共查询到20条相似文献,搜索用时 296 毫秒
1.
We present an easy proof that p-Hardy’s inequality implies uniform p-fatness of the boundary when p = n. The proof works also in metric space setting and demonstrates the self-improving phenomenon of the p-fatness. We also explore the relationship between p-fatness, p-Hardy inequality, and the uniform perfectness for all p ≥ 1, and demonstrate that in the Ahlfors Q-regular metric measure space setting with p = Q, these three properties are equivalent. When p ≠ 2, our results are new evenin the Euclidean setting. 相似文献
2.
We prove an estimate on denominators of rational Drinfeld associators. To obtain this result, we prove the corresponding estimate
for the p-adic associators stable under the action of suitable elements of
Gal([`(\mathbbQ)]/\mathbbQ){{\rm Gal}(\bar{\mathbb{Q}}/\mathbb{Q})} . As an application, we settle in the positive Duflo’s question on the Kashiwara–Vergne factorizations of the Jacobson element
J
p
(x, y) = (x + y)
p
− x
p
− y
p
in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant. 相似文献
3.
Laura Paladino 《Annali di Matematica Pura ed Applicata》2010,189(1):17-23
Let ${\mathcal{E}}Let E{\mathcal{E}} be an elliptic curve defined over
\mathbbQ{\mathbb{Q}} . Let
P ? E(\mathbb Q){P\in {\mathcal{E}}(\mathbb {Q})} and let q be a positive integer. Assume that for almost all valuations
v ? \mathbbQ{v\in \mathbb{Q}} , there exist points
Dv ? E(\mathbb Qv){D_v\in {\mathcal{E}}(\mathbb {Q}_v)} such that P = qD
v
. Is it possible to conclude that there exists a point
D ? E(\mathbb Q){D\in {\mathcal{E}}(\mathbb {Q})} such that P = qD? A full answer to this question is known when q is a power of almost all primes
p ? \mathbbN{p\in \mathbb{N}} , but some cases remain open when p ? S={2,3,5,7,11,13,17,19,37,43,67,163}{p\in S=\{2,3,5,7,11,13,17,19,37,43,67,163\}} . We now give a complete answer in the case when q = 4. 相似文献
4.
Yasutsugu Fujita 《manuscripta mathematica》2005,118(3):339-360
Let E be an elliptic curve over Q and p a prime number. Denote by Qp,∞ the Zp-extension of Q. In this paper, we show that if p≠3, then where E(Qp,∞)(2) is the 2-primary part of the group E(Qp,∞) of Qp,∞-rational points on E. More precisely, in case p=2, we completely classify E(Q2,∞)(2) in terms of E(Q)(2); in case p≥5 (or in case p=3 and E(Q)(2)≠{O}), we show that E(Qp,∞)(2)=E(Q)(2). 相似文献
5.
Francesco Petitta Augusto C. Ponce Alessio Porretta 《Journal of Evolution Equations》2011,11(4):861-905
Given a parabolic cylinder Q = (0, T) × Ω, where
W ì \mathbb RN{\Omega\subset \mathbb {R}^N} is a bounded domain, we prove new properties of solutions of
ut-Dp u = m \textin Qu_t-\Delta_p u = \mu \quad \text{in }Q 相似文献
6.
B. Wilkens 《Israel Journal of Mathematics》2009,172(1):357-369
Let P be a finite p-group, p a prime. We prove that there is a finite p-group Q ≥ P such that every normal subgroup of Q is characteristic in Q. 相似文献
7.
