共查询到20条相似文献,搜索用时 15 毫秒
1.
CHENG NAIDNG 《数学年刊B辑(英文版)》1980,1(2):214-222
In this paper,we have discussed constructive properties of a kind of uniformly
almost periodic functions, of which the sequence of its Fourier exponents has unique
limit point at infinity.
\[\begin{gathered}
f(x) \sim \sum\limits_{k = - \infty }^\infty {{A_k}} {e^{i{\Lambda _k}x}} \hfill \ {\Lambda _0} = \alpha ,0 < \alpha \leqslant {\Lambda _k} < {\Lambda _{k + 1}}(k = 0,1,2,...) \hfill \ \mathop {\lim }\limits_{k \to \infty } {\Lambda _k} = \infty ,{\Lambda _k} = - {\Lambda _k} \hfill \ |{\Lambda _k}| + |{\Lambda _{ - k}}| > 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (k \ne 0) \hfill \\
\end{gathered} \]
Analogons to the approximation theory of periodic functioiis, we get some theorems
similar to the Jackson theorem, Bernstein theorem and Zygmund theorem of periodio
functions. 相似文献
2.
Xiao Erjian 《数学年刊B辑(英文版)》1993,14(4):497-506
The author defines, using jets, cohomology $H^p(\Lambda _{f,k-})$ for hypersurfaces, which are invariant under contact transformations. For isolated hypersurface singularities, it is proved that
$H^0(\Lambda _{f,k-})=O_{U,0}/f^{k+1}O_{U,0},$
$H^p(\Lambda _{f,k-})=0,1\leq p \leq N-3 or p=N,$
$dimH^{N-2}(\Lambda _{f,k-})-dimH^{N-1}(\Lambda _{f,k-})=\[\left( {\begin{array}{*{20}{c}}
k \ N
\end{array}} \right)\dim {O_{U,0}}/(f,\frac{{\partial f}}{{\partial {x_1}}}, \cdots ,\frac{{\partial f}}{{\partial {x_N}}}){O_{U,0}}\] $
The algorithm of computation for H^{N-2} and H^{N-1} is given, and it is proved that $H^{N-1}=0$ when f is quasi-homogeneous. 相似文献
3.
设$\Lambda=\{\lambda_{n}\}_{n=1}^{\infty}$为正的实数数列, 且当$n\rightarrow\infty$时, 有$\lambda_{n}\searrow 0$.本文给出了当 $\lambda_{n}\leq Mn^{-\frac{1}{2}},\;n=1,2, \cdots ,$(其中$M>0$为一正常数)时M\"{u}ntz系统$\{x^{\lambda_n}\}$的有理函数在$ L_{[0,1]} ^{p}$空间的逼近速度,主要结论为$R_{n} (f, \Lambda )_{L^{p}}\leq C_M \omega (f, n^{-\frac{1}{2}})_{L^{p}},\;1 \leq p \leq \infty.$ 相似文献
4.
M. B. Zwyagina 《Journal of Mathematical Sciences》2002,112(4):4337-4347
Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let
be a Noetherian commutative ring, let
be a set of maximal ideals in
, and let
. Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles. 相似文献
5.
A. Gerlo 《Applied Categorical Structures》2008,16(4):479-493
In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical
Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge,
2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature.
In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability.
The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO). 相似文献
6.
Ya. G. Sinai 《Regular and Chaotic Dynamics》2007,12(5):490-501
We consider the recurrent equation
. which depends on the initial condition Λ1 = x. Under some conditions on f we show that there exists the value of x for which Λp tends to a constant as p tends to infinity.
相似文献
7.
Yifan Yang 《Transactions of the American Mathematical Society》2000,352(6):2581-2600
We investigate the asymptotic behavior of the partition function defined by , where denotes the von Mangoldt function. Improving a result of Richmond, we show that , where is a positive constant and denotes the times iterated logarithm. We also show that the error term can be improved to if and only if the Riemann Hypothesis holds.
8.
M. B. Zvyagina 《Journal of Mathematical Sciences》2004,120(4):1591-1602
Let
be an associative ring with identity, and let
be the category of left unitary
-modules. A complete characterization of continuous additive co- and contravariant functors
is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to
and, therefore, are equivalent to the category of compact right
-modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right
-modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles. 相似文献
9.
