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1.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
2.
A. M. Semikhatov 《Theoretical and Mathematical Physics》2007,153(3):1597-1642
For positive integers p = k + 2, we construct a logarithmic extension of the
conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a butterfly
resolution of a three-boson realization of
. The currents W−(z) and W+(z) of a W-algebra acting in the kernel are determined by a highest-weight state of dimension 4p − 2 and charge 2p − 1 and
by a (θ=1)-twisted highest-weight state of the same dimension 4p − 2 and opposite charge −2p+1. We construct 2p W-algebra
representations, evaluate their characters, and show that together with the p−1 integrable representation characters, they
generate a modular group representation whose structure is described as a deformation of the (9p−3)-dimensional representation
R
p+1⊕ℂ2⊗R
p+1ʕR
p−1⊕ℂ2
R
p−1⊕ℂ3
R
p−1, where R
p−1 is the SL(2, ℤ)-representation on
integrable-representation characters and R
p+1 is a (p+1)-dimensional SL(2, ℤ)-representation known from the logarithmic (p, 1) model. The dimension 9p − 3 is conjecturally
the dimension of the space of torus amplitudes, and the ℂn with n = 2 and 3 suggest the Jordan cell sizes in indecomposable W-algebra modules. We show that under Hamiltonian reduction,
the W-algebra currents map into the currents of the triplet W-algebra of the logarithmic (p, 1) model.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 291–346, December, 2007. 相似文献
3.
This work is concerned with the proof of Lp -Lq decay estimates for solutions of the Cauchy problem for utt -λ2(t)b2(t)/Δu =0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. The authors‘ main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part. 相似文献
4.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
5.
The notion of p-adic multiresolution analysis (MRA) is introduced. We discuss a “natural” refinement equation whose solution (a refinable function) is the characteristic function
of the unit disc. This equation reflects the fact that the characteristic function of the unit disc is a sum of p characteristic functions of mutually disjoint discs of radius p
−1. This refinement equation generates a MRA. The case p=2 is studied in detail. Our MRA is a 2-adic analog of the real Haar MRA. But in contrast to the real setting, the refinable
function generating our Haar MRA is 1-periodic, which never holds for real refinable functions. This fact implies that there
exist infinity many different 2-adic orthonormal wavelet bases in ℒ2(ℚ2) generated by the same Haar MRA. All of these new bases are described. We also constructed infinity many different multidimensional 2-adic Haar orthonormal wavelet bases for ℒ2(ℚ2
n
) by means of the tensor product of one-dimensional MRAs. We also study connections between wavelet analysis and spectral
analysis of pseudo-differential operators. A criterion for multidimensional p-adic wavelets to be eigenfunctions for a pseudo-differential operator (in the Lizorkin space) is derived. We proved also
that these wavelets are eigenfunctions of the Taibleson multidimensional fractional operator. These facts create the necessary
prerequisites for intensive using our wavelet bases in applications. Our results related to the pseudo-differential operators
develop the investigations started in Albeverio et al. (J. Fourier Anal. Appl. 12(4):393–425, 2006).
相似文献
6.
Xiaodong Wang 《Journal of Geometric Analysis》2008,18(1):272-284
Let (M
n
,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ
0 of its universal covering satisfies λ
0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.
The author was partially supported by NSF Grant 0505645. 相似文献
7.
D. Dryanov 《Constructive Approximation》2009,30(1):137-153
Kolmogorov ε-entropy of a compact set in a metric space measures its metric massivity and thus replaces its dimension which is usually infinite. The notion quantifies the compactness property of sets in metric
spaces, and it is widely applied in pure and applied mathematics. The ε-entropy of a compact set is the most economic quantity of information that permits a recovery of elements of this set with
accuracy ε. In the present article we study the problem of asymptotic behavior of the ε-entropy for uniformly bounded classes of convex functions in L
p
-metric proposed by A.I. Shnirelman. The asymptotic of the Kolmogorov ε-entropy for the compact metric space of convex and uniformly bounded functions equipped with L
p
-metric is ε
−1/2, ε→0+.