We have considered a class of square Fibonacci matrix of order (p + 1) whose elements are based on the Fibonacci p numbers with determinant equal to +1 or −1. There is a relation between Fibonacci numbers with initial terms which is known as cassini formula. Fibonacci series and the golden mean plays a very important role in the construction of a relatively new space–time theory, which is known as E-infinity theory. An original Fibonacci coding/decoding method follows from the Fibonacci matrices. There already exists a relation between the code matrix elements for the case p = 1 [Stakhov AP. Fibonacci matrices, a generalization of the cassini formula and a new coding theory. Chaos, Solitons and Fractals 2006;30:56–66.]. In this paper, we have established generalized relations among the code matrix elements for all values of p. For p = 2, the correct ability of the method is 99.80%. In general, correct ability of the method increases as p increases. 相似文献
8.
Julio Delgado 《Integral Equations and Operator Theory》2010,68(1):61-74
Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets M{\mathcal{M}}. Let T be a nuclear operator on Lp(W,M,m){L^p({\Omega},{\mathcal{M}},\mu) }, 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on operator ideals introduced by Pietsch
and a characterization of nuclear operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal. 相似文献
9.
Anand Pillay 《Archive for Mathematical Logic》1989,29(1):1-7
We prove that any field definable in (Q
p, +, ·) is definably isomorphic to a finite extension ofQ
p
. 相似文献
10.
Benedict H. Gross 《Israel Journal of Mathematics》1999,113(1):61-93
In this paper, we develop an algebraic theory of modular forms, for connected, reductive groupsG overQ with the property that every arithmetic subgroup Γ ofG(Q) is finite. This theory includes our previous work [15] on semi-simple groupsG withG(R) compact, as well as the theory of algebraic Hecke characters for Serre tori [20]. The theory of algebraic modular forms
leads to a workable theory of modular forms (modp), which we hope can be used to parameterize odd modular Galois representations.
The theory developed here was inspired by a letter of Serre to Tate in 1987, which has appeared recently [21]. I want to thank
Serre for sending me a copy of this letter, and for many helpful discussions on the topic. 相似文献
11.
E. S. Afanas’eva 《Ukrainian Mathematical Journal》2012,63(10):1479-1493
We study the problems of continuous and homeomorphic extensions to the boundary for so-called ring Q-homeomorphisms between domains on the Riemannian manifolds and establish conditions for the function Q(x) and the boundaries of the domains under which every ring Q-homeomorphism admits a continuous or homeomorphic extension to the boundary. This theory can be applied, in particular, to
the Sobolev classes. 相似文献
12.
Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Qp and Qp,0 on the unit ball of are defined as
13.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
14.
Jorge García-Melián Julio D. Rossi José C. Sabina de Lis 《Calculus of Variations and Partial Differential Equations》2008,31(2):187-204
In this work we consider the behaviour for large values of p of the unique positive weak solution u
p
to Δ
p
u = u
q
in Ω, u = +∞ on , where q > p − 1. We take q = q(p) and analyze the limit of u
p
as p → ∞. We find that when q(p)/p → Q the behaviour strongly depends on Q. If 1 < Q < ∞ then solutions converge uniformly in compacts to a viscosity solution of with u = +∞ on . If Q = 1 then solutions go to ∞ in the whole Ω and when Q = ∞ solutions converge to 1 uniformly in compact subsets of Ω, hence the boundary blow-up is lost in the limit. 相似文献
15.
