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1.
Let M be a compact Riemannian symmetric space. Then M=G/K, where G is the identity component of the isometry group of M and K is the isotropy subgroup of G at a point. In 1965 Nagano studied and classified the geometric transformation groups of compact symmetric spaces. Roughly speaking they are larger groups L that act on M, (i) G/L; (ii) L is a Lie transformation group acting effectively on M; (iii) L preserves the symmetric structure of M; and (iv) L is simple.Using Helgason spheres, S(), the minimal totally geodesic spheres in a compact irreducible symmetric space, we define an arithmetic distance for compact irreducible symmetric spaces and prove: THEOREM. Let M=G p(K n ), K=, H, or R, or M=AI(n), of rank greater that 1 and dimension greater that 3, let L be the geometric transformation group of M. Let L={: MM: is a diffeomorphism and preserves arithmetic distance}. Then L=L  相似文献   

2.
Summary Let (, A, P) be a probability space and E be a Banach space. We study the approximation of an E-valued random variable X, which is an element of the Orlicz space L(, A, P; E), by a function YL, which is measurable with respect to a sub--field of A and takes values in a closed convex subset of E. Two types of approximation are considered: (X – Y) dP=inf, and N(X–Y)=inf with the Orlicz space norm N. We give conditions for the existence of best approximants. If E is reflexive, we obtain martingale type convergence theorems for best approximants and discuss the continuity of the operator X best approximant of X.This paper is a part of the authors doctoral thesis, written under the guidance of D. Landers  相似文献   

3.
In this paper the steady-state behavior of many symmetric queues, under the head of the line processor-sharing discipline, is investigated. The arrival process to each of n queues is Poisson, with rateA, and each queue hasr waiting spaces. A job arriving at a full queue is lost. The queues are served by a single exponential server, which has a mean raten, and splits its capacity equally amongst the jobs at the head of each nonempty queue. The normal traffic casep=/< 1 is considered, and it is assumed thatn1 andr= 0(1). A 2-term asymptotic approximation to the loss probabilityL is derived, and it is found thatL = 0(n r ), for fixedp. If6=(1–p)/p 1, then the approximation is valid if n2 1 and (r+ 1)2n, and in this caseL r!/(n)r. Numerical values ofL are obtained forr = 1,2,3,4 and 5,n = 1000,500 and 200, and various values ofp< 1. Very small loss probabilities may be obtained with appropriate values of these parameters.  相似文献   

4.
The dam problem with general geometry is considered. Fluid is drawn from the bottomS 1 at a ratek where 0 k N, S 1 k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk 0, that is,k 0 = 0 on a setA andk 0 =N on the complement setS 1 A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk 0 is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896.  相似文献   

5.
Let the functionQ be holomorphic in he upper half plane + and such that ImQ(z 0 and ImzQ(z) 0 ifz +. A basic result of M.G. Krein states that these functionsQ are the principal Titchmarsh-Weyl coefficiens of a (regular or singular) stringS[L,m] with a (non-decreasing) mass distribution functionm on some interval [0,L) with a free left endpoint 0. This string corresponds to the eigenvalue problemdf + fdm = 0; f(0–) = 0. In this note we show that the set of functionsQ which are holomorphic in + and such that the kernel has negative squares of + and ImzQ(z) 0 ifz + is the principal Titchmarsh-Weyl coefficient of a generalized string, which is described by the eigenvalue problemdf +f dm + 2 fdD = 0 on [0,L),f(0–) = 0. Here is the number of pointsx whereD increases or 0 >m(x + 0) –m(x – 0) –; outside of these pointsx the functionm is locally non-decreasing and the functionD is constant.To the memory of M.G. Krein with deep gratitude and affection.This author is supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 09832  相似文献   

