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1.
We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation $i\epsilon \varPsi _{t}+\frac{\epsilon^{2}}{2}\varPsi _{xx}+|\varPsi |^{2}\varPsi =0We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the
focusing nonlinear Schr?dinger equation
, ε
≪1, with analytic initial data of the form
is approximately described by a particular solution to the Painlevé-I equation.
相似文献
2.
3.
Hans Volkmer 《The Ramanujan Journal》2008,16(3):235-245
Ramanujan’s sequence {y
n
}
n=0∞ defined by
is expanded in factorial series derived from a series representing the Lambert W function. As a corollary, it is shown that the sequence {y
n
} is completely monotonic.
相似文献
4.
Alina Sîntămărian 《Numerical Algorithms》2007,46(2):141-151
The purpose of this paper is to evaluate the limit γ(a) of the sequence , where a ∈ (0, + ∞ ).
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5.
Dmitrii Zholud 《Extremes》2009,12(1):1-17
Let (ξ
i
, i ≥ 1) be a sequence of independent standard normal random variables and let be the corresponding random walk. We study the renormalized Shepp statistic and determine asymptotic expressions for when u,N and T→ ∞ in a synchronized way. There are three types of relations between u and N that give different asymptotic behavior. For these three cases we establish the limiting Gumbel distribution of when T,N→ ∞ and present corresponding normalization sequences.
相似文献
6.
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
7.
Liselott Flodén Anders Holmbom Marianne Olsson Nils Svanstedt 《Annali dell'Universita di Ferrara》2007,53(2):217-232
Reiterated homogenization is studied for divergence structure parabolic problems of the form . It is shown that under standard assumptions on the function a(y
1,y
2,t,ξ) the sequence of solutions converges weakly in to the solution u of the homogenized problem .
相似文献
8.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
, where
is a continuous function with
,
runs over
, the set of Farey fractions of order Q in the unit interval [0,1] and
are consecutive elements of
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
9.
10.
Among various functions used to count the factorizations of an integer n, we consider here the number of ways of writing n as an ordered product of primes, which, if
, is equal to the multinomial coefficient
. The function P(s)=∑
p prime
p
−s
, sometimes called the prime zeta function, plays an important role in the study of the function h. We denote by λ=1.399433… the real number defined by P(λ)=1. The mean value of the function h satisfies
. In this paper, we study how large h(n) can be. We prove that there exists a constant C
1>0 such that, for all n≥3,
holds. We also prove that there exists a constant C
2 such that, for all n≥3, there exists m≤n satisfying
. Let us call h-champion an integer N such that M<N implies h(M)<h(N). S. Ramanujan has called highly composite a τ-champion number, where τ(n)=∑
d∣n
1 is the number of divisors of n. We give several results about the number of prime factors of an h-champion number N, about the exponents in the standard factorization into primes of such an N and about the number Q(X) of h-champion numbers N≤X. At the end of the paper, several open problems are listed.
Recherche partiellement financée par le CNRS, Institut Camille Jordan, UMR 5208 et par l’action de coopération franco-algérienne
01 MDU 514, Arithmétique, Géométrie Algébrique et Applications. 相似文献
11.
12.
Jun Wu 《Monatshefte für Mathematik》2006,149(3):259-264
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
13.
H. Rindler 《Monatshefte für Mathematik》2006,147(3):265-272
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
14.
15.
Vladimir Markovic 《Inventiones Mathematicae》2007,168(3):523-566
In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms
of that surface. More precisely, let denote the standard projection of the group of homeomorphisms to the mapping class group of a closed surface M of genus g>5. We show that there is no homomorphism , such that is the identity. This answers a question by Thurston (see [11]).
Mathematics Subject Classification (2000) Primary 20H10, 37F30 相似文献
16.
Jean-Paul Bézivin 《manuscripta mathematica》2008,126(1):41-47
Résumé Let with |q| > 1, and a be a rational number such that a
2 is not equal to for . In this note, we prove that the sum is irrational. 相似文献
17.
Adrien Dubouloz 《Transformation Groups》2009,14(3):531-539
In 1996 Makar-Limanov established that the Koras–Russell cubic threefold
is not isomorphic to the affine space because it admits fewer algebraic -actions than . More precisely, he showed that the subalgebra ML(X) of its coordinate ring consisting of regular functions invariant under all algebraic -actions on X is isomorphic to the polynomial ring . In contrast, . Here we show that . 相似文献
18.
A new necessary and sufficient condition for the row
-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the
extended vertical linear complementarity problem under the row
-property, which extend the error bounds given in Chen and Xiang (Math. Program. 106:513–525, 2006) and Mathias and Pang (Linear Algebra Appl. 132:123–136, 1990) for the P-matrix linear complementarity problem, respectively. We show that one of the new error bounds is sharper than
the other, and it can be computed easily for some special class of the row
-property block matrix. Numerical examples are given to illustrate the error bounds.
The work was in part supported by a Grant-in-Aid from Japan Society for the Promotion of Science, and the National Natural
Science Foundation of China (10671010). 相似文献
19.
Juan Dávila Manuel del Pino Monica Musso Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2008,32(4):453-480
We consider the elliptic problem Δu + u
p
= 0, u > 0 in an exterior domain, under zero Dirichlet and vanishing conditions, where is smooth and bounded in , N ≥ 3, and p is supercritical, namely . We prove that this problem has infinitely many solutions with slow decay
at infinity. In addition, a solution with fast decay
O(|x|2-N
) exists if p is close enough from above to the critical exponent. 相似文献
20.
Ursula Hamenstädt 《Inventiones Mathematicae》2009,175(3):545-609
We construct a geometric model for the mapping class group of a non-exceptional oriented surface S of genus g with k punctures and use it to show that the action of on the compact metrizable Hausdorff space of complete geodesic laminations for S is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of . 相似文献