共查询到20条相似文献，搜索用时 31 毫秒
1.
Lewin 《Semigroup Forum》2008,66(1):43-62
Abstract. Given a set A and a function
, we study the set of all functions
that are continuous for all topologies for which f continuous.
We prove that in a sense to be made precise in the text, for any essentially infinitary function f , any non-constant such g equals f
n
, for some n∈ N. We also prove a similar result for the clone of n -ary functions from
. 相似文献
2.
Abstract. Let Ω and Π be two simply connected domains in the complex plane C which are not equal to the whole plane C and let λ
Ω
and λ
Π
denote the densities of the Poincare metric in Ω and Π , respectively. For f: Ω → Π analytic in Ω , inequalities of the type
are considered where M
n
(z,Ω, Π) does not depend on f and represents the smallest value possible at this place. We prove that
if Δ is the unit disk and Π is a convex domain. This generalizes a result of St. Ruscheweyh.
Furthermore, we show that
holds for arbitrary simply connected domains whereas the inequality 2
n-1
≤ C
n
(Ω,Π) is proved only under some technical restrictions upon Ω and Π . 相似文献
3.
Denoting Δ? the Laplacian operator on the (2N+1)-dimensional Heisenberg group ?
N
, we prove some nonexistence results for solutions of inequalities of the three types
in ?
N
and ?
N
×ℝ}+, with a∈L
∞, when 1<p≤p
0, where p
0 depends on N and the type of equation.
Received: 17 June 1999 相似文献
4.
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
5.
Viorel Barbu Aurel Răşcanu Gianmario Tessitore 《Applied Mathematics and Optimization》2003,47(2):97-120
Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat
equation (with Dirichlet boundary conditions in the bounded domain D
⊂ R
d
and multiplicative noise):
and for the corresponding backward dual equation:
We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward
equation.
\par 相似文献
6.
Bogdan Batko Jacek Tabor 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):67-73
Let G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L
+ the inequality
Then there exists a unique additive mappingA : G → L such that
As the method of the proof we use the Johnson-Kist Representation Theorem. 相似文献
7.
Equations with two time scales (refinement equations or dilation equations) are central to wavelet theory. Several applications
also include an inhomogeneous forcing term F(t). We develop here a part of the existence theory for the inhomogeneous refinement
equation
where a (k) is a finite sequence and F is a compactly supported distribution on ℝ.
The existence of compactly supported distributional solutions to an inhomogeneous refinement equation is characterized in
terms of conditions on the pair (a, F).
To have Lp solutions from F ∈ Lp(ℝ), we construct by the cascade algorithm a sequence of functions φ0 ∈ Lp(ℝ) from a compactly supported initial function ℝ as
A necessary and sufficient condition for the sequence {φn} to converge in Lp(ℝ)(1 ≤ p ≤ ∞) is given by the p-norm joint spectral radius of two matrices derived from the mask a. A convexity property
of the p-norm joint spectral radius (1 ≤ p ≤ ∞) is presented.
Finally, the general theory is applied to some examples and multiple refinable functions.
Acknowledgements and Notes. Research supported in part by Research Grants Council and City University of Hong Kong under Grants #9040281, 9030562, 7000741. 相似文献
8.
Micciancio 《Discrete and Computational Geometry》2003,29(1):133-138
Abstract. We prove that the best way to reduce the volume of the n -dimensional unit cube by a linear transformation that maps each of the main vertices
to a point within distance ɛ <
from
is to shorten all edges by a factor (1-ɛ) . In particular, the minimal volume of such an almost cubic parallelepiped is (1-ɛ)
n
. This problem naturally arises in the construction of lattice-based one-way functions with worst-case/ average-case connection. 相似文献
9.
A. V. Demyanov 《Journal of Mathematical Sciences》2006,136(2):3706-3717
The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special
class of functionals:
with respect to the convergence un → u in measure, vn ⇀ v in Lp(Ω;ℝd)
in W−1,p(Ω), and χn ⇀ χ in Lp(Ω), where χn ∈ Z:= {χ ∈ L∞(Ω): 0 ≤ χ(x) ≤ 1 for a.e. x}. Here
is a constant-rank partial differential operator. The main result is that if the characteristic cone of
has the full dimension, then the l.s.c. is equivalent to the fact that the F± are both
-quasiconvex and
for a.e. x ∈ Ω and for all u ∈ ℝd. As a corollary, we obtain several results for the functional
with respect to the same convergence. We show that this functional is l.s.c. iff
Bibliography: 14 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 100–119. 相似文献
10.
Consider the probability spaceW={−1, 1}
n
with the uniform (=product) measure. Letf: W →R be a function. Letf=Σf
IXI be its unique expression as a multilinear polynomial whereX
I=Π
i∈I
x
i. For 1≤m≤n let
=Σ|I|=m
f
IXI. LetT
ɛ
(f)=Σf
Iɛ|I|
X
I where 0<ɛ<1 is a constant. A hypercontractive inequality, proven by Bonami and independently by Beckner, states that
This inequality has been used in several papers dealing with combinatorial and probabilistic problems. It is equivalent to
the following inequality via duality: For anyq≥2
In this paper we prove a special case with a slightly weaker constant, which is sufficient for most applications. We show
where
. Our proof uses probabilistic arguments, and a generalization of Shearer’s Entropy Lemma, which is of interest in its own
right.
