共查询到20条相似文献,搜索用时 625 毫秒
1.
We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg
group . The model case is the non-degenerate p-Laplacean operator where , and p is not too far from 2. 相似文献
2.
Octavian G. Mustafa 《Annali di Matematica Pura ed Applicata》2008,187(2):187-196
Via an integral transformation, we establish two embedding results between the Emden-Fowler type equation , t ≥ t
0 > 0, with solutions x such that as , , and the equation , u > 0, with solutions y such that for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic
equation , , that blow up as in the two dimensional case.
相似文献
3.
Franc Forstnerič Björn Ivarsson Frank Kutzschebauch Jasna Prezelj 《Mathematische Annalen》2007,338(3):545-554
Given a Stein manifold x of dimension n > 1, a discrete sequence , and a discrete sequence where , there exists a proper holomorphic embedding satisfying f(a
j
) = b
j
for every j = 1,2,...
Forstnerič and Prezelj supported by grants P1-0291 and J1-6173, Republic of Slovenia.
Kutzschebauch supported by Schweizerische National fonds grant 200021-107477/1.
Ivarsson supported by The Wenner-Gren Foundations. 相似文献
4.
Noriko Mizoguchi 《Mathematische Annalen》2007,339(4):839-877
A solution u of a Cauchy problem for a semilinear heat equation
is said to undergo Type II blowup at t = T if lim sup Let be the radially symmetric singular steady state. Suppose that is a radially symmetric function such that and (u
0)
t
change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data
u
0 in the case of p > p
L
, where p
L
is the Lepin exponent. 相似文献
5.
Hiroki Masuda 《Annals of the Institute of Statistical Mathematics》2009,61(1):181-195
We study joint efficient estimation of two parameters dominating either the inverse-Gaussian or gamma subordinator, based
on discrete observations sampled at satisfying as . Under the condition that as we have two kinds of optimal rates, and . Moreover, as in estimation of diffusion coefficient of a Wiener process the -consistent component of the estimator is effectively workable even when T
n
does not tend to infinity. Simulation experiments are given under several h
n
’s behaviors. 相似文献
6.
Claudie Hassenforder Sabine Mercier 《Annals of the Institute of Statistical Mathematics》2007,59(4):741-755
Let
be a sequence of letters taken in a finite alphabet Θ. Let
be a scoring function and
the corresponding score sequence where X
i
= s(A
i
). The local score is defined as follows:
. We provide the exact distribution of the local score in random sequences in several models. We will first consider a Markov
model on the score sequence
, and then on the letter sequence
. The exact P-value of the local score obtained with both models are compared thanks to several datasets. They are also compared with previous
results using the independent model. 相似文献
7.
Neculai Andrei 《Numerical Algorithms》2008,47(2):143-156
Another hybrid conjugate gradient algorithm is subject to analysis. The parameter β
k
is computed as a convex combination of (Hestenes-Stiefel) and (Dai-Yuan) algorithms, i.e. . The parameter θ
k
in the convex combination is computed in such a way so that the direction corresponding to the conjugate gradient algorithm
to be the Newton direction and the pair (s
k
, y
k
) to satisfy the quasi-Newton equation , where and . The algorithm uses the standard Wolfe line search conditions. Numerical comparisons with conjugate gradient algorithms show
that this hybrid computational scheme outperforms the Hestenes-Stiefel and the Dai-Yuan conjugate gradient algorithms as well
as the hybrid conjugate gradient algorithms of Dai and Yuan. A set of 750 unconstrained optimization problems are used, some
of them from the CUTE library.
相似文献
8.
Peter Bundschuh 《Results in Mathematics》2007,51(1-2):29-42
Let K be or an imaginary quadratic number field, and q
K an integer with |q| > 1. We give a quantitative version of the linear independence over K of the three numbers 1, , and an equivalent power series version. We also mention several open problems.
Received: February 5, 2007. Revised: April 18, 2007. 相似文献
9.
Yuan Zhang 《Mathematische Annalen》2007,337(2):457-478
Let
and
denote the complexifications of Heisenberg hypersurfaces in
and
, respectively. We show that non-degenerate holomorphic Segre mappings from
into
with
possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from
into
with
propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2. 相似文献
10.
Jean-Philippe Furter 《Mathematische Annalen》2009,343(4):901-920
Let be the group of polynomial automorphisms of the complex affine plane. On one hand, can be endowed with the structure of an infinite dimensional algebraic group (see Shafarevich in Math USSR Izv 18:214–226,
1982) and on the other hand there is a partition of according to the multidegree (see Friedland and Milnor in Ergod Th Dyn Syst 9:67–99, 1989). Let denote the set of automorphisms whose multidegree is equal to d. We prove that is a smooth, locally closed subset of and show some related results. We give some applications to the study of the varieties (resp. ) of automorphisms whose degree is equal to m (resp. is less than or equal to m). 相似文献
11.
Christer Borell 《Probability Theory and Related Fields》2008,140(1-2):195-205
Let be an integer, let γ be the standard Gaussian measure on , and let . Given this paper gives a necessary and sufficient condition such that the inequality is true for all Borel sets A
1,...,A
m
in of strictly positive γ-measure or all convex Borel sets A
1,...,A
m
in of strictly positive γ-measure, respectively. In particular, the paper exhibits inequalities of the Brunn–Minkowski type
for γ which are true for all convex sets but not for all measurable sets.
相似文献
12.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
13.
