共查询到20条相似文献,搜索用时 31 毫秒
1.
Bent and almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are studied in this paper. By calculating certain exponential sum and using a technique due to Hou (Finite Fields Appl 10:566–582,
2004), we obtain a degree bound for quasi-bent functions, and prove that almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are equivalent to a degenerate quadratic form. From the viewpoint of relative difference sets, we also characterize bent
functions on
\mathbbZp2{\mathbb{Z}_p^2} in two classes of M{\mathcal{M}} ’s and PS{\mathcal{PS}} ’s, and show that the graph set corresponding to a bent function on
\mathbbZp2{\mathbb{Z}_p^2} can be written as the sum of a graph set of M{\mathcal{M}} ’s type bent function and another group ring element. By using our characterization and some technique of permutation polynomial,
we obtain the result: a bent function must be of M{\mathcal{M}} ’s type if its corresponding set contains more than (p − 3)/2 flats. A problem proposed by Ma and Pott (J Algebra 175:505–525, 1995) is therefore partially answered. 相似文献
2.
Enumerating Constrained Non-crossing Minimally Rigid Frameworks 总被引:2,自引:1,他引:1
David Avis Naoki Katoh Makoto Ohsaki Ileana Streinu Shin-ichi Tanigawa 《Discrete and Computational Geometry》2008,40(1):31-46
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid
bar-and-joint frameworks under edge constraints, which we call constrained non-crossing Laman frameworks, on a given set of
n points in the plane. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph
in O(n
4) time and O(n) space, or, with a slightly different implementation, in O(n
3) time and O(n
2) space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is
connected by flips which preserve the Laman property.
D. Avis’s research was supported by NSERC and FQRNT grants.
N. Katoh’s, M. Ohsaki’s and S.-i. Tanigawa’s research was supported by NEXT Grant-in-Aid for Scientific Research on priority
areas of New Horizons in Computing.
I. Streinu’s research was supported by NSF grant CCF-0430990 and NSF-DARPA CARGO CCR-0310661. 相似文献
3.
Thomas H. Wolff 《Journal d'Analyse Mathématique》2007,102(1):371-394
Highly oscillatory bounded solutions of div(∇u|∇u|
p−2) = 0 are constructed when p > 2. Fatou’s theorem is shown to fail for this equation.
Tom Wolff wrote this paper in 1984, but he never published it. With his family’s permission, we have edited it for publication
here. Except for the shorter proof of Lemma 2.1 and the citations of [1] and [12], our alterations to the paper have mostly
been typographical. We thank Juan Manfredi for help on Section 3. 相似文献
4.
H. Aleksanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2012,47(2):86-96
We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions
are found for system’s normalization to guarantee almost everywhere convergence, and convergence in L
p
(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees
convergence almost everywhere for functions from L
1(T), or uniform convergence for continuous functions. 相似文献
5.
Xue Gong Sun 《数学学报(英文版)》2010,26(1):155-160
Consider all the arithmetic progressions of odd numbers, no term of which is of the form 2^k + p, where k is a positive integer and p is an odd prime. ErdSs ever asked whether all these progressions can be obtained from covering congruences. In this paper, we characterize all arithmetic progressions in which there are positive proportion natural numbers that can be expressed in the form 2^k + p, and give a quantitative form of Romanoff's theorem on arithmetic progressions. As a corollary, we prove that the answer to the above Erdos problem is affirmative. 相似文献
6.
Yong Hua Mao 《数学学报(英文版)》2009,25(12):2055-2064
Lp Poincare inequalities for general symmetric forms are established by new Cheeger's isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger's constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied. 相似文献
7.
Khalid KOUFANY 《数学学报(英文版)》2006,22(5):1467-1472
Let Ω be a symmetric cone. In this note, we introduce Hilbert's projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g(Ω) = Ω and a real number p, |p| 〉 1, there exists a unique element x ∈ Ω satisfying g(x) = x^p. 相似文献
8.
Siegfried Böcherer Shoyu Nagaoka 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2010,80(2):227-231
J.-P. Serre proved that the congruences for elliptic modular forms mod p
m
descend to those of weights mod p
m−1(p−1). Later, this result was generalized by T. Ichikawa to the case of Siegel modular forms. In this note we use elementary
methods to reduce Ichikawa’s result to a similar question about elliptic modular forms with level, where results of Katz are
available. 相似文献
9.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
10.
Masayoshi Takeda 《Journal of Theoretical Probability》2011,24(4):1097-1129
We establish a large deviation principle for the occupation distribution of a symmetric Markov process with Feynman–Kac functional.
As an application, we show the L
p
-independence of the spectral bounds of a Feynman–Kac semigroup. In particular, we consider one-dimensional diffusion processes
and show that if no boundaries are natural in Feller’s boundary classification, the L
p
-independence holds, and if one of the boundaries is natural, the L
p
-independence holds if and only if the L
2-spectral bound is non-positive. 相似文献
11.
