共查询到20条相似文献,搜索用时 125 毫秒
1.
Shiqi Song 《应用数学学报(英文版)》1993,9(2):115-124
LetX be the solution of the SDE:dX
t = (X
t)dB
t +b(X
t)dt, with andb C
b
(R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form:
k
(u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if
k
is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of
k
, must be a constant function. 相似文献
2.
Let * be the equilateral triangulation of the plane and let 1
* be the equilateral triangle formed by four triangles of *. We study the space of piecewise polynomial functions in C
k
(R
2) with support 1
*, having a sufficiently high degree n and which are invariant with respect to the group of symmetries of 1
*. Such splines are called 1
*-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k0, we prove the existence of 1
*-splines of class C
k
and minimal degree, but these splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of these splines. 相似文献
3.
C. Calderón 《Lithuanian Mathematical Journal》1995,35(1):18-29
We obtain an elementary derivation for Selberg's formula related to the function ψ r, k * (x; q, ?) for allr, k positive integers. 相似文献
4.
V. I. Myagkov 《Journal of Mathematical Sciences》1990,51(2):2284-2290
We study complexes 2 and 3 with symmetrically situated fourfold inflection centers, two or three of which respectively are infinitely distant on each ray. The class of complexes 3 turns out to be known. The complex 2 is new and may involve three arbitrary functions of a single argument. The study of the geometric properties of the complex 2 culminates in an integral-free representation for it which makes it possible to write out explicitly a solution of the original system of differential equations for the complex.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 125–132. 相似文献
5.
A. Okounkov 《Transformation Groups》1998,3(2):181-207
We consider 3-parametric polynomialsP
*
(x; q, t, s) which replace theA
n-series interpolation Macdonald polynomialsP
*
(x; q, t) for theBC
n-type root system. For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation. Ass the polynomialsP
*
(x; q, t, s) becomeP
*
(x; q, t). We also prove a binomial formula for 6-parametric Koornwinder polynomials. 相似文献
6.
A difference scheme is constructed for a boundary-value problem for a one-dimensional biharmonic equation with nonlinear boundary condition. Under the hypothesis that the exact solution of the problem belongs to the Sobolev space W
2
k(),k [2, 4], in the lattice norm L
2
(), an estimate is obtained of the precision of the difference scheme to O(hk–1,5).Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 43–50, 1989. 相似文献
7.
V. É. Geit 《Mathematical Notes》1971,10(5):768-776
We prove the following: for every sequence {Fv}, Fv ? 0, Fv > 0 there exists a functionf such that
- En(f)?Fn (n=0, 1, 2, ...) and
- Akn?k? v=1 n vk?1 Fv?1?Ωk (f, n?1) (n=1, 2, ...).
8.
Noga Alon 《Graphs and Combinatorics》1994,10(1):11-18
We say that two hypergraphsH
1 andH
2 withv vertices eachcan be packed if there are edge disjoint hypergraphsH
1
andH
2
on the same setV ofv vertices, whereH
i
is isomorphic toH
i.It is shown that for every fixed integersk andt, wheretk2t–2 and for all sufficiently largev there are two (t, k, v) partial designs that cannot be packed. Moreover, there are twoisomorphic partial (t, k, v)-designs that cannot be packed. It is also shown that for every fixedk2t–1 and for all sufficiently largev there is a (1,t,k,v) partial design and a (1,t,k,v) partial design that cannot be packed, where 1 2O(v
k–2t+1
logv). Both results are nearly optimal asymptotically and answer questions of Teirlinck. The proofs are probabilistic. 相似文献
9.
A. U. Abdukhamidov 《Journal of Mathematical Sciences》1994,70(1):1572-1574
An asymptotically optimal method for finding a minimal point x* for a function f(x) C2, unimodal on an interval [ak,bk], is proposed. This method partitions the intervals k = bk – ak, k = 1, 2, ..., and locates x* by means of a decreasing geometric progression.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 70, 104–108, 1990. 相似文献
10.
11.
IstvÁn Talata 《Geometriae Dedicata》1999,74(1):61-71
For a collection C of convex bodies let h(C) be the minimum number m with the property that every element K of C can be covered by m or fewer smaller homothetic copies of K. Denote by C
d
*
the collection of all duals of cyclic d-polytopes, d 2. We show that h(C
2k
*
)=(k +1)2 for any k 2. We also prove the inequalities (d+1) (d+3)/4 h(C
d
*
) (d+1) 2/2$ for any d 2. 相似文献
12.
M. R. Foster 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1975,26(6):789-806
Summary Very slow flow of a rapidly rotating fluid past a right cylindrical obstacle of heightd on one of two co-rotating parallel planes, separated by a distanceh, is studied. The elliptic boundaryvalue problem for the geostrophic flow is formulated quite generally, and solutions are given for an infinitely-long ridge and an elliptic cylinder. A modified Ekman number,E
*v/d
2, where is the inverse aspect ratio of the cylinder, characterizes the latter solution. ForE
*<1, the fluid flows around a stagnant Taylor column over the elliptic cylinder; forE
*1, the fluid flows over the cylinder as though it were an infinitely-long ridge;E
*=O(1) shows part of the fluid flowing over, and part around, the cylinder. The drag increases from orderE
–1/4 to orderE
–1 asE
* increases from small to large values.
