共查询到20条相似文献,搜索用时 109 毫秒
1.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
2.
{p
mn
} -
00>0, (1, 1) (1.1) (1.2). {s
mn
} J
p
- ( bJ
p
-lims
mn
=), (1.3) 0<x,y<1 p
s
(, )/p(x, y) x, y 1-. {r
mn
} - , (1.5) 0<, <1. N
rp
- , (1.6). , bJ
p
-lims
mn
= bJ
q
-lim(N
rps)
mn
=. J
p
- . , . 相似文献
3.
In this paper solutions in series form for the stresses due to a nucleus of thermo-elastic strain in an infinite elastic solid in the presence of a spherical cavity and also in an elastic solid sphere have been found.
Nomenclature x, y, z Cartesian coordinates; - r, , spherical polar coordinates; - u x ,u y ,u z components of displacement in Cartesian coordinates; - u r ,u ,u components of displacement in spherical coordinates; - r , , , , r , components of stress in spherical coordinates; - E coefficient of elasticity in stress; - G coefficient of elasticity in shear; - coefficient of linear expansion; - Poisson's ration The following nomenclature has been used in this paper: 相似文献
Zusammenfassung Die thermischen Spannungen in einem festen Körper unendlicher Ausdehnung, welcher einen sphärischen Hohlraum enthält, sind bei einer Temperatur von 0°C in Gegenwart eines erhitzten Elementes, das sich in endlichem Abstand vom Hohlraum befindet, hergeleitet worden, wobei zahlenmässige Angaben für die Spannungen und Verschiebungen an der Oberfläche des Hohlraums gemacht werden können. Die Ergebnisse sind mit den entsprechenden, für den zweidimensionalen Fall gültigen Zahlenwerten verglichen worden. Ferner was es möglich, auch für das Problem einer festen Kugel von der Temperatur 0°C und einem erhitzten Kern in ihrem Innern eine Lösung zu finden.
Nomenclature x, y, z Cartesian coordinates; - r, , spherical polar coordinates; - u x ,u y ,u z components of displacement in Cartesian coordinates; - u r ,u ,u components of displacement in spherical coordinates; - r , , , , r , components of stress in spherical coordinates; - E coefficient of elasticity in stress; - G coefficient of elasticity in shear; - coefficient of linear expansion; - Poisson's ration The following nomenclature has been used in this paper: 相似文献
4.
Chang -Pao Chen 《Analysis Mathematica》1996,22(2):99-112
f(x,y)
jk
. , {c
jk} , f(x, )(, ) [0,1)х[0,1) , - (0,0). , , f, - f. , , , [1] . . - [5] [6].
This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026. 相似文献
This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026. 相似文献
5.
Michel Sebille 《Designs, Codes and Cryptography》2001,22(3):215-219
In 1987, Teirlinckproved that if t and are two integers such that v t(mod(t + 1)!(2t+1) and v t + 1 >0, then there exists a t - (v, t + 1, (t + 1)!(2t+1)) design. We prove that if there exists a (t+1)-(v,k,)design and a t-(v-1,k-2, (k-t-1)/(v-k+1))design with t 2, then there exists a t-(v+1,k, (v-t+1)(v-t)/
(v-k+1)(k-t))design. Using this recursive construction, we prove that forany pair (t,n) of integers (t 2and n 0), there exists a simple non trivial t-(v,k,) design having an automorphism groupisomorphic to n
2. 相似文献
6.
It is proved that if S, T are two elliptic Dirichlet operators on an ordered Hilbert space such that the excessive (resp. coexcessive) elements with respect to S and T are the same then there exists > 0 with T = S. Particularly if , are two elliptic Dirichlet forms on L2 ( ) having the same domain of definition and the same -excessive (resp. -coexcessive) elements for any > 0 then = . 相似文献
7.
V. F. Gapoškin 《Analysis Mathematica》1980,6(2):105-119
a
k
f
k
, f
k
L
2, w-, (2), w(n) — .
a
k
f
k
N {a
k
}l
2, {a
k
}l
2 ( 1, 2, 1a, 2a). ( 2) [8]. , {a
k
} w-. 相似文献
8.
Summary The aim of this paper is to generalize the well-known Eulerian numbers, defined by the recursion relationE(n, k) = (k + 1)E(n – 1, k) + (n – k)E(n – 1, k – 1), to the case thatn is replaced by . It is shown that these Eulerian functionsE(, k), which can also be defined in terms of a generating function, can be represented as a certain sum, as a determinant, or as a fractional Weyl integral. TheE(, k) satisfy recursion formulae, they are monotone ink and, as functions of , are arbitrarily often differentiable. Further, connections with the fractional Stirling numbers of second kind, theS(, k), > 0, introduced by the authors (1989), are discussed. Finally, a certain counterpart of the famous Worpitzky formula is given; it is essentially an approximation ofx
in terms of a sum involving theE(, k) and a hypergeometric function.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
9.