Supported partially by NSF Award Abstract #0071261. 相似文献
11.
Suppose λ is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal functionL
λ(x)
x∈R, satisfying the interpolatory conditionsL
k = δ0k,k∈Z
. One objective of this paper is to derive several additional properties ofL
λ. For example, it is shown thatL
λ possesses the signregularity property sgn[L
λ(x)]=sgn[sin(πx)/(πx)],x∈R, and that |L
λ (x)|≤2e
8 min {(⌊|x|⌋+1)-1,exp(-λ⌊|x|⌋)},x∈R. The analysis is based on a simple representation formula forL
λ and employs some methods from classical function theory. A second consideration in the paper is the Gaussian cardinal-interpolation
operatorL
λ, defined by the equation (L
λy)(x):=
,x∈R, y=(yk)k∈Z. On account of the exponential decay of the cardinal functionL
λ,L
λ is a well-defined linear map froml
∞ (Z) intoL
∞ (R). Its associated operatornorm ‖L
λ‖ is called the Lebesgue constant ofL
λ. The latter half of the paper establishes the following estimates for the Lebesgue constant: ‖L
λ‖≍1, λ→∞, and ║Lλ║≍log(1/λ), λ→0+. Suitable multidimensional analogues of these results are also given.
For Carl de Boor, on the occasion of his sixtieth birthday 相似文献
12.
O. M. Fomenko 《Journal of Mathematical Sciences》2007,143(3):3174-3181
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
∞
cnn−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, sym2f)xρ and the “error term”
.
Using the Voronoi formula for Δρ(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
13.
On a periodic boundary value problem for cyclic feedback type linear functional differential systems
Sulkhan Mukhigulashvili 《Archiv der Mathematik》2006,87(3):255-260
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
where ω > 0, ℓi : C([0, ω])→ L([0,ω]) are linear bounded operators, and qi∈L([0, ω]).
Received: 11 June 2005 相似文献
14.
Katalin Gyarmati 《The Ramanujan Journal》2008,17(3):387-403
Let τ(n) be the number of positive divisors of an integer n, and for a polynomial P(X)∈ℤ[X], let
R. de la Bretèche studied the maximum values of τ
P
(n) in intervals. Here the following is proved: if P(X)∈ℤ[X] is not of the form a(X+b)
k
with a,b∈ℚ, and k∈ℕ then
This improves partially on La Bretèche’s results.
Research partially supported by Hungarian National Foundation for Scientific Research, Grants T043631, T043623 and T049693. 相似文献
15.
Xiaojing Yang 《Archiv der Mathematik》2005,85(5):460-469
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
16.
We investigate the large time behavior of positive solutions with finite mass for the viscous Hamilton-Jacobi equationu
t
= Δu + |Δu|
p
,t>0,x ∈ ℝ
N
, wherep≥1 andu(0,.)=u
0≥0,u
0≢0,u
0∈L
1. DenotingI
∞=lim
t→∞‖u(t)‖1≤∞, we show that the asymptotic behavior of the mass can be classified along three cases as follows:
We also consider a similar question for the equationu
t=Δu+u
p
. 相似文献
| – | • ifp≤(N+2)/(N+1), thenI ∞=∞ for allu 0; |
| – | • if (N+2)/(N+1)<p<2, then bothI ∞=∞ andI ∞<∞ occur; |
| – | • ifp≥2, thenI ∞<∞ for allu 0. |
17.
Abstract. Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth
surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called
-subdivision , has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix 2I ,
-subdivision is based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points.
This paper concerns the problem of achieving maximal sum rule orders for stationary
-subdivision schemes with given mask support, which is important because the sum rule order characterizes the order of the
polynomial reproduction, and provides an upper bound on the Sobolev smoothness of the surface. We study both interpolating
and approximating schemes for a natural family of symmetric mask support sets related to squares of sidelength 2n in Z
2
, and obtain exact formulas for the maximal sum rule order for arbitrary n . For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit
family of schemes based on repeated averaging [15].
In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of
interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in
size by using symmetries. From this, we construct some new examples of smooth (C
2
,C
3
) interpolating
-subdivision schemes with maximal sum rule order and symmetric masks. The construction of associated dual schemes is also
discussed. 相似文献
18.
Let B
0,B
1, ⋯ ,B
n
be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time
where 0<b
i
≤ 1, 1 ≤i≤n. In particular, we have ?τ3=∞ and ?τ5<∞. Various generalizations are also studied.
Received: 10 January 2000 / Revised version: 12 January 2001 /?Published online: 14 June 2001 相似文献
19.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
20.
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