共查询到20条相似文献,搜索用时 46 毫秒
1.
Nikolay Moshchevitin 《Czechoslovak Mathematical Journal》2012,62(1):127-137
Let Θ = (θ
1,θ
2,θ
3) ∈ ℝ3. Suppose that 1, θ
1, θ
2, θ
3 are linearly independent over ℤ. For Diophantine exponents
$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered} 相似文献
2.
A. I. Aptekarev J. S. Dehesa A. Martínez-Finkelshtein R. Yáñez 《Constructive Approximation》2009,30(1):93-119
Given a nontrivial Borel measure on ℝ, let p
n
be the corresponding orthonormal polynomial of degree n whose zeros are λ
j
(n), j=1,…,n. Then for each j=1,…,n,
3.
Abdelmajid Siai 《Potential Analysis》2006,24(1):15-45
Let Ω be an open bounded set in ℝN, N≥3, with connected Lipschitz boundary ∂Ω and let a(x,ξ) be an operator of Leray–Lions type (a(⋅,∇u) is of the same type as the operator |∇u|p−2∇u, 1<p<N). If τ is the trace operator on ∂Ω, [φ] the jump across ∂Ω of a function φ defined on both sides of ∂Ω, the normal derivative
∂/∂νa related to the operator a is defined in some sense as 〈a(⋅,∇u),ν〉, the inner product in ℝN, of the trace of a(⋅,∇u) on ∂Ω with the outward normal vector field ν on ∂Ω. If β and γ are two nondecreasing continuous real functions everywhere
defined in ℝ, with β(0)=γ(0)=0, f∈L1(ℝN), g∈L1(∂Ω), we prove the existence and the uniqueness of an entropy solution u for the following problem,
4.
O. P. Filatov 《Mathematical Notes》1999,66(3):348-354
For a continuous almost periodic function
, we show that the function
5.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
6.
Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups
Wen-Bin Zhang 《The Ramanujan Journal》2008,15(1):47-75
We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic
semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let
be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in
with “degree” ∂(a)=m satisfies
7.
ON A CLASS OF BESICOVITCHFUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION
This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given byB(t) := ∞∑k=1 λs-2k sin(λkt),where 1 < s < 2, λk > 0 tends to infinity as k →∞ and λk satisfies λk 1/λk ≥λ> 1. The results show thatlimk→∞ log λk 1/log λk = 1is a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions.For the fractional Riemann-Liouville differential operator Du and the fractional integral operator D-v,the results show that if λ is sufficiently large, then a necessary and sufficient condition for box dimension of Graph(D-v(B)),0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)),0 < u < 2 - s, to be s uis also lim k→∞logλk 1/log λk = 1. 相似文献
8.
The asymptotic expressions of the covariance matrices for both the least square estimates
L
α
T
and Markov (best linear) estimates
are obtained, based on a sample in a finite interval (0, T) of the regression co-efficients α = (α
1, …, α
m
0)′ of a parameter-continuous process with a stationary residual. We assume that the regression variables φ
ν(t), t ⩾ 0, ν = 1, …, m
0, are continuous in t, and satisfy conditions (3.1)–(3.3). For the residual, we assume that it is a stationary process that possesses a bounded
continuous spectral density f(λ). Under these assumptions, it is proven that
9.
Elton Pasku 《Semigroup Forum》2008,76(3):427-468
If a monoid S is given by some finite complete presentation ℘, we construct inductively a chain of CW-complexes
10.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
11.
Walter Allegretto Yanping Lin Zhiyong Zhang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,22(5):848-868
We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations,
12.
Let G be a multigraph. The star number s(G) of G is the minimum number of stars needed to decompose the edges of G. The star arboricity sa(G) of G is the minimum number of star forests needed to decompose the edges of G. As usual λK
n
denote the λ-fold complete graph on n vertices (i.e., the multigraph on n vertices such that there are λ edges between every pair of vertices). In this paper, we prove that for n ⩾ 2
13.
This paper deals with the existence of weak solutions in W
01(Ω) to a class of elliptic problems of the form
14.
15.
Wen-Bin Zhang 《Mathematische Zeitschrift》2009,261(1):233-234
Let be the generalized integers n
j
associated with a set of generalized primes p
i
in Beurling’s sense. On the basis of the general mean-value theorems, established in our previous work, for multiplicative
function f(n
j
) defined on , we prove extensions, in functional form and in mean-value form, of the Elliott–Daboussi theorem to high order mean-values.
For the main result, let α,ρ, and τ be positive real constants such that α > 1,ρ≥1 and . Then a multiplicative function f satisfies the following conditions, with some constant , (1) All four series
16.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
17.
Let β
0=0.308443… denote the Littlewood-Salem-Izumi number, i.e., the unique solution of the equation
18.
Witold Bednorz 《Journal of Theoretical Probability》2007,20(4):917-934
For a Young function φ and a Borel probability measure m on a compact metric space (T,d) the minorizing metric is defined by
19.
O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1733-1748
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
20.
A. E. Shiganov 《Moscow University Computational Mathematics and Cybernetics》2009,33(3):158-166
Realization of Boolean functions in the class of oriented contact circuits (OCCs) with certain restrictions on the weight,
number, and types of adjacent contacts is studied. Oriented contact circuits are considered in which, from an arbitrary vertex,
at most λ arcs issue and at most ν different Boolean variables are used in the marks of the issuing arcs. The weight of a
vertex of an OCC is defined as being equal to λ if one arc enters a vertex and equal to λ(1 + ω), where ω > 0, otherwise.
Then, as usual, the weight of an OCC is defined as the sum of the weights of its vertices; the weight of a Boolean function,
as the minimum weight of OCCs realizing it; and Shannon function W
λ, ν, ω(n), as the maximum weight of the Boolean function of n variables. For this Shannon function, the so-called high-accuracy bound
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