相似文献
8.
In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem
of optimizing the cost functional
over some admissible class of loads f where u is the (unique) solution to the problem −Δ
p
u+|u|
p−2
u=0 in Ω with |∇
u|
p−2
u
ν
=f on ∂Ω.
Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and CONICET (Argentina) PIP 5478/1438.
J. Fernández Bonder is a member of CONICET. Leandro M. Del Pezzo is a fellow of CONICET. 相似文献
9.
Hyunsuk Moon 《The Ramanujan Journal》2008,16(1):73-81
Let F(z)=∑
n=1∞
A(n)q
n
denote the unique weight 6 normalized cuspidal eigenform on Γ0(4). We prove that A(p)≡0,2,−1(mod 11) when p≠11 is a prime. We then use this congruence to give an application to the number of representations of an integer by quadratic
form of level 4.
相似文献
10.
Yongjun Tian Tiansheng Wang Ke Chen Lie Chen Dongning Zheng Hanhong Qi Sven Linzen Frank Schmidl Paul Seidel 《中国科学A辑(英文版)》2000,43(1):82-87
A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO3 bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO2/YSZ multilayer on ϕ50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is
0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73
fT.cm−1Hz−1/2 in the white region and 596 fT.cm−1Hz−1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type
gradiometer in an unshielded environment. 相似文献
11.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
12.
M. R. Salehirad A. Badamchizadeh 《Central European Journal of Operations Research》2009,17(2):131-139
In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general
distribution. After the completion of the i-th phase, with probability θ
i
the (i + 1)-th phase starts, with probability p
i
the customer feedback to the tail of the queue and with probability 1 − θ
i
− p
i
= q
i
departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p
k
feedback to the tail of the queue and with probability 1 − p
k
departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue
size at departure epoch is obtained. 相似文献
13.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
14.
A. M. Semikhatov 《Theoretical and Mathematical Physics》2009,159(1):424-447
15.
Meng-xiao Yin 《应用数学学报(英文版)》2006,22(3):451-456
Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as a subgraph, where Kr+1 -K3 is a graph obtained from a complete graph Kr+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(Kr+1 - K3,n) for r ≥ 3 and n ≥ 3r+ 5. 相似文献
16.
Wenguang Zhai 《中国科学A辑(英文版)》1999,42(11):1173-1183
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x
1
c
1,⋯,c
k
) denote the number of primesp withp⩽x,
, where 1<c
1<⋯<c
k
are fixed constants. It is proved that π(x;c
1,⋯,c
k
) has an asymptotic formula ifc
1
−1
+⋯+c
k
−1
>k−k/(4k
2+2).
Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation
of Shandong Province (Grant No.Q98A02110). 相似文献
17.
Nick Dungey 《Semigroup Forum》2009,78(2):226-237
For suitable bounded operator semigroups (e
tA
)
t≥0 in a Banach space, we characterize the estimate ‖Ae
tA
‖≤c/F(t) for large t, where F is a function satisfying a sublinear growth condition. The characterizations are by holomorphy estimates on the semigroup,
and by estimates on powers of the resolvent. We give similar characterizations of the difference estimate ‖T
n
−T
n+1‖≤c/F(n) for a power-bounded linear operator T, when F(n) grows faster than n
1/2 for large n. 相似文献
18.
Guizhen LIU 《Frontiers of Mathematics in China》2009,4(2):311-323
Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g
−, g
+) and ƒ = (ƒ
−, ƒ
+) be pairs of positive integer-valued functions defined on V(G) such that g
−(x) ⩽ ƒ
−(x) and g
+(x) ⩽ ƒ
+(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g
−(x) ⩽ id
H
(x) ⩽ ƒ
−(x) and g
+(x) ⩽ od
H
(x) ⩽ ƒ
+(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let
= {F
1, F
2,…, F
m} and H be a factorization and a subdigraph of G, respectively.
is called k-orthogonal to H if each F
i
, 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g
−(x), g
+(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.
相似文献
19.
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
20.
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ)× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p. 相似文献