共查询到20条相似文献，搜索用时 31 毫秒
1.
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur’s for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli–Vershik transformation is uniquely ergodic. Related questions are explored. 相似文献
2.
A simplicial algorithm is proposed for computing an integer point of a convex set
CRn
satisfying
with
The algorithm subdivides R
n into integer simplices and assigns an integer labelto each integer point of R
n. Starting at an arbitraryinteger point, the algorithm follows a finite simplicial path that leads either to an integer point of C or to the conclusion that C has no integer point. 相似文献
3.
We present a norm estimate for the partial transpose map Θ on the tensor product
with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on Mm,n in terms of the spectral norm of
:
We show further that in the special case of
as well as AX + XB and AX + XBT those estimates are much improved and that
for certain Schatten p-norms.
Dedicated to the memory of late Professor Helmut H. Schaefer 相似文献
4.
Let f( x, y) be a periodic function defined on the region D
with period 2π for each variable. If f( x, y) ∈ C
p ( D), i.e., f( x, y) has continuous partial derivatives of order p on D, then we denote by ω
α,β( ρ) the modulus of continuity of the function and write For p = 0, we write simply C( D) and ω( ρ) instead of C
0( D) and ω
0( ρ).
Let T( x,y) be a trigonometrical polynomial written in the complex form We consider R = max( m
2 + n
2) 1/2 as the degree of T( x, y), and write T
R( x, y) for the trigonometrical polynomial of degree ⩾ R.
Our main purpose is to find the trigonometrical polynomial T
R( x, y) for a given f( x, y) of a certain class of functions such that attains the same order of accuracy as the best approximation of f( x, y).
Let the Fourier series of f( x, y) ∈ C( D) be and let Our results are as follows
Theorem 1 Let f( x, y) ∈ C
p( D ( p = 0, 1) and
Then
holds uniformly on D.
If we consider the circular mean of the Riesz sum S
R
δ
( x, y) ≡ S
R
δ
( x, y; f): then we have the following
Theorem 2 If f( x, y) ∈ C
p ( D) and ω
p( ρ) = O( ρ
α (0 < α ⩾ 1; p = 0, 1), then
holds uniformly on D, where λ
0
is a positive root of the Bessel function J
0( x)
It should be noted that either or implies that f( x, y) ≡ const.
Now we consider the following trigonometrical polynomial Then we have
Theorem 3 If f( x, y) ∈ C
p( D), then uniformly on D,
Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundarm, and Theorem 3 is a generalization of a theorem
of Zygmund, which can be extended to the multiple case as follows
Theorem 3′ Let f( x
1, ..., x
n) ≡ f( P) ∈ C
p
and let
where
and
being the Fourier coefficients of f(P). Then
holds uniformly.
__________
Translated from Acta Scientiarum Naturalium Universitatis Pekinensis, 1956, (4): 411–428 by PENG Lizhong. 相似文献
5.
Let the coordinate x=( x
0, x
1, x
2, x
3) of the Minkowski space M
4 be arranged into a matrix Then the Minkowski metric can be written as . Imbed the space of 2 × 2 Hermitian matrices into the complex Grassmann manifold F(2,2), the space of complex 4-planes passing through the origin of C
2×4. The closure
of M
4 in F(2,2) is the compactification of M
4. It is known that the conformal group acts on
. It has already been proved that on F(2,2) there is an Su(2)-connection where Z is a 2 × 2 complex matrix and Z
†the complex conjugate and transposed matrix of Z. Restrict this connection to
which is an Su(2)-connection on
. It is proved that its curvature form satisfies the Yang-Mills equation .
Project partially supported by the National Natural Science Foundation of China (Grant No. 19131010) and Fundamental Research
Bureau of CAS. 相似文献
6.
