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1.
Bent functions have many applications in the fields of coding theory, communications and cryptography. This paper studies
the constructions of bent functions having the form
for odd n and
for even n, over the finite field
of odd characteristic p, where
. Based on the irreducibility of some polynomials on
, we focus on characterizing the bent functions for n=p
v
q
r
and n=2p
v
q
r
, where
is an odd prime and p a primitive root modulo q
2. Moreover, the enumerations of those functions are also considered.
Partially supported by the NSF of China under Grants No. 60603012 and No. 60573053. 相似文献
2.
Let be independent and identically distributed random variables with heavy-tailed distributions. Consider a sequence of random
weights , independent of and focus on the weighted sums , where μ involves a suitable centering. We establish sufficient conditions for these weighted sums to converge to non-trivial limit
processes, as n→∞, when appropriately normalized. The convergence holds, for example, if is strictly stationary, dependent, and W
1 has lighter tails than U
1. In particular, the weights W
j
s can be strongly dependent. The limit processes are scale mixtures of stable Lévy motions. We establish weak convergence
in the Skorohod J
1-topology. We also consider multivariate weights and show that they converge weakly in the strong Skorohod M
1-topology. The M
1-topology, while weaker than the J
1-topology, is strong enough for the supremum and infimum functionals to be continuous.
This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University
of Michigan and the NSF Grants BCS-0318209 and DMS-0505747 at Boston University. 相似文献
3.
We describe the Chow ring with rational coefficients of as the subring of invariants of a ring , relative to the action of the group of symmetries Sd. We compute by following a sequence of intermediate spaces for . 相似文献
4.
Norbert Hegyvári 《The Ramanujan Journal》2009,19(1):1-8
We investigate additive-multiplicative bases in
. Let
, s>2, and
. It is proved that
, provided min {|B|
s/2|A|(s−2)/2,|A|
s/2|B|(s−2)/2}>p
s/2.
This note is supported by “Balaton Program Project” and OTKA grants K 61908, K 67676. 相似文献
5.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
6.
Béatrice Vedel 《Journal of Fourier Analysis and Applications》2009,15(1):101-123
We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces
, s−n/2∈ℕ. They provide a confinement of the infrared divergence by decomposing
as a direct sum X
⊕
Y where X is a “small” space which carries the divergence and Y can be embedded in
. In the case of
we also construct such an orthonormal basis, which provides a confinement of the Mumford process. 相似文献
7.
J. Bagherian Ilia Ponomarenko A. Rahnamai Barghi 《Journal of Algebraic Combinatorics》2008,27(2):173-185
We introduce a concept of cyclotomic association scheme over a finite near-field
. It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with
. A sufficient condition on a cyclotomic scheme
that guarantee the inclusion
where
is a finite field with
elements, is given.
I. Ponomarenko partially supported by RFFI, grants 03-01-00349, NSH-2251.2003.1. 相似文献
8.
We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations
where u>e, W={(W
t
1,…,W
t
k
),0≤t≤1} is a standard k-dimensional Wiener process,
are functions of class
with bounded partial derivatives up to order 2, X
0
u
is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral.
The work is partially supported by DGES grant BFM2003-01345. 相似文献
9.
Richard Nickl 《Journal of Theoretical Probability》2009,22(1):38-56
Let μ
n
be a sequence of random finite signed measures on the locally compact group G equal to either
or ℝ
d
. We give weak conditions on the sequence μ
n
and on functions K such that the convolution product μ
n
*K, and its derivatives, converge in law, in probability, or almost surely in the Banach spaces
or L
p
(G). Examples for sequences μ
n
covered are the empirical process (possibly arising from dependent data) and also random signed measures
where
is some (nonparametric) estimator for the measure ℙ, including the usual kernel and wavelet based density estimators with
MISE-optimal bandwidths. As a statistical application, we apply the results to study convolutions of density estimators.
相似文献
10.