Pierre Angl��s 《Advances in Applied Clifford Algebras》2011,21(2):233-246
This self-contained short note deals with the study of the properties of some real projective compact quadrics associated
with a a standard pseudo-hermitian space H
p,q
, namely [(Q(p, q))\tilde], [(Q2p+1,1)\tilde], [(Q1,2q+1)\tilde], [(Hp,q)\tilde]. [(Q(p, q))\tilde]{\widetilde{Q(p, q)}, \widetilde{Q_{2p+1,1}}, \widetilde{Q_{1,2q+1}}, \widetilde{H_{p,q}}. \, \widetilde{Q(p, q)}} is the (2n – 2) real projective quadric diffeomorphic to (S
2p–1 × S
2q–1)/Z
2. inside the real projective space P(E
1), where E
1 is the real 2n-dimensional space subordinate to H
p,q
. The properties of [(Q(p, q))\tilde]{\widetilde{Q(p, q)}} are investigated. [(Hp,q)\tilde]{\widetilde{H_p,q}} is the real (2n – 3)-dimensional compact manifold-(projective quadric)- associated with H
p,q
, inside the complex projective space P(H
p,q
), diffeomorphic to (S
2p–1 × S
2q–1)/S
1. The properties of [(Hp,q)\tilde]{\widetilde{H_{p,q}}} are studied. [(Q2p+1,1)\tilde]{\widetilde{Q_{2p+1,1}}} is a 2p-dimensional standard real projective quadric, and [(Q1,2q+1)\tilde]{\widetilde{Q_{1,2q+1}}} is another standard 2q-dimensional projective quadric. [(Q2p+1,1)\tilde] è[(Q1,2q+1)\tilde]{\widetilde{Q_{2p+1,1}} \cup \widetilde{Q_{1,2q+1}}}, union of two compact quadrics plays a part in the understanding of the "special pseudo-unitary conformal compactification"
of H
p,q
. It is shown how a distribution y → D
y
, where y ? H\{0},H{y \in H\backslash\{0\},H} being the isotropic cone of H
p,q
allows to [(Hp+1,q+1)\tilde]{\widetilde{H_{p+1,q+1}}} to be considered as a "special pseudo-unitary conformal compactified" of H
p,q
× R. The following results precise the presentation given in [1,c]. 相似文献
16.
M. Tetruashvili 《Georgian Mathematical Journal》1994,1(5):561-565
The unquantified set theory MLSR containing the symbols ∪, ∖, ≠, ∈,R (R(x) is interpreted as a rank ofx) is considered. It is proved that there exists an algorithm which for any formulaQ of the MLSR theory decides whetherQ is true or not using the spacec|Q|3 (|Q| is the length ofQ). 相似文献
17.
Hee-Kap Ahn Sang Won Bae Otfried Cheong Joachim Gudmundsson 《Discrete and Computational Geometry》2008,40(3):414-429
The aperture angle
α(x,Q) of a point x
∉
Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q⊂C is the minimum aperture angle of any x∈C∖Q with respect to Q. We show that for any compact convex set C in the plane and any k>2, there is an inscribed convex k-gon Q⊂C with aperture angle approximation error
. This bound is optimal, and settles a conjecture by Fekete from the early 1990s.
The same proof technique can be used to prove a conjecture by Brass: If a polygon P admits no approximation by a sub-k-gon (the convex hull of k vertices of P) with Hausdorff distance σ, but all subpolygons of P (the convex hull of some vertices of P) admit such an approximation, then P is a (k+1)-gon. This implies the following result: For any k>2 and any convex polygon P of perimeter at most 1 there is a sub-k-gon Q of P such that the Hausdorff-distance of P and Q is at most
.
This research was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-311-D00763).
NICTA is funded through the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian
Research Council. 相似文献
18.
David G. Glynn 《Designs, Codes and Cryptography》2011,58(2):215-218
There is polynomial function X
q
in the entries of an m × m(q − 1) matrix over a field of prime characteristic p, where q = p
h
is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left
by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of
points in projective spaces of prime characteristic, to make visible hidden structure. There are connections with coding theory,
permanents, and additive bases of vector spaces. 相似文献
19.
20.
Forp∈(0, 1), letQp(Qp, 0) be the space of analytic functionsfon the unit diskΔwith supw∈Δ ‖f°?w‖p<∞ (lim|w|→1 ‖f°?w‖p=0), where ‖·‖pmeans the weighted Dirichlet norm and?wis the Möbius map ofΔonto itself with?w(0)=w. In this paper, we prove the Corona theorem for the algebraQp∩H∞(Qp, 0∩H∞); then we provide a Fefferman–Stein type decomposition forQp(Qp, 0), and finally we describe the interpolating sequences forQp∩H∞(Qp, 0∩H∞)). 相似文献
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