Zusammenfassung In dieser Arbeit wird die sehr langsame Strömung in einem rasch rotierenden Fluid untersucht um einen zylindrischen Körper, dessen Höhed die viel kleiner ist als die Distanzh der zwei unendlich ausgedehnten mitrotierenden parallelen Platten, welche das Fluid begrenzen; der Körper sitzt auf der unteren Platte. Eine allgemeine Formulierung des elliptischen Randwertproblems wurde für die geostrophische Strömung angegeben. Lösungen wurden für ein unendlich langes Wehr und einen elliptischen Zylinder gefunden. Eine modifizierte Ekman-Zahl,E *=v/d 2 E, in welcher das reziproke Verhältnis von Länge zu Durchmesser darstellt, charakterisiert die Lösung für den elliptischen Zylinder. WennE *1, umgeht die Flüssigkeit die stagnierende Taylorsäule, die auf dem elliptischen Zylinder ruht; wennE *1, geht die Flüssigkeit über den Zylinder, als ob er ein unendlich langes Wehr wäre; wennE *=0(1), geht ein Teil der Flüssigkeit über den Zylinder und ein anderer um ihn herum. Der Reibungswiderstand erhöht sich von 0(E –1/4) zu 0(E –1), wennE * von kleinen zu grossen Werten ansteigt.相似文献
13.
Jianxing Yin 《Designs, Codes and Cryptography》2001,23(1):99-110
By a T
*(2, k, v)-code we mean a perfect(k-2)-deletion-correcting code of length k over an alphabet ofsize v, which is capable of correcting any combination of up to(k-2) deletions and insertions of letters occured in transmission ofcodewords. In this paper, we provide a combinatorial construction forT
*(2, k, v-codes. As an application, we show that aT
*(2, 6, v-code exists for all positive integersv 3 (mod 5), with at most 12 possible exceptions of v. In theprocedure, a result on incomplete directed BIBDs is also established which is ofinterest in its own right. 相似文献
14.
A. D. Korshunov 《Mathematical Notes》1971,9(3):155-160
LetG(n) be the set of all nonoriented graphs with n enumerated points without loops or multiple lines, and let vk(G) be the number of mutually nonisomorphic k-point subgraphs of G G(n). It is proved that at least |G(n)| (1–1/n) graphs G G(n) possess the following properties: a) for any k [6log2n], where c=–c log2c–(1–c)×log2(1–c) and c>1/2, we havev
k(G) > C
n
k
(1–1/n2); b) for any k [cn + 5 log2n] we havev
k(G) = C
n
k
. Hence almost all graphs G G(n) containv(G) 2n pairwise nonisomorphic subgraphs.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 263–273, March, 1971. 相似文献
15.
We investigate the stochastic parabolic integral equation of convolution type
u=k1*Apu +?k=1¥ k2*gk+u0, t 3 0, u=k_1\ast A_pu +\sum\limits_{k=1}^{\infty} k_2\star g^k+u_0, \; t\geq 0, 相似文献
16.
N. Temirgaliev 《Mathematical Notes》1976,20(6):1026-1030
For any sequence {Nk} with {Nk} O we find sharp theorems on the inclusion of the classes {f: f l (0, 2),e
k
(1)
(f) = O(Nk)¦, whereE
k
(1)
(f) is the best approximation (in L) of f by trigonometric polynomials of order no greater than k, in the classL
with slowly growing and in the class Lv, 1 <v < .Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 835–841, December, 1976. 相似文献
17.
Jaikumar Radhakrishnan 《Combinatorica》1994,14(3):345-374
A II formula has the form, where eachL is either a variable or a negated variable. In this paper we study the computation of threshold functions by II formulas. By combining the proof of the Fredman-Komlós bound [5, 10] and a counting argument, we show that fork andn large andkn/2, every II formula computing the threshold functionT
k
n
has size at least exp
. Fork andn large andkn
2/3, we show that there exist II formulas for computingT
k
n
with size at most exp
. 相似文献
18.
H. Scheerer 《manuscripta mathematica》1985,51(1-3):63-87
Let R be a subring of the rationals with 1/2, 1/3R; let S
R
n
denote the R-local n-sphere and define
R
n
:=S
R
n
for n odd,
R
n
:=S
R
n
for n>0 even. An H-space (resp. a 1-conn. co-H-space) is decomposable over R, if it is homotopy equivalent to a weak product of spaces
R
n
(resp. to a wedge of R-local spheres). We prove that, if E is grouplike decomposable of finite type over R, the functor [-,E] is determined on finite dim. complexes by the Hopf algebra M*(E;R); here M* denotes the unstable cohomotopy functor of H.J. Baues. If C is cogrouplike decomposable over R, the functor [C,-] is determined on 1-conn. R-local spaces by *(C) as a cogroup in the category of M-Lie algebras. For R = the functor [-,E] is also determined by the Lie algebra *(E) and [C,-] by the Berstein coalgebra associated to the comultiplication of C. 相似文献
19.
A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...
20.
We characterize pairs of convex setsA, B in thek-dimensional space with the property that every probability distribution (p
1,...,p
k
) has a repsesentationp
i
=a
l
.b
i
, aA, bB.Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect graphs.Research was partially sponsored by the Hungarian National Foundation, Scientific Research Grants No 1806 and 1812. 相似文献
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