共查询到20条相似文献,搜索用时 31 毫秒
1.
V. L. Vereschagin 《Theoretical and Mathematical Physics》2009,160(3):1229-1237
We apply the Laplace cascade method to systems of discrete equations of the form u i+1,j+1 = f(u i+1,j , u i,j+1, u i,j , u i,j?1), where u ij , i, j ∈ ?, is an element of a sequence of unknown vectors. We introduce the concept of a generalized Laplace invariant and the related property that the systems is “of the Liouville type.” We prove a series of statements about the correctness of the definition of the generalized invariant and its applicability for seeking solutions and integrals of the system. We give some examples of systems of the Liouville type. 相似文献
2.
In the space {ol
p
2
of vector sequences, we consider the symmetric operatorL generated by the expression (lu)j:=Bj
uj+1+Aj
uj+
B
j−1/*
uj−1, whereu−1 = 0,u
0,u
1, … ∈ ℂ
p
,A
j andB
j arep × p matrices with entries from ℂ,A
j
*
=Aj, and the inversesB
j
−1
(j = 0, 1, …) exist. We state a necessary and sufficient condition for the deficiency numbers of the operatorL to be maximal; this corresponds to the completely indefinite case for the expressionl. Tests for incomplete indefiniteness and complete indefiniteness forl in terms of the coefficientsA
j andB
j are derived.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 709–716, May, 1998.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00333. 相似文献
3.
We discuss local solvability of operators of the form
where theV
j
are left-invariant vector fields on the Heisenberg group such that [V
j
,V
j+n
]=U for 1≤j≤n andA=(a
jk
)=A
1+iA
2 is a complex symmetric matrix satisfying the “cone condition” |A
2|≤CA
1.
The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis”
and the TMR network “Harmonic Analysis”. 相似文献
4.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,133(3):1308-1313
Let {Xi, Yi}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn(j) = max0≤k≤n-j (Xk+1 + ... Xk+j)Ik,j, where Ik,k+j = I{Yk+1 < ⋯ < Yk+j} denotes the indicator function for the event in brackets, 1 ≤ j ≤ n. Let Ln be the largest index l ≤ n for which Ik,k+l = 1 for some k = 0, 1, ..., n - l. The strong law of large numbers for “the maximal gain over the longest increasing runs,”
i.e., for Mn(Ln) has been recently derived for the case where X1 has a finite moment of order 3 + ε, ε > 0. Assuming that X1 has a finite mean, we prove for any a = 0, 1, ..., that the s.l.l.n. for M(Ln - a) is equivalent to EX
1
3+a
I{X1 > 0} < ∞. We derive also some new results for the a.s. asymptotics of Ln. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 179–189. 相似文献
5.
Assume that the leaves of a planted plane tree are enumerated from left to right by 1, 2, .... Thej-ths-turn of the tree is defined to be the root of the (unique) subtree of minimal height with leavesj, j+1, ...,j+s−1. If all trees withn nodes are regarded equally likely, the average level number of thej-ths-turn tends to a finite limitα
s
(j), which is of orderj
1/2. Thej-th ”s-hyperoscillation”α
1(j)−α
s+1(j) is given by 1/2α
1(s)+O(j
−1/2) and therefore tends (forj → ∞) to a constant behaving like √8/π·s
1/2 fors → ∞. These results are obtained by setting up appropriate generating functions, which are expanded about their (algebraic)
singularities nearest to the origin, so that the asymptotic formulas are consequences of the so-called Darboux-Pólyamethod. 相似文献
6.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):163-166
Summary LetX be a non-negative random variable with probability distribution functionF. SupposeX
i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X
i+1,n−Xi,n) and (n−j)(X
j+1,n−Xj,n) for somei, j andn, (1≦i<j<n).
The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil. 相似文献
7.
Maciej Paluszyński Hrvoje Šikić Guido Weiss Shaoliang Xiao 《Journal of Geometric Analysis》2001,11(2):311-342
A tight frame wavelet ψ is an L
2(ℝ) function such that {ψ jk(x)} = {2j/2
ψ(2
j
x −k), j, k ∈ ℤ},is a tight frame for L
2 (ℝ).We introduce a class of “generalized low pass filters” that allows us to define (and construct) the subclass of MRA tight
frame wavelets. This leads us to an associated class of “generalized scaling functions” that are not necessarily obtained
from a multiresolution analysis. We study several properties of these classes of “generalized” wavelets, scaling functions
and filters (such as their multipliers and their connectivity). We also compare our approach with those recently obtained
by other authors. 相似文献
8.
