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1.
G. I. Ivanova 《Journal of Mathematical Sciences》1991,57(4):3240-3241
We are considering the problem of controlling a one-dimensional Wiener process (t) (0)=0,E=0,D=
2t.Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 53–55. 相似文献
2.
Barbara Priwitzer 《Geometriae Dedicata》1995,58(3):245-258
LetP=(P, L) be a compact projective plane with 0P< and let be a compact connected subgroup of Aut(P). If dim dimE – dimP, whereE is the elliptic motion group of the corresponding classical plane, then E or is isomorphic to a point stabilizerE
0 inE, cf. [31]. Here we consider the case E
0. It is shown that the action of on the point spaceP is equivalent to the classical action ofE
0. For dimP {8, 16} the planeP is uniquely determined by a 2-dimensional subplane with SO2 Aut().Für H. Reiner Salzmann zum 65. Geburtstag 相似文献
3.
Prof. Dr. Reinhold Böhme 《manuscripta mathematica》1987,57(2):205-223
Let F denote a surface with boundary F, being contained in a Riemann surface R, such that R\F is somedisk. If we vary the boiundary curve o parametrizing F, we will get a manifold of real dimension 6g–3, such that any bounds some F and any local deformation
of F is conformally equivalent to just one F for .This result also implies that none of the conformal invariants of R will be an invariant of this F, since its neighbors {F|} cover all possible deformations of F at all. 相似文献
4.
Takashi Hara 《Probability Theory and Related Fields》1990,86(3):337-385
Summary Extending the method of [27], we prove that the corrlation length of independent bond percolation models exhibits mean-field type critical behaviour (i.e. (p(p
c
–p)–1/2 aspp
c
) in two situations: i) for nearest-neighbour independent bond percolation models on ad-dimensional hypercubic lattice
d
, withd sufficiently large, and ii) for a class of spread-out independent bond percolation models, which are believed to belong to the same universality class as the nearest-neighbour model, in more than six dimensions. The proof is based on, and extends, a method developed in [27], where it was used to prove the triangle condition and hence mean-field behaviour of the critical exponents , , , and 2 for the above two cases. 相似文献
5.
Marcel Erné 《Algebra Universalis》1988,25(1):290-321
By a result of Pigozzi and Kogalovskii, every algebraic latticeL having a completely join —irreducible top element can be represented as the lattice L() of equational theories extending some fixed theory . Conversely, strengthening a recent result due to Lampe, we show that such a representationL=L() forcesL to satisfy the following condition: if the top element ofL is the join of a nonempty subsetB ofL then there are elementsb..., B such thata=(... (((b1 a) b2) a) ... bn) a for alla L. In presence of modularity, this equation reduces to the identitya=(a b1) ... (a bn). Motivated by these facts, we study several weak forms of distributive laws in arbitrary lattices and related types of prime elements. The main tool for applications to universal algebra is a generalized version of Lampe's Zipper Lemma.Presented by Ralph Freese. 相似文献
6.
