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1.
Summary Let (X
t
n
) be a Poisson sequence of independent Brownian motions in
d
,d3; Let be a compact oriented submanifold of d, of dimensiond–2 and volume ; let t be the sum of the windings of (X
s
n
, 0st) around ; then t/t converges in law towards a Cauchy variable of parameter /2. A similar result is valid when the winding is replaced by the integral of a harmonic 1-form in
d
. 相似文献
2.
We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d
t
=db
t
+T(
t
)dt with the initial data 0=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C
B
consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d
t
=
db
t
+
t
dt
with initial data 0=0, where ,R,0 and 0<. 相似文献
3.
Hiroshi Suzuki 《Graphs and Combinatorics》1991,7(4):363-375
Let be a distance regular graph with diameterd, and
d
() the set of vertices at distanced from. is said to be thin if the induced subgraph on
d
() is a union of cliques for every vertex. We show that the diameterd is bounded above by a function depending only onk
d, which is the cardinality of
d
(), if is not thin. We also investigate thin distance regular graphs witha
d 0. 相似文献
4.
E. P. Dolzhenko 《Mathematical Notes》1996,60(2):130-136
Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))2. LetH(x) be an arbitrary primitive of 1/h
–1(x). Note that the functionH
–1
x is positive and increasing on (–, +),H
–1 0 asx– andH
–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000. 相似文献
5.
Let {W(s)}
s
0 be a standard Wiener process. The supremum of the squared Euclidian norm Y (t)2, of the R2-valued process Y(t)=(1/t
W(t), {12/t
3 int0
t
s dW (s)– {3/t} W(t)), t [, 1], is the asymptotic, large sample distribution, of a test statistic for a change point detection problem, of appearance of linear trend. We determine the asymptotic behavior P {sup
t
[, 1] Y(t)2 > u as u , of this statistic, for a fixed (0,1), and for a moving = (u) 0 at a suitable rate as u . The statistical interest of our results lie in their use as approximate test levels. 相似文献
6.
Let be a fixed point free group given by the presentation
where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d. 相似文献
7.
S. I. Novikov 《Analysis Mathematica》1992,18(1):73-86
n
(D) — ,s —
n
(D),
v
(v=1, 2, ...,s/2) — .
m={0x
0<x
1<...<x
2m–1<2,x
2m
=x
0+2} , x
j
+1–x
j
<(4s max
v
)–1,j=0, 1, ..., 2m –1, ( ) 2- -
n,m
2m ,
m
. , L
q
- (1q) W
(
n
)={f
2
:f
(n–1)AC
2
,
n
(D)f 1} 2- - (s
n
f),
m
. , - -
n,m
.
The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper. 相似文献
The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper. 相似文献
8.
We study different notions of subsolutions for an abstract evolution equation du/dt+Auf where A is an m-accretive nonlinear operation in an ordered Banach space X with order-preserving resolvents. A first notion is related to the operator d/dt+A in the ordered Banach space L
1(0, T; X); a second one uses the evolution equation du/dt+A
uf where A
:x{y;zy for some zAx}; other notions are also considered. 相似文献
9.
Hiroshi Ezawa 《Acta Appl Math》2000,63(1-3):119-135
Introducing a path integral for the Ornstein–Uhlenbeck process distorted by a potential V(x), we find out the T limit of the probability distributions of X[]:=1/T
0
T
V((t))dt for Ornstein–Uhlenbeck process (t), with appropriate values of the exponent that depend on V. The results are compared with those for the Wiener process. 相似文献
10.
Michio Shimura 《Probability Theory and Related Fields》1992,93(2):197-229
Summary SupposeZ(·) is a two-dimensional Brownian motion. It is shown that a.s. there existt
0 and >0 such thatZ(t
0) is an extremal point of the convex hull of {Z(t)|t
0–tt0} and also an extremal point of the convex hull of {Z(t)|t
0tt0+} and, moreover, the tangent lines to the convex hulls atZ(t
0) form a non-zero angle.The result is related to the following unsolved problem of S.J. Taylor. Do there exist a.s.t
0 and >0 such that the intersection of the convex hulls of {Z(t)|t
0–tt0} and {Z(t)|t
0tt0+} contains onlyZ(t
0)?This research was partially supported by Grant-in-Aid for Scientific Research (No. 400101540202), Ministry of Education, Science and Culture 相似文献
11.
Zusammenfassung Es wird die Spannungsverteilung untersucht, die sich in einem breiten Balken mit konstanter Höhe unter einem konstanten Biegemoment ausbildet, wenn er eine kleine elliptische Einschliessung mit Zentrum auf der Neutralachse enthält. Insbesondere werden die Fälle eines sehr starren Einschlusses sowie eines elliptischen Loches im Detail diskutiert.
Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - x , y normal stress in Cartesian coordinates - xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h 1, 1/h 2 stretch ratios - e x + y dilatation - 2 rotation - M bending moment 相似文献
Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - x , y normal stress in Cartesian coordinates - xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h 1, 1/h 2 stretch ratios - e x + y dilatation - 2 rotation - M bending moment 相似文献
12.
Summary We consider the problem of comparing large finite and infinite systems with locally interacting components, and present a general comparison scheme for the case when the infinite system is nonergodic. We show that this scheme holds for some specific models. One of these is critical branching random walk onZ
d
. Let
t
denote this system, and let
t
N
denote a finite version of
t
defined on the torus [–N,N]
d
Z
d
. Ford3 we prove that for stationary, shift ergodic initial measures with density , that ifT(N) andT(N)/(2N+1)d s[0,] asN, then {v
}, 0 is the set of extremal invariant measures for the infinite system
t
andQ
s
is the transition function of Feller's branching diffusion. We prove several extensions and refinements of this result. The other systems we consider are the voter model and the contact process.Work supported in part by the National Science Foundation under Grant DMS-8802055, by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University and by the Deutsche Forschungsgemeinschaft through the SFB 123 at the Universität Heidelberg 相似文献
13.
The (,d, d, – 1)-problem is that of finding large graphs with maximum degree and diameterd such that the subgraphs obtained by deleting any set of up to – 1 vertices have diameterd. In this paper, we deduce upper bounds on the order of such graphs and present some of the largest known ones. We argue that these graphs can be used to construct extremely "robust" networks, and explain why we require this robustness property when designing transputer networks for certain applications. In particular, we investigate the suitability of the odd graphO
4 as a topology for such networks. 相似文献
14.
We study the oscillatory behavior of solutions of the fourth-order Emden–Fowler equation: (E) y(iv)+q(t)|y|sgny=0, where >1 and q(t) is a positive continuous function on [t0,), t0>0. Our main results Theorem 2 – if (q(t)t(3+5)/2)0, then equation (E) has oscillatory solutions; Theorem 3 – if limtq(t)t4+(-1)=0, >0, then every solution y(t) of equation (E) is either non-oscillatory or satisfies limsuptt-+i|y(i)(t)|= for < and i=0,1,2,3,4. These results complement those given by Kura for equation (E) when q(t)<0 and provide analogues to the results of the second-order equation, y+q(t)|y|sgny=0,>1. Mathematics Subject Classification (2000) 34C10, 34C15 相似文献
15.
N. L. Gordeev 《Journal of Mathematical Sciences》2003,116(1):2961-2971
Let be a linear representation of a finite group over a field of characteristic 0. Further, let R
be the corresponding algebra of invariants, and let P
(t) be its Hilbert–Poincaré series. Then the series P
(t) represents a rational function (t)/(t). If R
is a complete intersection, then (t) is a product of cyclotomic polynomials. Here we prove the inverse statement for the case where is an almost regular (in particular, regular) representation of a cyclic group. This yields an answer to a question of R. Stanley in this very special case. Bibliography: 3 titles. 相似文献
16.
Tassilo Küpper 《Numerische Mathematik》1976,25(2):201-214
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea
2 and for given functions = we require =C
0[0, 1] C
2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and . 相似文献
17.
Let
n
be n-dimensional Euclidean space, and let : [0, L]
n
and : [0, L]
n
be closed rectifiable arcs in
n
of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C
2 curves. In this paper we prove the conjecture in general. 相似文献
18.
A variety of Galerkin methods are studied for the parabolic equationu
t
=(a(x)
u),x
n
,t (O,T], subject to the nonlinear boundary conditionu
v
=g(x,t,u),x,t (O,T] and the usual initial condition. Optimal order error estimates are derived both inL
2 () andH
1 () norms for all methods treated, including several that produce linear computational procedures.The authors were partially supported by The National Science Foundation during the preparation of this paper. 相似文献
19.
G. E. Tkebuchava 《Analysis Mathematica》1994,20(2):147-153
. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]2 f , ¦f¦ L([0, 1]2), - [0, 1]2. 相似文献
20.
V. A. Slousch 《Journal of Mathematical Sciences》2003,115(2):2267-2271
Let A be a self-adjoint operator, let (, ) be an inner gap in the spectrum of the operator A, and let B(t) = A + tW
*
W, where the operator W(A – iI)-1 is not necessarily bounded. Conditions are obtained under which the spectrum of B(t) in (, ) is discrete. Let N(, A, W, ), (, ), > 0, be the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to . The asymptotics of N(, A, W, ) as + is obtained in terms of the spectral asymptotics of a certain self-adjoint compact operator. Bibliography: 5 titles. 相似文献