Dong Guangchang 《数学年刊B辑(英文版)》1986,7(3):277-302
In this paper, the author proves the existence and uniqueness of nonnegative solution for the first boundary value problem of uniform degenerated parabolic equation
$$\[\left\{ {\begin{array}{*{20}{c}}
{\frac{{\partial u}}{{\partial t}} = \sum {\frac{\partial }{{\partial {x_i}}}\left( {v(u){A_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}} \right) + \sum {{B_i}(x,t,u)} \frac{{\partial u}}{{\partial {x_i}}}} + C(x,t,u)u\begin{array}{*{20}{c}}
{}&{(x,t) \in [0,T]}
\end{array},}\{u{|_{t = 0}} = {u_0}(x),x \in \Omega ,}\{u{|_{x \in \partial \Omega }} = \psi (s,t),0 \le t \le T}
\end{array}} \right.\]$$
$$\[\left( {\frac{1}{\Lambda }{{\left| \alpha \right|}^2} \le \sum {{A_{ij}}{\alpha _i}{\alpha _j}} \le \Lambda {{\left| \alpha \right|}^2},\forall a \in {R^n},0 < \Lambda < \infty ,v(u) > 0\begin{array}{*{20}{c}}
{and}&{v(u) \to 0\begin{array}{*{20}{c}}
{as}&{u \to 0}
\end{array}}
\end{array}} \right)\]$$
under some very weak restrictions, i.e. $\[{A_{ij}}(x,t,r),{B_i}(x,t,r),C(x,t,r),\sum {\frac{{\partial {A_{ij}}}}{{\partial {x_j}}}} ,\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}} \in \overline \Omega } \times [0,T] \times R,\left| {{B_i}} \right| \le \Lambda ,\left| C \right| \le \Lambda ,\],\[\left| {\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}}} } \right| \le \Lambda ,\partial \Omega \in {C^2},v(r) \in C[0,\infty ).v(0) = 0,1 \le \frac{{rv(r)}}{{\int_0^r {v(s)ds} }} \le m,{u_0}(x) \in {C^2}(\overline \Omega ),\psi (s,t) \in {C^\beta }(\partial \Omega \times [0,T]),0 < \beta < 1\],\[{u_0}(s) = \psi (s,0).\]$ 相似文献
10.
There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code
which contain
and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space
over the vector space
for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on
. 相似文献
11.
Michael Struwe 《Mathematische Zeitschrift》2007,256(2):397-424
For concentrating solutions weakly in H
2(Ω) to the equation on a domain with Navier boundary conditions the concentration energy is shown to be strictly quantized in multiples of the number . 相似文献
12.
The Ramanujan Journal - Let $$\Lambda =\{ \lambda _j\}_{j=1}^\infty $$ be a set of positive integers, and let $$p_\Lambda (n)$$ be the number of ways of writing n as a sum of positive integers... 相似文献
13.
Salomón Alarcón Leonelo Iturriaga Alexander Quaas 《Calculus of Variations and Partial Differential Equations》2012,45(3-4):443-454
We study the problem $$ \left\{\begin{array}{ll} {-\varepsilon^{2}\mathcal{M}^+_{\lambda,\Lambda}(D^{2}u) = f (x, u)} \quad\; {\rm in} \; \Omega,\\ {u = 0} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {\rm on} \; \partial{\Omega}, \end{array} \right.$$ where Ω is a smooth bounded domain in ${\mathbb{R}^{N},N > 2,}$ and show it possesses nontrivial solutions for small values of ε provided f is a nonnegative continuous function which has a positive zero. The multiplicity result is based on degree theory together with a new Liouville type theorem for ${-{M}^+_{\lambda,\Lambda}(D^{2}u) = f(u)}$ in ${\mathbb{R}^{N}}$ for nonnegative nonlinearities with zeros. 相似文献
14.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
15.
The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of
4 which we call the the affine part
of Knarr's surface. We compute all affinities leaving
invariant. After embedding
4 into PG(4,
) we calculate the uniquely determined projective closure
Kn
of
. Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3,
). In this way we determine all planes carrying 1-dimensional algebraic varieties of
Kn
. We exhibit all automorphic collineations of
Kn
. 相似文献
16.
Enrico Laeng Carlo Morpurgo 《Proceedings of the American Mathematical Society》1999,127(12):3565-3572
We derive a sharp uncertainty inequality of the form
with . As a consequence of this inequality we derive an upper bound for the so-called Laue constant, that is, the infimum of the functional , taken over all with (). Precisely, we obtain that which improves a previous bound of T. Gneiting.
17.
Let Γ be an arithmetic lattice in an absolutely simple Lie group G with trivial centre. We prove that there exists an integer N ≥ 2, a subgroup Λ of finite index in Γ, and an action of Λ on
such that the pair (
) has property (T). If G has property (T), then so does
. If G is the adjoint group of Sp(n, 1), then
is a property (T) group satisfying the Baum–Connes conjecture. If Γ is an arithmetic lattice in SO(n, 1), then the associated von Neumann algebra
is a II1-factor in Popa’s class
. Elaborating on this result of Popa, we construct a countable family of pairwise nonstably isomorphic group II1-factors in the class
, all with trivial fundamental groups and with all L2-Betti numbers being zero.Mathematics Subject Classiffications (2000). 22E40, 22E47, 46L80, 37A20 相似文献
18.
The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose, we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators. Immediately after, applying the characterizations of TriebelLizorkin space with variable exponent, we obtain that b ∈■β if and only if the commutator of Calderón-Zygmund singular integral operator is bounded, respectively, from■ to■,from■ to■ with■. Moreover, we prove that the commutator of Riesz potential operator also has corresponding results. 相似文献
19.
Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .
20.
We consider microlocal defect distributions associated to a weakly convergent sequences \(u_n\) in \(H^{-s,p}_{\Lambda }\) and \(v_n\) in \(H^{s+m,q}_{\Lambda }\) through the space of pseudo-differential operators with the symbols in \((s^{m,N+1}_\Lambda )_0\). Symbols correspond to a weight function \(\Lambda \) determining a quasi-elliptic symbol. Results are applied to partial differential equations with symbols related to weights of the type \(\Lambda \). 相似文献