Saugata Basu 《Discrete and Computational Geometry》2008,40(4):481-503
Let
be an o-minimal structure over ℝ,
a closed definable set, and
the projection maps as depicted below:
For any collection
of subsets of
, and
, let
denote the collection of subsets of
where
. We prove that there exists a constant C=C(T)>0 such that for any family
of definable sets, where each A
i
=π
1(T∩π
2−1(y
i
)), for some y
i
∈ℝ
ℓ
, the number of distinct stable homotopy types amongst the arrangements
is bounded by
while the number of distinct homotopy types is bounded by
This generalizes to the o-minimal setting, bounds of the same type proved in Basu and Vorobjov (J. Lond. Math. Soc. (2) 76(3):757–776,
2007) for semi-algebraic and semi-Pfaffian families. One technical tool used in the proof of the above results is a pair of topological
comparison theorems reminiscent of Helly’s theorem in convexity theory. These theorems might be of independent interest in
the quantitative study of arrangements.
The author was supported in part by NSF grant CCF-0634907. 相似文献
11.
Álvaro Lozano-Robledo 《manuscripta mathematica》2008,126(3):393-407
Let S be an infinite set of rational primes and, for some p ∈ S, let be the compositum of all extensions unramified outside S of the form , for . If , let be the intersection of the fixed fields by , for i = 1, . . , n. We provide a wide family of elliptic curves such that the rank of is infinite for all n ≥ 0 and all , subject to the parity conjecture. Similarly, let be a polarized abelian variety, let K be a quadratic number field fixed by , let S be an infinite set of primes of and let be the maximal abelian p-elementary extension of K unramified outside primes of K lying over S and dihedral over . We show that, under certain hypotheses, the -corank of sel
p
∞(A/F) is unbounded over finite extensions F/K contained in . As a consequence, we prove a strengthened version of a conjecture of M. Larsen in a large number of cases. 相似文献
12.
Noboru Okazawa 《Mathematische Zeitschrift》2009,262(3):475-515
Several L
∞-estimates are obtained for in terms of and , where are determined by m. If p = 2, then the estimates are given with explicit constants. However, if p ≠ 2, it is difficult to derive explicit constants except in two simple cases. Applicability to PDE’s is illustrated. 相似文献
13.
Martin Kassabov 《Inventiones Mathematicae》2007,170(2):327-354
We construct explicit generating sets S
n
and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all n. 相似文献
14.
Let (X
t
)
t⩾0 be the n-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space having the Laplace–Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer
transform of the Poisson kernel and the Green function of the ball for the process (X
t
)
t⩾0. Under additional hypotheses we prove integral representations for the Poisson kernel. This yields explicit formulas in and spaces for the Poisson kernel and the Green function as well.
相似文献
15.
Emmanuel Rio 《Journal of Theoretical Probability》2009,22(1):146-163
We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in
for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am.
Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of
-norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular
Markov chain are given.
相似文献
16.
Peer Christian Kunstmann 《Archiv der Mathematik》2008,91(2):178-186
We consider the Stokes operator A on unbounded domains of uniform C
1,1-type. Recently, it has been shown by Farwig, Kozono and Sohr that – A generates an analytic semigroup in the spaces , 1 < q < ∞, where for q ≥ 2 and for q ∈ (1, 2). Moreover, it was shown that A has maximal L
p
-regularity in these spaces for p ∈ (1,∞). In this paper we show that ɛ + A has a bounded H
∞-calculus in for all q ∈ (1, ∞) and ɛ > 0. This allows to identify domains of fractional powers of the Stokes operator.
Received: 12 October 2007 相似文献
17.
Any algebraic surface in which is fibered in cubics, so that the generic fibre is a twisted cubic, gives rise to a curve Γ in a suitable compactification
X of the space of smooth rational cubics of In this paper the case n = 4 is addressed and the corresponding space X is studied. We apply our results to complete the classification of smooth, rational surfaces in ruled in cubics.
This work is within the framework of the national research project “Geometry on Algebraic Varieties” Cofin 2006 of MIUR. 相似文献
18.
In this paper, we prove that if a sequence of homeomorphisms , with bounded planar domains, of Sobolev space has uniformly equibounded distortions in EXP(Ω) and weakly converges to f in then the matrices A(x, f
j
) of the corresponding Laplace-Beltrami operators Γ-converge in the Orlicz–Sobolev space , where Q(t) = t
2log(e + t), to the matrix A(x, f) of the Laplace-Beltrami operator associated to f.
相似文献
19.
Luigi Santocanale 《Order》2007,24(3):155-179
20.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献