,x). In this paper, we prove that
holds uniformly on [0,1].
In Memory of Professor M. T. Cheng
Supported by the Science Foundation of CSBTB and the Natural Science Foundatioin of Zhejiang. 相似文献
18.
Camil Muscalu 《Journal of Geometric Analysis》1999,9(4):683-691
If N ∈ ℕ, 0 < p ≤ 1, and(Xk)
k=1
N
are r.i.p-spaces, it is shown that there is C(= C(p, N)) > 0, such that for every ƒ ∈ ∩
k=1
N
Xk, there exists
with
, for every 1 ≤ k ≤ N. Also, if ⊓ is a convex polygon in ℝ2, it is proved that the N-tuple (H(X1),…, H(Xn)) is K⊓-closed with respect to (X1,…, XN) in the sense of Pisier. Everything follows from Theorem 2.1, which is a general analytic partition of unity type result. 相似文献
19.
Ioannis Parissis 《Journal of Geometric Analysis》2010,20(3):771-785
Let ℳ denote the maximal function along the polynomial curve (γ
1
t,…,γ
d
t
d
):
$\mathcal{M}(f)(x)=\sup_{r>0}\frac{1}{2r}\int_{|t|\leq r}|f(x_1-\gamma_1t,\ldots,x_d-\gamma_dt^d)|\,dt.$\mathcal{M}(f)(x)=\sup_{r>0}\frac{1}{2r}\int_{|t|\leq r}|f(x_1-\gamma_1t,\ldots,x_d-\gamma_dt^d)|\,dt. 相似文献
20.
J. Bourgain 《Israel Journal of Mathematics》1988,61(1):39-72
It is shown that the set of squares {n
2|n=1, 2,…} or, more generally, sets {n
t|n=1, 2,…},t a positive integer, satisfies the pointwise ergodic theorem forL
2-functions. This gives an affirmative answer to a problem considered by A. Bellow [Be] and H. Furstenberg [Fu]. The previous
result extends to polynomial sets {p(n)|n=1, 2,…} and systems of commuting transformations. We also state density conditions for random sets of integers in order to
be “good sequences” forL
p-functions,p>1. 相似文献
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