We consider existence and qualitative properties of standing wave solutions $\Psi(x,t) = e^{-iEt/h}u(x)We consider existence and qualitative properties of standing wave solutions to the nonlinear Schr?dinger equation with E being a critical frequency in the sense that inf . We verify that if the zero set of W − E has several isolated points x
i
() near which W − E is almost exponentially flat with approximately the same behavior, then for h > 0 small enough, there exists, for any integer k, , a standing wave solution which concentrates simultaneously on , where is any given subset of . This generalizes the result of Byeon and Wang in 3 (Arch Rat Mech Anal 165: 295–316, 2002).Supported by the Alexander von Humboldt foundation and NSFC(No:10571069). 相似文献
14.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T.
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian
measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries,
yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for
The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L
2 sphere. The estimates are given in terms of the γ
2 functional with respect to the ψ
2 metric on F, and hold both in exponential probability and in expectation.
Received: November 2005, Revision: May 2006, Accepted: June 2006 相似文献
15.
Futoshi Takahashi 《Archiv der Mathematik》2009,93(2):191-197
In this note, we consider the problem
on a smooth bounded domain Ω in for p > 1. Let u
p
be a positive solution of the above problem with Morse index less than or equal to . We prove that if u
p
further satisfies the assumption as p → ∞, then the number of maximum points of u
p
is less than or equal to m for p sufficiently large. If Ω is convex, we also show that a solution of Morse index one satisfying the above assumption has a
unique critical point and the level sets are star-shaped for p sufficiently large.
相似文献
16.
In the 1970s, Birman–Craggs–Johnson (BCJ) (Trans AMS 237: 283–309, 1978; Trans AMS 261(1):423–422, 1980) used Rochlin’s invariant
for homology 3-spheres to construct a remarkable surjective homomorphism , where is the Torelli group and B
3 is a certain -vector space of Boolean (square-free) polynomials. By pulling back cohomology classes and evaluating them on abelian cycles,
we construct dimensions worth of nontrivial elements of which cannot be detected rationally. These classes in fact restrict to nontrivial classes in the cohomology of the subgroup
generated by Dehn twists about separating curves. We also use the “Casson–Morita algebra” and Morita’s integral lift of the
BCJ map restricted to to give the same lower bound on .
The first author is partially supported by NSF grant DMS-0606882 and was also supported in part by NSF grant DMS-0504208 and
by a VIGRE postdoc under NSF grant 9983660 to Cornell University. The second author is supported in part by NSF grant DMS-0244542. 相似文献
17.
Let R be a commutative Noetherian ring, be an ideal of R and M be a finitely generated R-module. Melkersson and Schenzel asked whether the set becomes stable for a fixed integer i and sufficiently large j. This paper is concerned with this question. In fact, we prove that if s ≥ 0 and n ≥ 0 such that for all i with i < n, then is finite for all i with i < n, and is finite for all i with i ≤ n, where for a subset T of Spec(R), we set . Also, among other things, we show that if n ≥ 0, R is semi-local and is finite for all i with i < n, then is finite for all i with i ≤ n.
K. Khashyarmanesh was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM)
Iran (No. 86130027). 相似文献
18.
Let denote the set of simultaneously - approximable points in and denote the set of multiplicatively ψ-approximable points in . Let be a manifold in . The aim is to develop a metric theory for the sets and analogous to the classical theory in which is simply . In this note, we mainly restrict our attention to the case that is a planar curve . A complete Hausdorff dimension theory is established for the sets and . A divergent Khintchine type result is obtained for ; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on of is full. Furthermore, in the case that is a rational quadric the convergent Khintchine type result is obtained for both types of approximation. Our results for
naturally generalize the dimension and Lebesgue measure statements of Beresnevich et al. (Mem AMS, 179 (846), 1–91 (2006)). Moreover, within the multiplicative framework, our results for constitute the first of their type.
The research of Victor V. Beresnevich was supported by an EPSRC Grant R90727/01. Sanju L. Velani is a Royal Society University
Research Fellow.
For Iona and Ayesha on No. 3. 相似文献
19.
Let be such that each is a signed measure on R
d
belonging to the Kato class K
d, 1. A Brownian motion in R
d
with drift is a diffusion process in R
d
whose generator can be informally written as . When each is given by U
i
(x)dx for some function U
i
, a Brownian motion with drift is a diffusion in R
d
with generator . In Kim and Song (Ill J Math 50(3):635–688, 2006), some properties of Brownian motions with measure-value drifts in bounded
smooth domains were discussed. In this paper we prove a scale invariant boundary Harnack principle for the positive harmonic
functions of Brownian motions with measure-value drifts in bounded Lipschitz domains. We also show that the Martin boundary
and the minimal Martin boundary with respect to Brownian motions with measure-valued drifts coincide with the Euclidean boundary
for bounded Lipschitz domains. The results of this paper are also true for diffusions with measure-valued drifts, that is,
when is replaced by a uniformly elliptic divergence form operator with C
1 coefficients or a uniformly elliptic non-divergence form operator with C
1 coefficients.
The research of R. Song is supported in part by a joint US-Croatia grant INT 0302167. The research of P. Kim is supported
by Research Settlement Fund for the new faculty of Seoul National University. 相似文献
20.
Alexander Prestel 《manuscripta mathematica》2007,123(1):95-103
Let K be an algebraically closed field with a valuation ring or a real closed field with a convex valuation ring . We show that the projection of a basic (see “Introduction”) subset of to K
n
is again basic. 相似文献