共查询到20条相似文献,搜索用时 31 毫秒
1.
Our main result is that the simple Lie group G = Sp(n, 1) acts metrically properly isometrically on L
p
(G) if p > 4n + 2. To prove this, we introduce Property , with V being a Banach space: a locally compact group G has Property if every affine isometric action of G on V, such that the linear part is a C
0-representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic
groups over a local field of characteristic zero, have Property . As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on L
2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L2-Betti number is nonzero.
相似文献
2.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
3.
We give a concrete and surprisingly simple characterization of compact sets
K ì \mathbbR2 ×2 K \subset \mathbb{R}^{{2 \times 2}} for which families of approximate solutions to the inclusion problem Du∈K are compact. In particular our condition is algebraic and can be tested algorithmically. We also prove that the quasiconvex
hull of compact sets of 2 × 2 matrices can be localized. This is false for compact sets in higher dimensions in general. 相似文献
4.
Dragan Djurčić Rale M. Nikolić Aleksandar Torgašev 《Lithuanian Mathematical Journal》2011,51(4):472-476
We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the
class A \mathcal {A} of all nondecreasing unbounded positive functions on a half-axis [a,+∞) (a > 0). As a main result, we prove a proper characterization of the functional class R
∞
∩
A \mathcal {A} , where R
∞
is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI
*
∩
A \mathcal {A} . 相似文献
5.
Let N be a compact simply connected smooth Riemannian manifold and, for p ∈ {2,3,...}, W
1,p
(R
p+1, N) be the Sobolev space of measurable maps from R
p+1 into N whose gradients are in L
p
. The restriction of u to almost every p-dimensional sphere S in R
p+1 is in W
1,p
(S, N) and defines an homotopy class in π
p
(N) (White 1988). Evaluating a fixed element z of Hom(π
p
(N), R) on this homotopy class thus gives a real number Φ
z,u
(S). The main result of the paper is that any W
1,p
-weakly convergent limit u of a sequence of smooth maps in C
∞(R
p+1, N), Φ
z,u
has a rectifiable Poincaré dual
. Here Γ is a a countable union of C
1 curves in R
p+1 with Hausdorff -measurable orientation and density function θ: Γ→R. The intersection number between and S evaluates Φ
z,u
(S), for almost every p-sphere S. Moreover, we exhibit a non-negative integer n
z
, depending only on homotopy operation z, such that even though the mass may be infinite. We also provide cases of N, p and z for which this rational power p/(p + n
z
) is optimal. The construction of this Poincaré dual is based on 1-dimensional “bubbling” described by the notion of “scans”
which was introduced in Hardt and Rivière (2003). We also describe how to generalize these results to R
m
for any m ⩾ p + 1, in which case the bubbling is described by an (m–p)-rectifiable set with orientation and density function determined by restrictions of the mappings to almost every oriented
Euclidean p-sphere. 相似文献
6.
A note on nil power serieswise Armendariz rings 总被引:1,自引:0,他引:1
Sana Hizem 《Rendiconti del Circolo Matematico di Palermo》2010,59(1):87-99
A ring R is called nil power serieswise Armendariz if $
\forall f = \sum\limits_{i = 0}^\infty {a_i X^i }
$
\forall f = \sum\limits_{i = 0}^\infty {a_i X^i }
and $
g = \sum\limits_{i = 0}^\infty {b_i X^i }
$
g = \sum\limits_{i = 0}^\infty {b_i X^i }
in R[[X]] such that f g ∈ Nil(R)[[X]], then a
i
b
j
∈ Nil(R) for all i and j. In this note we characterize completely nil power serieswise Armendariz rings with their nilradical Nil(R) (where the nilradical is the set of nilpotent elements). We prove that a ring is nil power serieswise Armendariz if and
only if Nil(R) is an ideal of R. We prove that each power serieswise Armendariz ring is nil power serieswise Armendariz and we give examples of nil power
serieswise Armendariz rings. 相似文献
7.