Beitrag zur Reduktion des Entscheidungsproblems auf Klassen von Hornformeln mit kurzen Alternationen
Egon Börger 《Archive for Mathematical Logic》1974,16(1-2):67-84
Ohne Zusammenfassung
Zusatz bei der Korrektur: Ein vollständiger und korrekter Beweis für die Entscheidbarkeit der eingangs angeführten Aanderaaschen Klasse ((0, ), (, , ...)) erscheint demnächst im JSL (S.O. Aanderaa/H.R.Lewis: Prefix classes of Krom formulas). Ebendort wird auch die Reduktionstypeneigenschaft für ((0, ), (0, 0, )) und ((0, )), (0, 0, )) nachgewiesen, während ((0, ), (, )) sich als entscheidbar herausgestellt hat (s. E. Börger: Eine entscheidbare Klasse von Kromformeln. ZMLG 19 (1973), 117–120.) Der Kromsche Reduktionstyp konnte mittlerweile einerseits zu ((0, ), (0, 4)) verschärft werden (s. D. Rödding, E. Börger: The undecidability of (0, 4)-formulae with binary disjunctions, vorgetragen auf dem Logic Coll. Bristol 1973, ein abstract erscheint im JSL), andererseits kündigt H.R.Lewis die Reduktionstypeneigenschaft für ((0, ), (0, 1)) an (s. H.R.Lewis: Krom formulas with one dyadic predicate letter. Notices AMS 20, 5 (1973) A-500, abstr. no. 73T-E78.)Dieser Aufsatz geht aus der Dissertation [2] hervor, die dem Fachbereich Mathematik der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster im Sommersemester 1971 vorgelegt worden ist. Die Ergebnisse stammen aus dem Wintersemester 1970/71. Eine Ankündigung der hauptsächlichen Resultate ist in den Notices of the American Mathematical Society 19, 2 (1972) A-333 unter der abstract no. * 72T-E24 erschienen. 相似文献
7.
Yuji Yoshino 《Algebras and Representation Theory》2001,4(2):171-200
We provide a general method to construct the Tate–Vogel homology theory for a general half-exact functor with one variable, aiming at a good generalization of Cohen–Macaulay approximations of modules over commutative Gorenstein rings. For a half exact functor F, using the left and right satellites (S
n
and S
n
), we define F
(X)=lim
S
n
S
n
F(X) and F
(X)=lim
S
n
S
n
F(X), and call F
and F
the Tate–Vogel completions of F. We provide several properties of F
and F
, and their relations with the G-dimension and the projective dimension of the functor F. A comparison theorem of Tate–Vogel completions with ordinary Tate–Vogel homologies is proved. If F is a half exact functor over the category of R-modules, where R is a commutative Noetherian local ring inspired by Martsinkovsky's works, we can define the invariants (F) and (F) of F. If F=Ext
R
i
(M, ), then they coincide with Martsinkovsky's -invariants and Auslander's delta invariants. Our advantage is that we can consider these invariants for any half exact functors. We also compute these invariants for the local cohomology functors. 相似文献
8.
If E is a vector space over a field K, then any regular symmetric bilinear form on E induces a polarity
on the lattice of all subspaces of E. In the particular case where E is 3-dimensional, the set of all subspaces M of E such that both M and
are not N-subspaces (which, in most cases, is equivalent to saying that M is nonisotropic), ordered by inclusion and endowed with the restriction of the above polarity, is an orthomodular lattice T(E, ). We show that if K is a proper subfield of K, with K F2, and E a 3-dimensional K -subspace of E such that the restriction of to E × E is, up to multiplicative constant, a bilinear form on the K -space E , then T(E , ) is isomorphic to an irreducible 3-homogeneous proper subalgebra of T(E, ). Our main result is a structure theorem stating that, when K is not of characteristic 3, the converse is true, i.e., any irreducible 3-homogeneous proper subalgebra of T(E, ) is of this form. As a corollary, we construct infinitely many finite orthomodular lattices which are minimal in the sense that all their proper subalgebras are modular. In fact, this last result was our initial aim in this paper.Received June 4, 2003; accepted in final form May 18, 2004. 相似文献
9.
We address the problem of monitoring a linear functional (c, x)Eof an unknown vectorx of a Hilbert spaceE, the available data being the observationz, in a Hilbert spaceF, of a vectorAx depending linearly onx through some known operatorA(E; F). WhenE=E
1×E
2,c=(c
1 0), andA is injective and defined through the solution of a partial differential equation, Lions ([6]–[8]) introduced sentinelssF such that (s, Ax)Fis sensitive to x1 E
1 but insensitive to x2 E2. In this paper we prove the existence, in the general case, of (i) a generalized sentinel (s, ) ×E, where F withF dense in 80, such that for anya priori guess x0 ofx, we have s, Ax + (, x0)E=(c, x)E, where x is the least-squares estimate ofx closest tox
0, and (ii) a family of regularized sentinels (s
n
,
n
) F×E which converge to (s, ). Generalized sentinels unify the least-squares approach (by construction !) and the sentinel approach (whenA is injective), and provide a general framework for the construction of sentinels with special sensitivity in the sense of Lions [8]). 相似文献
10.