We prove that if aC
1 smooth change of variable : generates a bounded composition operatorff° in the spaceA
p()=L
p
,p2, then is linear (affine).We also prove that for a nonlinearC
1 mapping , the norms of exponentialse
i as Fourier multipliers inL
p
() tend to infinity (,||). In both results the condition C
1 is sharp, it cannot be replaced by the Lipschitz condition. 相似文献
10.
S. Sivaganesan 《Annals of the Institute of Statistical Mathematics》1993,45(1):187-199
Range of the posterior probability of an interval over the -contamination class ={=(1–)0+q:qQ} is derived. Here, 0 is the elicited prior which is assumed unimodal, is the amount of uncertainty in 0, andQ is the set of all probability densitiesq for which =(1–)0+q is unimodal with the same mode as that of 0. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1–)0 except in one interval (resp. two disjoint intervals) where it is constant. 相似文献
11.
Summary Let be a natural exponential family on and (V, ) be its variance function. Here, is the mean domain of andV, defined on , is the variance of . A problem of increasing interest in the literature is the following: Given an open interval and a functionV defined on , is the pair (V, ) a variance function of some natural exponential family? Here, we consider the case whereV is a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, ) to be such a variance function. These conditions are also sufficient for the class of third degree polynomials and certain subclasses of polynomials of higher degree. 相似文献
12.
А. В. Резцов 《Analysis Mathematica》1995,21(2):129-135
Q (.. , L). Q . P(Sr(2)) — 2 (S
r(2) (r — ). , M(P(S
r(m=sup{t(·)t(·)1:t P(S
r(2)),t 0}. , /4+(1)M(P(S
r(2)))/r
215/17+(1)(r+). (Q), Q L. 相似文献
13.
Dr. Richard Koch 《Monatshefte für Mathematik》1977,83(2):133-146
Let ={e(u)|uI} be a one-parameter family of straight lines forming a ruledC
r-2-surface E
n (n2,r1) without singular generatorse(u) (uI). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces E
n (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u) under the minimal assumptions thate(u)E
n
(n2) be noncylindrical andr1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces E
n are proved.
Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag 相似文献
Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag 相似文献
14.
M. B. Nathanson 《Acta Mathematica Hungarica》2000,87(3):179-195
Let A be a set of positive integers with gcd (A) = 1, and let p
A
(n) be the partition function of A. Let c
0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p
A
(n)/c
0 n and lim sup log p
A
(n)/c
0 n . In particular, if A has asymptotic density > 0, then log p
A
(n) c0n. Conversely, if > 0 and log p
A
(n) c
0 n, then the set A has asymptotic density . 相似文献
15.
Ulrike Tillmann 《K-Theory》1992,6(1):57-86
TheK-theory of the group algebra [] for a countable, discrete group is defined in terms of the simplicial ring of smooth simplices on [], where [] is given the fine topology with respect to its finite-dimensional, linear subspaces. The assembly map for this theory :K
*
B K
* [] is studied and shown to be a rational injection. The proof uses the Connes-Karoubi Chern character fromK-theory of Banach algebras to cyclic homology, here generalized to any fine topological algebra, and proved to be multiplicative. 相似文献
16.
R. K. Getoor 《Potential Analysis》1995,4(1):79-100
SupposeX is a Borel right process andm is a -finite excessive measure forX. Given a positive measure not chargingm-semipolars we associate an exact multiplicative functionalM(). No finiteness assumptions are made on . Given two such measures and ,M()=M() if and only if and agree on all finely open measurable sets. The equation (q–L)u+u=f whereL is the generator of (a subprocess of)X may be solved for appropriatef by means of the Feynman-Kac formula based onM(). Both uniqueness and existence are considered.Supported in part by NSF Grant DMS 92-24990. 相似文献
17.
Alan D. Sokal 《Probability Theory and Related Fields》1981,56(4):537-548
Summary Let (, , ) be a perfect probability space with countably generated, and let IB be a family of sub--fields of . Under a countability condition on the family IB, I show that there exists a family {}IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the
can furthermore be chosen to be everywhere proper. It follows that in the Dobrushin-Lanford-Ruelle formulation of the statistical mechanics of classical lattice systems, every (perfect) probability measure is a Gibbs measure for some specification.Research supported in part by NSF PHY-78-23952NSF Predoctoral Fellow (1976–79) and Danforth Fellow (1979–81). 相似文献
18.
19.
Andriy Panasyuk 《Annals of Global Analysis and Geometry》1997,15(4):313-324
Given a complex manifold Mi, structures of Poisson algebras on (Mi)=C(Mi,C) which are associated with a nondegenerate -closed (2,0)-form i on Mi are considered. It is shown that every isomorphism of Poisson structures (M1) (M2) is generated by a biholomorphic map :M2 M1 such that 2 = *1 相似文献
20.
R. Ž. Nurpeisov 《Analysis Mathematica》1989,15(2):127-143
H
(G), f(g)H
(G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp
n=, , ,n .. . , 117 234 . . - 相似文献