We analyze the stability and solvability of the Cauchy problem for the equations λu
jt
− u
jtxx
= βu
jxx
− αu
jxxxx
+γu
j
+ f
j
, which appear in filtration theory and are defined on a finite connected directed graph with continuity and flow balance
conditions at its vertices. 相似文献
9.
Sets of Double and Triple Weights of Trees 总被引:1,自引:0,他引:1
Elena Rubei 《Annals of Combinatorics》2011,15(4):723-734
Let T be a weighted tree with n leaves numbered by the set {1, . . . , n}. Let D
i, j
(T) be the distance between the leaves i and j. Let
Di,j,k(T) = \frac12(Di,j(T)+Dj,k(T)+Di,k(T)){{D_{i,j,k}(T) = \frac{1}{2}(D_{i,j}(T)+D_{j,k}(T)+D_{i,k}(T))}} . We will call such numbers “triple weights” of the tree. In this paper, we give a characterization, different from the previous
ones, for sets indexed by 2-subsets of a n-set to be double weights of a tree. By using the same ideas, we find also necessary and sufficient conditions for a set of
real numbers indexed by 3-subsets of an n-set to be the set of the triple weights of a tree with n leaves. Besides we propose a slight modification of Saitou-Nei’s Neighbour-Joining algorithm to reconstruct trees from the
data D
i, j
. 相似文献
10.
We study the boundary value problem wt=ℵ0Δw+ℵ1w-ℵ2w|w|2,w|∂Ω0=0 in the domain Ω0={(x,y):0 ≤ x ≤ l1,0 ≤ y ≤ l2}. Here, w is a complex-valued function, Δ is the laplace operator, and ℵj, j=0,1,2, are complex constants withRe ℵj > 0. We show that under a rather general choice of the parameters l1 and l2, the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely asRe ℵ0 → 0 andRe ℵ0 → 0.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 205–220, November, 2000. 相似文献
11.
The method of cyclic relaxation for the minimization of a function depending on several variables cyclically updates the value
of each of the variables to its optimum subject to the condition that the remaining variables are fixed.
We present a simple and transparent proof for the fact that cyclic relaxation converges linearly to an optimum solution when
applied to the minimization of functions of the form
for a
i,j
,b
i
,c
i
∈ℝ≥0 with max {min {b
1,b
2,…,b
n
},min {c
1,c
2,…,c
n
}}>0 over the n-dimensional interval [l
1,u
1]×[l
2,u
2]×⋅⋅⋅×[l
n
,u
n
] with 0<l
i
<u
i
for 1≤i≤n. Our result generalizes several convergence results that have been observed for algorithms applied to gate- and wire-sizing
problems that arise in chip design. 相似文献
12.
Paul C. Fife 《Annali di Matematica Pura ed Applicata》1971,90(1):99-147
Summary The paper treats elliptic operators of the form L(ɛ∂1, ..., ɛ∂n), where L is a polynomial in a variables of order 2m1, and ɛ is a small parameter. Solutionsu
ɛ of Lu=0 in a half space satisfyng conditions Bj(ɛ∂1, ɛ∂2, ..., ɛ∂n)u=ɛγjϕj(x)(j=1, ..., m1) on the boundary are constructed and estimated using H?lder norms, Poisson kernels, and an elaborate potential theory. Properties
of the interior limit u0=u
ɛ(κ) are studied. The paper is preparatory to a detailed investigation of Schauder estimates for such problems with variables
coefficients.
Supported in part by N. S. F. Grant GP-11660.
Entrata in Redazione il 9 gennaio 1971. 相似文献
13.
Peter Adams Elizabeth J. Billington Darryn E. Bryant Saad I. El-Zanati 《Graphs and Combinatorics》2002,18(1):31-51
The Hamilton-Waterloo problem asks for a 2-factorisation of K
v
in which r of the 2-factors consist of cycles of lengths a
1,a
2,…,a
t
and the remaining s 2-factors consist of cycles of lengths b
1,b
2,…,b
u
(where necessarily ∑
i=1
t
a
i
=∑
j=1
u
b
j
=v). In this paper we consider the Hamilton-Waterloo problem in the case a
i
=m, 1≤i≤t and b
j
=n, 1≤j≤u. We obtain some general constructions, and apply these to obtain results for (m,n)∈{(4,6),(4,8),(4,16),(8,16),(3,5),(3,15),(5,15)}.