On the homotopy fixed point problem for free loop spaces and other function complexes 总被引:1,自引:0,他引:1
Gunnar Carlsson 《K-Theory》1991,4(4):339-361
Let G be a finite group, let X and Y be finite G-complexes, and suppose that for each K
G, Y
K is dim(X
K)-connected and simple. G acts on the function complex F(X, Y) by conjugation of maps. We give a complete analysis of the homotopy fixed point set of the space
F(X, Y). As a corollary, we are able to analyze at a prime p, the homotopy fixed point set of the circle action on X, where X denotes the free loop space of X, and X is a simply connected finite complex.Supported in part by NSF DMS 86-02430.To A. Grothendieck on the occasion of his sixtieth birthday 相似文献
11.
Summary It is shown that if (X, ) is a product of totally ordered measure spaces andf
j (j=1,2,3,4) are measurable non-negative functions onX satisfyingf
1(x)f2(y)f3(xy)f4(xy), where (, ) are the lattice operations onX, then (f
1 d)(f
2 d)(f
3 d)(f
4 d). This generalises results of Ahlswede and Daykin (for counting measure on finite sets) and Preston (for special choices off
j). 相似文献
12.
Axel Schüler 《Compositio Mathematica》2001,126(1):57-77
Let be one of the N
2-dimensional bicovariant first-order differential calculi on the quantum groups O
q
(N) or Sp
q
(N), where q is not a root of unity. We show that the second antisymmetrizer exterior algebra
s
is the quotient of the universal exterior algebra
u
by the principal ideal generated by . Here denotes the unique up to scalars bi-invariant 1-form. Moreover, is central in
u
and
u
is an inner differential calculus. 相似文献
13.
A. N. Godunov 《Mathematical Notes》1974,15(3):273-279
We formulate a continuous function FR×HH, where H is a separable Hilbert space such that the Cauchy problem. x(t)=F(t, x(t)), x(t0)=x0 has no solution in any neighborhood of the point t0, no matter what t0 R and x0 H are considered.Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 467–477, March, 1974.In conclusion, the author thanks O. G. Smolyanov and V. I. Averbukh for their constant interest and for a number of useful remarks. 相似文献
14.
Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献
15.
Dr. Hermann Rost 《Probability Theory and Related Fields》1970,15(1):19-28
Summary Given a stochastic matrixP on the state spaceI an ordering for measures inI can be defined in the following way: iff(f)(f) for allf in a sufficiently rich subcone of the cone of positiveP-subharmonic functions. It is shown that, if, are probability measures with , then in theP-process (X
n)n0 having as initial distribution there exists a stopping time such thatX
is distributed according to. In addition, can be chosen in such a way, that for every positive subharmonicf with(f)< the submartingale (f(X
n))n0 is uniformly integrable. 相似文献
16.
