共查询到20条相似文献,搜索用时 178 毫秒
1.
V. A. Slousch 《Journal of Mathematical Sciences》2003,115(2):2272-2278
Let A be a self-adjoint elliptic second-order differential operator, let (, ) be an inner gap in the spectrum of A, and let B(t) = A + tW
*
W, where W is a differential operator of higher order. Conditions are obtained under which the spectrum of the operator B(t) in the gap (, ) is either discrete, or does not accumulate to the right-hand boundary of the spectral gap, or is finite. The quantity N(, A, W, ), (, ), > 0 (the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to ) is considered. Estimates of N(, A, W, ) are obtained. For the perturbation W
*
W of a special form, the asymptotics of N(, A, W, ) as + is given. Bibliography: 5 titles. 相似文献
2.
Summary LetB=(B
t,t0) be a planar Brownian motion and let >0. For anyt0, the pointz=B
t is called a one-sided cone point with angle if there exist >0 and a wedgeW(,z) with vertexz and angle such thatB
sW(,z) for everys[t, t+]. Burdzy and Shimura have shown independently that one-sided cone points with angle exist when >/2 but not when 2. The present paper deals with the critical case =/2. We show that cone points with angle /2 do not exist. 相似文献
3.
P. Révész 《Journal of Theoretical Probability》1993,6(2):353-383
Let be a Poisson process on d of intensity and letW
1(t),W
2
(t),..., be a sequence of independent Wiener processes. LetW
i
(t)=X
i
+W
i
(t) whereX
1,X
2,..., are the points of . Consider the processess(t)=#{i:X
i
(t)1}. These and related processes are studied. 相似文献
4.
Given a setX and subsetsX
1,...,X
m, we consider the problem of finding a graphG with vertex setX and the minimum number of edges such that fori=1,...,m, the subgraphG
i; induced byX
i is connected. Suppose that for any pointsx
1,...,x
X, there are at mostX
i 's containing the set {x1,...,x
}. In the paper, we show that the problem is polynomial-time solvable for ( 2, 2) and is NP-hard for (3,=1), (=l,6), and (2,3).Support in part by the NSF under grant CCR-9208913 and CCR-8920505.Part work was done while this author was visiting at DIMACS and on leave from Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing. 相似文献
5.
Toshio Honda 《Annals of the Institute of Statistical Mathematics》2000,52(3):459-470
Let (Xi,Y
i) be a set of observations form a stationary -mixing process and (x) be the conditional -th quantile of Y given X = x. Several authors considered nonparametric estimation of (x) in the i.i.d. setting. Assuming the smoothness of FF(x), we estimate it by local polynomial fitting and prove the asymptotic normality and the uniform convergence. 相似文献
6.
LetX be a complex Lebesgue space with a unique duality mapJ fromX toX
*, the conjugate space ofX. LetA be a bounded linear operator onX. In this paper we obtain a non-linear eigenvalue problem for (A)=sup{Re: W(A} whereW(A)={J(x)A(x)) : x=1}, under the assumption that (A) and the convex hull ofW(A) for some linear operatorsA onl
p
, 2<p<. 相似文献
7.
Emmanuel Germain 《K-Theory》2001,23(1):41-52
We consider for unital c
*-algebras the short exact sequence 0 I A *
C
B A max B 0and give an explicit formula for the boundary map for separable C
*-algebras for which the Künneth formula for tensor products holds without Tor-terms. In the course of the article, we study the similar case of an ideal concerning one-relator groups. 相似文献
8.
Simon Thomas 《Geometriae Dedicata》1996,63(3):247-253
Let
be a finite field, and let (, B) be a nontrivial 2-(n, k, 1)-design over
. Then each point induces a (k–1)-spread S on /. (, B) is said to be a geometric design if S is a geometric spread on / for each . In this paper, we prove that there are no geometric designs over any finite field
.Research partially supported by NSF grant DMS-8703229. 相似文献
9.
G. S. Karkarashvili 《Journal of Mathematical Sciences》1993,66(3):2236-2242
We consider numerical solution of an integro-differential equation with nonsmooth initspaial values. Unique solvability in Sobolev spaceW
2
(0, 1), =1,2, is proved. We establish the rate of convergence of the approximate solution to the exact solution in fractional spacesW
2
+1
, 01, with approximation order O(h
++1/2
) for 01/2 andO(h
+1
|ln h|1/2, for 1/2 #x2264;1.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 8–16, 1988. 相似文献
10.
Torben Maack Bisgaard 《Analysis Mathematica》2001,27(1):37-54
For >2, let Q
+() be the infimum of those q>0 for which the function n epn is positive definite on N
0 for every pq. We shall prove that Q
+()0 as 2. 相似文献
11.