Let h(d) be the class number of properly equivalent primitive binary quadratic forms ax 2+bxy+cy 2 with discriminant d=b 2-4ac. The behavior of h(5p 2), where p runs over primes, is studied. It is easy to show that there are few discriminants of the form 5p 2 with large class numbers. In fact, one has the estimate |
x^{1 - \delta } \} \ll x^{2\delta } ,$$
" align="middle" vspace="20%" border="0">
|
where is an arbitrary constant number in (0;1/2). Assume that (x) is a positive function monotonically increasing for x and (x). If , then (assuming the validity of the extended Riemann hypothesis for certain Dedekind zeta-functions) it is proved that |
\alpha (x)} \right\} \asymp \frac{{\pi (x)}}{{\alpha (x)}}.$$
" align="middle" vspace="20%" border="0">
|
It is also proved that for an infinite set of p with
one has the inequality where log
k
p is the k-fold iterated logarithm ( k is an arbitrary integer, k3). Results on mean values of h(5p
2
) are also obtained. Similar facts are true for the residual indices of an integer a2 modulo p: where o(a,p) is the order of a modulo p. Bibliography: 13 titles. 相似文献
7.
Let C(S) denote the Banach space of continuous, real-valued maps f: S and let A denote a positive linear map of C(S) into itself. We give necessary conditions that the operator A have a strictly positive periodic point of minimal period m. Under mild compactness conditions on the operator A, we prove that these necessary conditions are also sufficient to guarantee existence of a strictly positive periodic point of minimal period m. We study a class of Perron-Frobenius operators defined by and we show how to verify the necessary compactness conditions to apply our theorems concerning existence of positive periodic points.Partially supported by NSF DMS 97-06891 相似文献
8.
Let f(z) be a holomorphic Hecke eigencuspform of even weight k with respect to SL(2, Z) and let L(s, sym
2 f) = ∑
n=1
∞
c nn −s, Re s > 1, be the symmetric square L-function associated with f.
Represent the Riesz mean (ρ ≥ 0) as the sum of the “residue function” Γ(ρ+1) −1 Ł(0, sym 2f)x ρ and the “error term” .
Using the Voronoi formula for Δ ρ(x; sym
2f), obtained earlier (see Zap. Nauchn. Semin. POMI. 314, 247–256 (2004)), the integral is estimated. In this way, an asymptotics for 0 < ρ ≤ 1 and an upper bound for ρ = 0 are obtained. Also the existence of
a limiting distribution for the function , and, as a corollary, for the function , is established. Bibliography: 12 titles.
Dedicated to the 100th anniversary of G. M. Goluzin’s birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 274–286. 相似文献
9.
Let us consider the linear boundary value problem
where
and
is defined by
Classical Lyapunov inequality states that
for any function
where
The constant 4/ L is optimal. Let us note that Lyapunov inequality is given in terms of
the usual norm in the space L1(0, L). In this paper we review some recent results on Lp Lyapunovtype inequalities,
, for ordinary and partial differential equations on a bounded and regular domain in
In the last case, it is showed that the relation between the quantities p and N/2 plays a crucial role, pointing out a deep difference with respect to the ordinary case. In the proof, the best constants
are obtained by using a related variational problem and Lagrange multiplier theorem. Finally, the linear results are combined
with Schauder fixed point theorem in the study of resonant nonlinear problems.
The authors have been supported by the Ministry of Science and Technology of Spain MTM2005- 01331 and by Junta de Andalucia
(FQM116). 相似文献
10.
We present a semigroup approach to stochastic delay equations of the form
in the space of continuous functions C[-h,0]. We represent the solution as a C[-h,0]-valued process arising from a stochastic
weak *-integral in the bidual C[-h,0] ** and show how
this process can be interpreted as a mild solution of an associated stochastic abstract Cauchy problem. We obtain a necessary
and sufficient condition guaranteeing the existence of an invariant measure. 相似文献
11.