Convergence rates of Newton-Goldstein sequences are estimated for convex constrained minimization problems with singular solutions, i.e., solutions at which the local quadratic approximationQ(, x) to the objective functionF grows more slowly than x – 2 for admissible vectorsx near. For a large class of iterative minimization methods with quadratic subproblems, it is shown that the valuesr
n
=F(x
n
)–inf
F are of orderO(n
–1/3) at least. For the Newton—Goldstein method this estimate is sharpened slightly tor
n
=O(n
–1/2) when the second Fréchet differentialF is Lipschitz continuous and the admissible set is bounded. Still sharper estimates are derived when certain growth conditions are satisfied byF or its local linear approximation at. The most surprising conclusion is that Newton—Goldstein sequences can convergesuperlinearly to a singular extremal whenF(), x – Ax –
v
for someA > 0, somev (2,2.5) and allx in near, and that this growth condition onF() is entirely natural for a nontrivial class of constrained minimization problems on feasible sets =
1{[0,1],U} withU a uniformly convex set in
d
. Feasible sets of this kind are commonly encountered in the optimal control of continuous-time dynamical systems governed by differential equations, and may be viewed as infinite-dimensional limits of Cartesian product setsU
k
in
kd
. Superlinear convergence of Newton—Goldstein sequences for the problem (,F) suggests that analogous sequences for increasingly refined finite-dimensional approximation (U
kd
,F
k
) to (,F) will exhibit convergence properties that are in some sense uniformly good ink ask .Investigation partially supported by the U.S. Air Force through the Air Force Institute of Technology, and by NSF Grant ECS-8005958. 相似文献
17.
H. Andréka 《Algebra Universalis》1991,28(1):12-25
LetR(, , ¦) denote the class of all algebras isomorphic to ones whose elements are binary relations and whose operations are union, intersection, and relation composition (or relative product) of relations. We prove thatR(, , ¦) is not a variety and is not finitely axiomatizable. LetDLOS denote the class of all structures (A, , , ) where (A, , ) is a distributive lattice, (A, ) is a semigroup and is additive w.r.t. . We prove thatDLOS is the variety generated byR(, , ¦), and moreover, if (A, , , ) DLOS then it is representable whenever we disregard one of its operations.Presented by Boris M. Schein.Research supported by Hungarian National Foundation for Scientific Research grant No. 1810. 相似文献
18.
U. M. Swamy G. C. Rao R. V. G. Ravi Kumar Ch. Pragati 《Southeast Asian Bulletin of Mathematics》2003,26(3):509-516
In this paper, it is proved that the Boolean centre of a semigroup S with sufficiently many commuting idempotents is isomorphic to the inverse limit of the directed family of Birkhoff centres (or Boolean centres) of a class of bounded semigroups. The Birkhoff centre is defined for any poset and proved that it is a relatively complemented distributive lattice whenever it is nonempty. It is observed that for a semilattice S, the Birkhoff centres as a semigroup and as a poset coincide. Also it is observed that for a Lattice (L, , ), the Birkhoff centres of the semilattices (L, ) and (L, ) coincide with the Birkhoff centre of L. Finally it is proved that for a lattice (L, , ), the Boolean centres of the semilattices (L, ) and (L, ) coincide with the Boolean centre of L.AMS Subject classification (1991): 06A12, 20M15 相似文献
19.
Let X, X
1, X
2,... be a sequence of independent and identically distributed random variables with common distribution function F. Denote by F
n
the distribution function of centered and normed sum S
n
. Let F belong to the domain of attraction of the standard normal law , that is, lim F
n
(x)= (x), as n , uniformly in x . We obtain extended asymptotic expansions for the particular case where the distribution function F has the density p(x) = cx
––1 ln(x), x > r, where 2, , c > 0, and r > 1. We write the classical asymptotic expansion (in powers of n
–1/2) and then add new terms of orders n
–/2 ln
n, n
–/2 ln-1
n, etc., where 0. 相似文献
20.
Let be the angle between a line and a random k-space in Euclidean n-space R
n. Then the random variable cos2 has the beta distribution. This result is applied to show (1) in R
nthere are exponentially many (in n) lines going through the origin so that any two of them are nearly perpendicular, (2) any N-point set of diameter d in R
nlies between two parallel hyperplanes distance 2d{(log N)/(n-1)}1/2 apart and (3) an improved version of a lemma of Johnson and Lindenstrauss (1984, Contemp. Math., 26, 189–206). A simple estimate of the area of a spherical cap, and an area-formula for a neighborhood of a great circle on a sphere are also given. 相似文献