共查询到20条相似文献，搜索用时 62 毫秒
1.
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
2.
G. I. Laptev 《Journal of Mathematical Sciences》2008,150(5):2384-2394
This paper deals with conditions for the existence of solutions of the equations
considered in the whole space ℝn, n ≥ 2. The functions A
i
(x, u, ξ), i = 1,…, n, A
0(x, u), and f(x) can arbitrarily grow as |x| → ∞. These functions satisfy generalized conditions of the monotone operator theory in the arguments u ∈ ℝ and ξ ∈ ℝn. We prove the existence theorem for a solution u ∈ W
loc
1,p
(ℝn) under the condition p > n.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 133–147, 2006. 相似文献
3.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
4.
Katalin Marton 《Probability Theory and Related Fields》1998,110(3):427-439
Summary. Let X={X
i
}
i
=−∞
∞ be a stationary random process with a countable alphabet and distribution q. Let q
∞(·|x
−
k
0) denote the conditional distribution of X
∞=(X
1,X
2,…,X
n
,…) given the k-length past:
Write d(1,x
1)=0 if 1=x
1, and d(1,x
1)=1 otherwise. We say that the process X admits a joining with finite distance u if for any two past sequences −
k
0=(−
k
+1,…,0) and x
−
k
0=(x
−
k
+1,…,x
0), there is a joining of q
∞(·|−
k
0) and q
∞(·|x
−
k
0), say dist(0
∞,X
0
∞|−
k
0,x
−
k
0), such that
The main result of this paper is the following inequality for processes that admit a joining with finite distance:
Received: 6 May 1996 / In revised form: 29 September 1997 相似文献
5.
For every m≥3, let n=R (L
3 (m)) be the least integer such that for every 2-coloring of the set S={1, 2, …, n}, there exists in S a monochromatic solution to the following system.?
? The main result of this paper is that?
? Moreover, it is shown that, up to a switching of the colors, there exists a unique 2-coloring of the set {1, 2, …, R(L
3 (m)) −1} that avoids a monochromatic solution to the above system.
Received: July 29, 1996 Revised: December 21, 1998 相似文献
6.
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
7.
In ℝ
m
×ℝ
n−m
, endowed with coordinates x=(x′,x″), we consider bounded solutions of the PDE
We prove a geometric inequality, from which a symmetry result follows.
相似文献
8.
In the paper, the equation
is considered in the scale of the weighted spaces H
β
s
(ℝ
n
) (q > 1, a
kα
∈ ℂ). We prove that if the expression
does not vanish on the set {ξ ∈ ℝ
n
∖ 0, |z| ≤ q
β−s+n
/2−2m}, then this equation has a unique solution u ∈ H
β
s+2m
(ℝ
n
) for every function f ∈ H
β
s
(ℝ
n
) provided that β, s ≠ ∈ ℝ, β − s ≠ n/2 + p, and β − s − 2m ≠ − n/2 − p (p = 0, 1, ...).
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 37–55, 2007. 相似文献
9.
For the singular Cauchy problem, the authors find some sufficient conditions for the existence of continuously differentiable
solutions x: (0, ρ] → ℝ (ρ > 0 is sufficiently small) of the form
where m ≥ 2 and c
1,…, c
m
are definite constants.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
10.
John S. Caughman 《Graphs and Combinatorics》1998,14(4):321-343
Let Y=(X,{R
i
}0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A
0, A
1,…, A
D
of the associate matrices, and Q-polynomial with respect to the ordering E
0, E
1,…,E
D
of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv).
(i)
(ii) D is even, and
(iii) θ*
0>θ0, and
(iv) θ*
0>θ0, D is odd, and
Received: February 13, 1996 / Revised: October 16, 1996 相似文献
11.
A central limit theorem for convex sets 总被引：4，自引：1，他引：3
B. Klartag 《Inventiones Mathematicae》2007,168(1):91-131
We show that there exists a sequence for which the following holds: Let K⊂ℝn be a compact, convex set with a non-empty interior. Let X be a random vector that is distributed uniformly in K. Then there exist a unit vector θ in ℝn, t0∈ℝ and σ>0 such that
where the supremum runs over all measurable sets A⊂ℝ, and where 〈·,·〉 denotes the usual scalar product in ℝn. Furthermore, under the additional assumptions that the expectation of X is zero and that the covariance matrix of X is the
identity matrix, we may assert that most unit vectors θ satisfy (*), with t0=0 and σ=1. Corresponding principles also hold for multi-dimensional marginal distributions of convex sets. 相似文献
12.
This paper generalizes the mixed extension principle in L
2(ℝ
d
) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces H
s
(ℝ
d
) and H
−s
(ℝ
d
). In terms of masks for φ,ψ
1,…,ψ
L
∈H
s
(ℝ
d
) and
, simple sufficient conditions are given to ensure that (X
s
(φ;ψ
1,…,ψ
L
),
forms a pair of dual wavelet frames in (H
s
(ℝ
d
),H
−s
(ℝ
d
)), where
For s>0, the key of this general mixed extension principle is the regularity of φ, ψ
1,…,ψ
L
, and the vanishing moments of
, while allowing
,
to be tempered distributions not in L
2(ℝ
d
) and ψ
1,…,ψ
L
to have no vanishing moments. So, the systems X
s
(φ;ψ
1,…,ψ
L
) and
may not be able to be normalized into a frame of L
2(ℝ
d
). As an example, we show that {2
j(1/2−s)
B
m
(2
j
⋅−k):j∈ℕ0,k∈ℤ} is a wavelet frame in H
s
(ℝ) for any 0<s<m−1/2, where B
m
is the B-spline of order m. This simple construction is also applied to multivariate box splines to obtain wavelet frames with short supports, noting
that it is hard to construct nonseparable multivariate wavelet frames with small supports. Applying this general mixed extension
principle, we obtain and characterize dual Riesz bases
in Sobolev spaces (H
s
(ℝ
d
),H
−s
(ℝ
d
)). For example, all interpolatory wavelet systems in (Donoho, Interpolating wavelet transform. Preprint, 1997) generated by an interpolatory refinable function φ∈H
s
(ℝ) with s>1/2 are Riesz bases of the Sobolev space H
s
(ℝ). This general mixed extension principle also naturally leads to a characterization of the Sobolev norm of a function in
terms of weighted norm of its wavelet coefficient sequence (decomposition sequence) without requiring that dual wavelet frames
should be in L
2(ℝ
d
), which is quite different from other approaches in the literature.