LetA={a
1, …,a
k} and {b
1, …,b
k} be two subsets of an abelian groupG, k≤|G|. Snevily conjectured that, when |G| is odd, there is a numbering of the elements ofB such thata
i+b
i,1≤i≤k are pairwise distinct. By using a polynomial method, Alon affirmed this conjecture for |G| prime, even whenA is a sequence ofk<|G| elements. With a new application of the polynomial method, Dasgupta, Károlyi, Serra and Szegedy extended Alon’s result to
the groupsZ
p
r
andZ
p
rin the casek<p and verified Snevily’s conjecture for every cyclic group. In this paper, by employing group rings as a tool, we prove that
Alon’s result is true for any finite abelianp-group withk<√2p, and verify Snevily’s conjecture for every abelian group of odd order in the casek<√p, wherep is the smallest prime divisor of |G|.
This work has been supported partly by NSFC grant number 19971058 and 10271080. 相似文献
12.
Konstantin M. Dyakonov 《Journal d'Analyse Mathématique》2002,86(1):247-269
Given an inner function θ, let {Kskθ/p}:= Hp ∩θ {Hsk0/p} be the corresponding star-invariant subspace of the Hardy spaceH
p. We show that, unless θ is a finite Blaschke product, the zero sets for K
θ
p
-spaces are different for different p’s. We also investigate the (non)stability of zero sets when passing from {Kskθ/p} to {Ksku/q}, whereq > p and u is an inner function divisible by θ. This problem is motivated by the Beurling-Malliavin multiplier theorem for entire
functions, and we solve it (at least in a natural special case) by proving an appropriate multiplier theorem for K
θ
p
. 相似文献
13.
We study Schneider’s p-adic continued fraction algorithms. For p=2, we give a combinatorial characterization of rational numbers that have terminating expansions. For arbitrary p, we give data showing that rationals with terminating expansions are relatively rare. Finally, we prove an analogue of Khinchin’s
theorem. 相似文献
14.
We transfer a large part of the circle of theorems characterizing the generalization of classical H∞ known as ‘weak* Dirichlet algebras’, to Arveson’s very general noncommutative setting of subalgebras of finite von Neumann
algebras. This solves the long-standing open question of the equivalence of principles such as Szeg?’s theorem, the weak*
density of A + A*, and so on, within the noncommutative setting. The techniques should also be useful in future developments in noncommutative
Hp theory. 相似文献
15.
Jie Xiao 《Archiv der Mathematik》1997,68(5):398-406
Let H
p, p ∈ (0, ∞], BMOA and B
a, a ∈ (0, ∞) be the classical p-Hardy, analytic BMO(∂) (bounded mean oscillation on the unit circle) and a-Bloch space on the unit disk. In this paper, we prove that the Cesàro-type operator: C
α, α ∈ (−1, ∞) is bounded on H
p, p ∈ (0, ∞) and on B
a, a ∈ (1, ∞), but, unbounded on H
∞, BMOA and B
a, a ∈ (0, 1]. In particular, we give an answer to the Stempak’s open problem. 相似文献
16.
Jarosaw Górnicki 《Rendiconti del Circolo Matematico di Palermo》1997,46(1):89-118
In this paper we study in Banach spaces the existence of fixed points of (nonlinear) asymptotically regular semigroups. We
establish for these semigroups some fixed point theorems in spaces with weak uniform normal structure, in a Hilbert space,
inL
p
spaces, in Hardy spacesH
p
and in Sobolev spacesW
r.p
for 1<p<∞ andr≥0, in spaces with Lifshitz’s constant greater than one. These results are the generalizations of [8, 10, 16]. 相似文献
17.
In this paper we give an effective version of the Bombieri–Vinogradov theorem of Bombieri, Friedlander, and Iwaniec. As applications,
we refine Chen’s theorem on primes with difference h for h ≤ x
1/56, with a consequence on integers of the form p + 2
k
. 相似文献
18.
Armin Rainer 《Israel Journal of Mathematics》2011,184(1):157-182
We prove that the roots of a definable C
∞ curve of monic hyperbolic polynomials admit a definable C
∞ parameterization, where ‘definable’ refers to any fixed o-minimal structure on (ℝ,+, ·). Moreover, we provide sufficient
conditions, in terms of the differentiability of the coefficients and the order of contact of the roots, for the existence
of C
p
(for p ∈ ℕ) arrangements of the roots in both the definable and the non-definable case. These conditions are sharp in the definable
and, under an additional assumption, also in the non-definable case. In particular, we obtain a simple proof of Bronshtein’s
theorem in the definable setting. We prove that the roots of definable C
∞ curves of complex polynomials can be desingularized by means of local power substitutions t ↦ ±t
N
. For a definable continuous curve of complex polynomials we show that any continuous choice of roots is actually locally
absolutely continuous. 相似文献
19.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
20.
Brennan’s conjecture in univalent function theory states that if τ is any analytic univalent transform of the open unit disk
\mathbbD{\mathbb{D}} onto a simply connected domain G and −1/3 < p < 1, then 1/(τ′)
p
belongs to the Hilbert Bergman space of all analytic square integrable functions with respect to the area measure. We introduce
a class of analytic function spaces L2a(mp){L^2_a(\mu _p)} on G and prove that Brennan’s conjecture is equivalent to the existence of compact composition operators on these spaces for every
simply connected domain G and all p ? (-1/3,1){p\in(-1/3,1)}. Motivated by this result, we study the boundedness and compactness of composition operators in this setting. 相似文献