G. V. Kuz'mina 《Journal of Mathematical Sciences》1978,10(2):241-256
We obtain a complete solution of the problem of the maximum of the fourth diameter in the family of continua with capacity 1. Let E(o, ei, e–i). 0<2, be a continuum of minimum capacity containing the points o, ei, e–i; H(=cap E(o, ei, e–i). Let C() be the common point of three analytic arcs which form E(o, ei, e–i). One shows that the indicated maximum is realized by the continuum ={z:H(0)z
2E(o, ei, e–i)} where
0, o<02, is a solution of the equation. Any other extremal continuum of the gives problem is an image of under the mappingz ei
z+C ( is a real and C is a complex constant). One finds the value of the required maximum. The paper contains a brief exposition of the proof of this result.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 60–79, 1976. 相似文献
12.
Within Archimedean -groups, and with an infinite cardinal or , we consider X-hulls where X stands for any of the following classes of -groups: -projectable; laterally -complete; boundedly laterally -complete; conditionally -complete; combinations of the preceding, together with divisibility and/or relative uniform completeness. All these hulls exist, and may be obtained by iterated adjunction of the required extra elements, within the essential hull. When the -groups is relatively -complemented one step in the iteration suffices for several crucial properties. We derive from the above a considerable number of equations involving combinations of these hull operators. 相似文献
13.
Generalized convex functions and vector variational inequalities 总被引:3,自引:0,他引:3
X. Q. Yang 《Journal of Optimization Theory and Applications》1993,79(3):563-580
In this paper, (, ,Q)-invexity is introduced, where :X ×X intR
m
+
, :X ×X X,X is a Banach space,Q is a convex cone ofR
m
. This unifies the properties of many classes of functions, such asQ-convexity, pseudo-linearity, representation condition, null space condition, andV-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (, ,Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (, ,Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.The author is indebted to Dr. V. Jeyakumar for his constant encouragement and useful discussion and to Professor P. L. Yu for encouragement and valuable comments about this paper. 相似文献
14.
For a cardinal , we say that a subset B of a space X is C
-compact in X if for every continuous function
is a compact subset of
. If B is a C-compact subset of a space X, then (B, X) denotes the degree of C
-compactness of B in X. A space X is called -pseudocompact if X is C
-compact into itself. For each cardinal , we give an example of an -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in Some cardinal generalizations of pseudocompactness Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg's Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases. 相似文献
15.
Kevin O'Bryant 《Journal of Algebraic Combinatorics》2004,19(1):91-115
A Sturmian word is a map W :
{0,1} for which the set of {0, 1}-vectors F
n(W) {(W(i), W(i + 1),...,W(i + n – 1))
T
: i
} has cardinality exactly n + 1 for each positive integer n. Our main result is that the volume of the simplex whose n + 1 vertices are the n + 1 points in F
n(W) does not depend on W. Our proof of this motivates studying algebraic properties of the permutation ,n
(where is any irrational and n is any positive integer) that orders the fractional parts {}, {2},...,{n}, i.e., 0 < {,n
(1)} < {,n
(2)} < ··· < {,n
(n)} < 1. We give a formula for the sign of ,n
, and prove that for every irrational there are infinitely many n such that the order of ,n
(as an element of the symmetric group S
n) is less than n. 相似文献
16.
JirÍ Adámek 《Applied Categorical Structures》1996,4(1):121-126
For a topological category over Set we prove that if a functor T: has a fixed cardinal (i.e. for each object K with card (UK)= we have card (UTK)), then T has a least fixed point, and if T has a successive pair of fixed cardinals and +, then T has a greatest fixed point. This extends results of Adámek and Koubek.Partial financial support of the Grant Agency of the Czech Republic under Grant No. 201/93/0950 is gratefully acknowledged. 相似文献
17.
In this paper equivalent classes of the classes M and S
pr
, p > 1, > 0. r { 0,1,2, ... ,[]} defined by Shuyun [3] are obtained. Then, it is shown that the class S
pr
, 1 > p 2, 0, r {0,1,2,...,[]} is a subclass of BVC
r
, where S
pr
is the equivalent class of the Shuyun's class S
pr
, BV is the class of null sequences of bounded variation and C
r
is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7]. 相似文献
18.
R. J. Tomkins 《Journal of Theoretical Probability》1996,9(4):841-851
Forr1 and eachnr, letM
nr
be therth largest ofX
1,X
2, ...,X
n
, where {X
n
,n1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of
for all >0 and some –1, where {a
n
} is a real sequence. Furthermore, it is shown that this series converges for all >–1, allr1 and all >0 if it converges for some >–1, somer1 and all >0. 相似文献
19.
We characterize the Sobolev spaces W1,p(n) (p]1,+]), the space BV(n) of functions of bounded variation, the Nikol'skij spacesN
p
(R
n
=B
p
(R
n
) (p [1, + [, ]0,1[).This research was partially supported by M.U.R.S.T. 相似文献
20.
Let I be a finite interval, r
N and p(t)=dist{t,I}, tI. Denote by W
r
p
,, 0<<, the class of functions x on I with the seminorm x
(r)
p
Lp1. We obtain two-sided estimates of the Kolmogorov widths d
n(Wr
p,
)Lq and of the linear widths d
n(Wr
p,)Lq
lin 相似文献