In the complex Grassmann manifold ℱ( m, n), the space of complex n-planes passes through the origin of C m+n; the local coordinate of the space can be arranged into an m × n matrix Z. It is proved that is a U( m)-connection of ℱ( m, n) and its curvature form satisfies the Yang-Mills equation. Moreover, is an ( Sum)-connection and its curvature form satisfies the Yang-Mills equation.
Project partially supported by the National Natural Science Foundation of China (Grant No. 19631010) and Fundamental Research
Bureau of CAS. 相似文献
12.
Let Ω be a bounded open subset of ℝ
n
, n > 2. In Ω we deduce the global differentiability result for the solutions u ∈ H
1 (Ω, ℝ
n
) of the Dirichlet problem with controlled growth and nonlinearity q = 2.
The result was obtained by first extending the interior differentiability result near the boundary and then proving the global
differentiability result making use of a covering procedure. 相似文献
13.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
14.
In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator
is discussed, where α, β are positive constants satisfying
for some ω ∈ R+ / Q, h( t) ∈ L∞ [0, 2π ] is 2π-periodic, x±=max {± x, 0 }.
Received: 23 September 2004 相似文献
15.
We study the problem of the existence of multiple periodic solutions of the Hamiltonian system where u is a linear mapping, G is a C
1-function, and e is a continuous function. 相似文献
16.
For a trigonometric series
defined on [−π, π)
m
, where V is a certain polyhedron in R
m
, we prove that
if the coefficients a
k
satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008. 相似文献
17.
We study the solvability of the integral equation , where f∈ L
1
loc(ℝ) is the unknown function and g, T
1, and T
2 are given functions satisfying the conditions .
Most attention is paid to the nontrivial solvability of the homogeneous equation .
Translated from Matematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
18.
Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f（0）=0,｜f（u）｜→∞as ｜u｜→∞,and f∈C^1（R）,and there exist the following limits Lo=lim sup/u→o f（u）/u^3 and L∞=lim sup/u→∞ f（u）/u^5 Suppose that the initial function u0∈L^I（R）∩H^2（R）.By using energy estimates,Fourier transform,Plancherel＇s identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv（xxt）＋δvx＋γHv（xx）＋βv（xxx）=αv（xx）,v（x,0）=vo（x）, the author justifies the following limits（with sharp rates of decay） lim t→∞[（1＋t）^（m＋1/2）∫｜uxm（x,t）｜^2dx]=1/2π（π/2α）^（1/2）m!!/（4α）^m[∫R uo（x）dx]^2, if∫R uo（x）dx≠0, where 0!!=1,1!!=1 and m!!=1·3…（2m-3）…（2m-1）.Moreover lim t→∞[（1＋t）^（m＋3/2）∫R｜uxm（x,t）｜^2dx]=1/2π（x/2α）^（1/2）（m＋1）!!/（4α）^（m＋1）[∫Rρo（x）dx]^2, if the initial function uo（x）=ρo′（x）,for some functionρo∈C^1（R）∩L^1（R）and∫Rρo（x）dx≠0. 相似文献
19.
This paper is devoted to the sharpening of the asymptotics that arises in the definition, which was introduced by A. Vershik, of the entropy of decreasing sequences of measurable partitions. An example of sets that do not admit a good approximation by cylinders is presented: |
\alpha _{n_k } 2^{n_k } .$$
" align="middle" vspace="20%" border="0">
|
Bibliography: 1 title. 相似文献
20.
Here, we solve non-convex, variational problems given in the form
where u ∈ ( W
1,∞(0, 1))
k
and is a non-convex, coercive polynomial. To solve (1) we analyse the convex hull of the integrand at the point a, so that we can find vectors and positive values λ 1, . . . , λ
N
satisfying the non-linear equation
Thus, we can calculate minimizers of (1) by following a proposal of Dacorogna in (Direct Methods in the Calculus of Variations.
Springer, Heidelberg, 1989). Indeed, we can solve (2) by using a semidefinite program based on multidimensional moments.
We dedicate this work to our colleague Jesús Bermejo. 相似文献
|