Received: July 5, 2000 相似文献
14.
Paul Corazza 《Archive for Mathematical Logic》2007,46(2):61-72
We describe a fairly general procedure for preserving I3 embeddings j: V
λ → V
λ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency was established assuming an I1 embedding.
相似文献
15.
Saharon Shelah 《Israel Journal of Mathematics》1987,60(3):345-380
We prove that suitable iteration does not collapse ℵ1 [and does not add reals], i.e., that in such iteration, certain sealing of maximal antichains of stationary subsets ofω
1 is allowed. As an application, e.g., we prove from supercompact hypotheses, mainly, the consistency of: ZFC + GCH + “for
some stationary setS ⊆ω
1, {ie345-1}(ω
1)/(D
ω
1 +S) is the Levy algebra” (i.e., the complete Boolean Algebra corresponding to the Levy collapse Levy (ℵ0,<ℵ2) (and we can add “a variant of PFA”) and the consistency of the same, with “Ulam property” replacing “Levy algebra”). The
paper assumes no specialized knowledge (if you agree to believe in the semi-properness iteration theorem and RCS iteration).
This research was partially supported by the NSF.
This paper was largely written during the author’s visit at Cal Tech around the end of April 1985. The author would like to
thank M. Foreman, A. Kekris and H. Woodin for their hospitality. 相似文献
16.
Sándor Csörgő 《Acta Appl Math》2007,96(1-3):159-174
We consider the generalized convolution powers G
α
*u
(x) of an arbitrary semistable distribution function G
α
(x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G
α
(k,j)(x;u)=∂
k+j
G
α
*u
(x)/∂
x
k
∂
u
j
, x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in
merge theorems from the domain of geometric partial attraction of semistable laws.
An erratum to this article can be found at 相似文献
17.
For an additive subgroup G of a field F of characteristic zero, a Lie algebra B(G) of Block type is defined with basis {Lα,i| α∈G, i∈Z+} and relations [Lα,i, Lβ,j] = (β-α)Lα+β,i+j+(αj-βi)Lα+β,Lα+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B(G)0^*(the dual space of B(G)0 = span{L0,i|i∈Z+}), a Verma B(G)-module M(∧,λ) is defined, and the irreducibility of M(A,λ) is completely determined. 相似文献
18.
19.
A new generalized Radon transform R
α, β
on the plane for functions even in each variable is defined which has natural connections with the bivariate Hankel transform,
the generalized biaxially symmetric potential operator Δ
α, β
, and the Jacobi polynomials Pk(b, a)(t)P_{k}^{(\beta,\,\alpha)}(t). The transform R
α, β
and its dual Ra, b*R_{\alpha,\,\beta}^{\ast} are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for R
α, β
for functions in
La, bp(\mathbbR2+)L_{\alpha,\,\beta}^{p}(\mathbb{R}^{2}_{+}) are obtained in terms of the bivariate Hankel–Riesz potential. Moreover, the transform R
α, β
is used to represent the solutions of the partial differential equations Lu:=?j=1majDa, bju=fLu:=\sum_{j=1}^{m}a_{j}\Delta_{\alpha,\,\beta}^{j}u=f with constant coefficients a
j
and the Cauchy problem for the generalized wave equation associated with the operator Δ
α, β
. Another application is that, by an invariant property of R
α, β
, a new product formula for the Jacobi polynomials of the type Pk(b, a)(s)C2ka+b+1(t)=còòPk(b, a)P_{k}^{(\beta,\,\alpha)}(s)C_{2k}^{\alpha+\beta+1}(t)=c\int\!\!\int P_{k}^{(\beta,\,\alpha)} is obtained. 相似文献
20.
In this paper, a weak Cartan-type second theorem for holomorphic curve f : C→P^n(C) intersecting hypersurfaces Dj, 1≤j≤q, in P^n(C) in general position with degree dj is given as follows: For every ε〉0, there exists a positive integer M such that ||(q - (n + 1) ε)Tf(r)≤∑j^q=1 1/dj Nf^M(r,Dj)+o(Tf(r)), where "||" means the estimate holds for all large r outside a set of finite Lebesgue measure. 相似文献