We obtain the generalized codimension-p Cauchy–Kovalevsky extension of the exponential function in R
m
=R
p
⊕R
q
, where p>1, , and prove the corresponding codimension-p Paley–Wiener theorems. 相似文献
8.
Manel Sanchón 《Potential Analysis》2007,27(3):217-224
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u
* belongs to L
∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)).
This work was partially supported by MCyT BMF 2002-04613-CO3-02. 相似文献
9.
S. E. Pastukhova 《Journal of Mathematical Sciences》2012,181(5):668-700
We consider the operator exponential e
−tA
, t > 0, where A is a selfadjoint positive definite operator corresponding to the diffusion equation in
\mathbbRn {\mathbb{R}^n} with measurable 1-periodic coefficients, and approximate it in the operator norm
|| · ||L2( \mathbbRn ) ? L2( \mathbbRn ) {\left\| {\; \cdot \;} \right\|_{{{L^2}\left( {{\mathbb{R}^n}} \right) \to {L^2}\left( {{\mathbb{R}^n}} \right)}}} with order
O( t - \fracm2 ) O\left( {{t^{{ - \frac{m}{2}}}}} \right) as t → ∞, where m is an arbitrary natural number. To construct approximations we use the homogenized parabolic equation with constant
coefficients, the order of which depends on m and is greater than 2 if m > 2. We also use a collection of 1-periodic functions N
α
(x),
x ? \mathbbRn x \in {\mathbb{R}^n} , with multi-indices α of length
| a| \leqslant m \left| \alpha \right| \leqslant m , that are solutions to certain elliptic problems on the periodicity cell. These results are used to homogenize the diffusion
equation with ε-periodic coefficients, where ε is a small parameter. In particular, under minimal regularity conditions, we construct approximations of order O(ε
m
) in the L
2-norm as ε → 0. Bibliography: 14 titles. 相似文献
10.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
11.
We prove a time hierarchy theorem for inverting functions computable in a slightly nonuniform polynomial time. In particular,
we prove that if there is a strongly one-way function, then for any k and for any polynomial p, there is a function f computable in linear time with one bit of advice such that there is a polynomial-time probabilistic adversary that inverts
f with probability ≥ 1/p(n) on infinitely many lengths of input, while all probabilistic O(n
k
)-time adversaries with logarithmic advice invert f with probability less than 1/p(n) on almost all lengths of input. We also prove a similar theorem in the worst-case setting, i.e., if P ≠ NP, then for every l > k ≥ 1
Bibliography: 21 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 54–76. 相似文献
12.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
13.
In 1998, Kleinbock and Margulis proved Sprindzuk’s conjecture pertaining to metrical Diophantine approximation (and indeed
the stronger Baker–Sprindzuk conjecture). In essence, the conjecture stated that the simultaneous homogeneous Diophantine
exponent w
0(x) = 1/n for almost every point x on a nondegenerate submanifold M \mathcal{M} of
\mathbbRn {\mathbb{R}^n} . In this paper, the simultaneous inhomogeneous analogue of Sprindzuk’s conjecture is established. More precisely, for any
“inhomogeneous” vector θ ∈
\mathbbRn {\mathbb{R}^n} we prove that the simultaneous inhomogeneous Diophantine exponent w
0(x
,
θ) is 1/n for almost every point x on M \mathcal{M} . The key result is an inhomogeneous transference principle which enables us to deduce that the homogeneous exponent w
0(x) is 1/n for almost all x ∈ M \mathcal{M} if and only if, for any θ ∈
\mathbbRn {\mathbb{R}^n} , the inhomogeneous exponent w
0(x
,
θ) = 1/n for almost all x ∈ M \mathcal{M} . The inhomogeneous transference principle introduced in this paper is an extremely simplified version of that recently discovered
by us. Nevertheless, it should be emphasised that the simplified version has the great advantage of bringing to the forefront