相似文献
13.
In this paper we consider the problem of bounding the Betti numbers, b
i
(S), of a semi-algebraic set S⊂ℝ
k
defined by polynomial inequalities P
1≥0,…,P
s
≥0, where P
i
∈ℝ[X
1,…,X
k
], s<k, and deg (P
i
)≤2, for 1≤i≤s. We prove that for 0≤i≤k−1,
This improves the bound of k
O(s) proved by Barvinok (in Math. Z. 225:231–244, 1997). This improvement is made possible by a new approach, whereby we first bound the Betti numbers of non-singular complete
intersections of complex projective varieties defined by generic quadratic forms, and use this bound to obtain bounds in the
real semi-algebraic case.
The first author was supported in part by an NSF grant CCF-0634907. The second author was partially supported by NSF grant
CCF-0634907 and the European RTNetwork Real Algebraic and Analytic Geometry, Contract No. HPRN-CT-2001-00271. 相似文献
14.
This paper deals with the existence of weak solutions in W
01(Ω) to a class of elliptic problems of the form
in a bounded domain Ω of ℝ
N
. Here a satisfies
for all ξ∈ℝ
N
, a.e. x∈Ω,
, h
1∈L
loc
1(Ω), h
1(x)≧1 for a.e. x in Ω; λ
1 is the first eigenvalue for −Δ
p
on Ω with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.
相似文献
15.
In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation
has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C
(1) ([0, ∞), (0, ∞)), p ∈ C
(2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.
相似文献
16.
Do Yong Kwon 《Acta Mathematica Hungarica》2011,131(3):285-294
Let f(x)=a
d
x
d
+a
d−1
x
d−1+⋅⋅⋅+a
0∈ℝ[x] be a reciprocal polynomial of degree d. We prove that if the coefficient vector (a
d
,a
d−1,…,a
0) or (a
d−1,a
d−2,…,a
1) is close enough, in the l
1-distance, to the constant vector (b,b,…,b)∈ℝ
d+1 or ℝ
d−1, then all of its zeros have moduli 1. 相似文献
17.
O. V. Matveev 《Mathematical Notes》1997,62(3):339-349
Supposem, n ∈ℕ,m≡n (mod 2),K(x)=|x|
m
form odd,K(x)=|x|
m
In |x| form even (x∈ℝ
n
),P is the set of real polynomials inn variables of total degree ≤m/2, andx
1,...,x
N
∈ℝ
n
. We construct a function of the form
coinciding with a given functionf(x) at the pointsx
1,...,x
N
. Error estimates for the approximation of functionsf∈W
p
k
(Ω) and theirlth-order derivatives in the normsL
q
(Ωε) are obtained for this interpolation method, where Ω is a bounded domain in ℝ
n
, ε>0, and Ωε={x∈Ω:dist(x, ∂∈)>ε}.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 404–417, September, 1997.
Translated by N. K. Kulman 相似文献
18.
Song Li 《中国科学A辑(英文版)》2003,46(3):364-375
The purpose of this paper is to investigate the refinement equations of the form
where the vector of functions ϕ=(ϕ
1..., ϕ
r
)
T
is in (L
p
(ℝ
s
))
r
, 1⩽p⩽∞, a(α), α∈ℤ
s
is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vector of compactly supported functions φ
0∈(L
p
(ℝ
s
))
r
and use the iteration schemes f
n
:=Q
a
n
φ
0, n=1,2,..., where Q
n
is the linear operator defined on (L
p
(ℝ
s
))
r
given by
This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of some linear operators
determined by the sequence a and the set B restricted to a certain invariant subspace, where the set B is a complete set of representatives of the distinct cosets of the quotient group ℤs/Mℤs containing 0. 相似文献
19.
V. A. Kondratiev 《Journal of Mathematical Sciences》2006,135(1):2666-2674
The equations under consideration have the following structure:
where 0 < x
n < ∞, (x
1, …, x
n−1) ∈ Ω, Ω is a bounded Lipschitz domain,
is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations
as x
n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas
were obtained in the case of a
ij, ai depending only on (x
1, …, x
n−1).
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 98–111, 2005. 相似文献
20.
Olivier Teulié 《Monatshefte für Mathematik》2002,116(3):313-324
In this paper, we prove that if β1,…, β n are p-adic numbers belonging to an algebraic number field K of degree n + 1 over Q such that 1, β1,…,β n are linearly independent over Z, there exist infinitely many sets of integers (q 0,…, q n ), with q 0 ≠ 0 and
with H = H(q 0,…, q n ). Therefore, these numbers satisfy the p-adic Littlewood conjecture. To obtain this result, we are using, as in the real case by Peck [2], the structure of a group of units of K. The essential argument to obtain the exponent 1/(n-1) (the same as in the real case) is the use of the p-adic logarithm. We also prove that with the same hypothesis, the inequalities
have no integer solution (q 0,…, q n ) with q 0 ≠ 0, if ɛ > 0 is small enough. 相似文献