the main ideas while omitting the abstract and technical notions that come with describing the inhomogeneous transference
principle in all its glory. 相似文献
14.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
15.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(3):443-460
We consider a family of open discrete mappings
f:D ?[`(\mathbb Rn)] f:D \to \overline {{{\mathbb R}^n}} that distort, in a special way, the p-modulus of a family of curves that connect the plates of a spherical condenser in a domain D in
\mathbb Rn {{\mathbb R}^n} ; p > n-1; p < n; and bypass a set of positive p-capacity. We establish that this family is normal if a certain real-valued function that controls the considered distortion
of the family of curves has finite mean oscillation at every point or only logarithmic singularities of order not higher than
n - 1: We show that, under these conditions, an isolated singularity x
0 ∈ D of a mapping
f:D\{ x0 } ?[`(\mathbb Rn)] f:D\backslash \left\{ {{x_0}} \right\} \to \overline {{{\mathbb R}^n}} is removable, and, moreover, the extended mapping is open and discrete. As applications, we obtain analogs of the known Liouville
and Sokhotskii–Weierstrass theorems. 相似文献
16.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):135-140
Summary LetF be a distribution function over the real line. DefineR
p(y)=∫|x−y|pdF(x) forp≧1. Forp>1 there is a unique minimizer ofR
p(·), sayγ
p. Under mild conditions onF it is shown that
exists and that the limit is a median. Thus, one could use this limit as a definition of a unique median. Also it is shown
that
whereR is the right extremity ofF andL is the left extremity ofF provided that −∞<L≦R<∞. A similar result is available ifL=−∞,R=∞, yetF has symmetric tails. 相似文献
17.
Helmut Zöschinger 《Archiv der Mathematik》2010,95(3):225-231
Let
(R,\mathfrak m){(R,\mathfrak m)} be a noetherian, local ring with completion [^(R)]{\hat{R}} . We show that R ì [^(R)]{R \subset \hat{R}} satisfies the condition Going up if and only if there exists to every artinian R-module M with
AnnR(M) ì \mathfrakp{{\rm Ann}_R(M) \subset \mathfrak{p}} a submodule U ì M{U \subset M} with
AnnR(U)=\mathfrakp.{{\rm {Ann}}_R(U)=\mathfrak{p}.} This is further equivalent to R being formal catenary, to α(R) = 0 and to
Hd\mathfrakq/\mathfrakp(R/\mathfrakp)=0{H^d_{\mathfrak{q}/\mathfrak{p}}(R/\mathfrak{p})=0} for all prime ideals
\mathfrakp ì \mathfrakq \subsetneq \mathfrakm{\mathfrak{p} \subset \mathfrak{q} \subsetneq \mathfrak{m}} where
d = dim(R/\mathfrakp){d = {\rm {dim}}(R/\mathfrak{p})}. 相似文献
18.
Assume that the elliptic operator L=div (A(x)∇) is L
p
-resolutive, p>1, on the unit disc
\mathbbD ì \mathbb R2\mathbb{D}\subset \mathbb {R}^{2}
. This means that the Dirichlet problem
$\left\{{l@{\quad}l}Lu=0&\mbox{in }\mathbb{D},\\[3pt]u=g&\mbox{on }\partial\mathbb{D}\right.$\left\{\begin{array}{l@{\quad}l}Lu=0&\mbox{in }\mathbb{D},\\[3pt]u=g&\mbox{on }\partial\mathbb{D}\end{array}\right. 相似文献
19.
Consider a random smooth Gaussian field G(x):
F ? \mathbbR F \to \mathbb{R} , where F is a compact set in
\mathbbRd {\mathbb{R}^d} . We derive a formula for the average area of a surface determined by the equation G(x) = 0 and give some applications. As
an auxiliary result, we obtain an integral expression for the area of a surface determined by zeros of a nonrandom smooth
field. Bibliography: 13 titles. 相似文献
20.
Bronius Grigelionis 《Lithuanian Mathematical Journal》2011,51(2):194-206
We prove that the Thorin class $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 , is the minimal class of probability distributions on
\mathbbR+ {\mathbb{R}_{+} } that is closed under convolutions and weak limits and contains the Tweedie distributions Tw(κ+1)/κ
(μ, λ), μ > 0, λ > 0. 相似文献
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