6.
Summary IfX takes values in a Banach spaceB and is in the domain of attraction of a Gaussian law onB, thenX satisfies the compact law of the iterated logarithm (LIL) with respect to a regular normalizing sequence { n } iffX satisfies a certain integrability condition. The integrability condition is equivalent to the fact that the maximal term of the sample {X 1, X 2,..., X n} does not dominate the partial sums {S n}, and here we examine the precise influence of these maximal terms and its relation to the compactLIL. In particular, it is shown that if one deletes enough of the maximal terms there is always a compactLIL with non-trivial limit set.Supported in part by NSF Grant MCS-8219742Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742  相似文献   

7.
We consider the Ising model with external field h and coupling constant J on an infinite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h0 and some J<. On the other hand, if G is amenable and quasi-transitive, then phase transition cannot occur for h0. In particular, a group is nonamenable if and only if the Ising model on one (all) of its Cayley graphs exhibits a phase transition for some h0 and some J<.  相似文献   

8.
LetA be an r.e. nonrecursive set. We sayA has thestrong antisplitting property if there exists an r.e. setB with 0< T B< T A such that ifA 1 A 2=A andA 1A 2=0 thenA 1 T B impliesA 1 T 0 andB T A 1 impliesA 1 T A. It is shown that below any high r.e. degree there exists an r.e. set with the strong antisplitting property. The main ingredient of the proof is a localization of Ambos-Spies' result that the cup or cap theorem fails forW-degrees.Research partially supported by N.U.S. Grant RP 85/83 (Singapore).  相似文献   

9.
LetH be a germ of holomorphic diffeomorphism at 0 . Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze 2i )=HS(z) (1). IfH is an unfolding of diffeomorphisms depending on (,0), withH 0=Id, one introduces its ideal . It is the ideal generated by the germs of coefficients (a i (), 0) at 0 k , whereH (z)–z=a i ()z i . Then one can find a parameter solutionS (z) of (1) which has at each pointz 0 belonging to the domain of definition ofS 0, an expansion in seriesS (z)=z+b i ()(z–z 0) i with , for alli.This result may be applied to the bifurcation theory of vector fields of the plane. LetX be an unfolding of analytic vector fields at 0 2 such that this point is a hyperbolic saddle point for each . LetH (z) be the holonomy map ofX at the saddle point and its associated ideal of coefficients. A consequence of the above result is that one can find analytic intervals , , transversal to the separatrices of the saddle point, such that the difference between the transition mapD (z) and the identity is divisible in the ideal . Finally, suppose thatX is an unfolding of a saddle connection for a vector fieldX 0, with a return map equal to identity. It follows from the above result that the Bautin ideal of the unfolding, defined as the ideal of coefficients of the difference between the return map and the identity at any regular pointz, can also be computed at the singular pointz=0. From this last observation it follows easily that the cyclicity of the unfoldingX , is finite and can be computed explicity in terms of the Bautin ideal.Dedicated to the memory of R. Mañé  相似文献   

10.
Remmel  Jeffrey B.  Williamson  S. Gill 《Order》1999,16(3):245-260
Let N denote the set of natural numbers and let P =(N k , ) be a countably infinite poset on the k-dimensional lattice N k . Given x N k , we write max(x) (min(x)) for the maximum (minimum) coordinate of x. Let be the directed-incomparability graph of P which is defined to be the graph with vertex set equal to N k and edge set equal to the set of all (x, y) such that max(x) max(y) and x and y not comparable in P. For any subset D N k , we let P D and D denote the restrictions of P and to D. Points x N k with min(x) = 0 will be called boundary points. We define a geometrically natural notion of when a point is interior to P or relative to the lattice N k , and an analogous notion of monotone interior with respect to or D . We wish to identify situations where most of these interior points are exposed to the boundary of the lattice or, in the case of monotone interior points, not concealed very much from the boundary. All of these ideas restrict to finite sublattices F k and/or infinite sublattices E k of N k . Our main result shows that for any poset P and any arbitarily large integer M > 0, there is an F E with F = M where, relative to the sublattices F k E k , the ideal situation of total exposure of interior points and very little concealment of monotone interior points must occur. Precisely, we prove that for any P =(N k , ) and any integer M > 0, there is an infinite E N and a finite D F k with F E and F = M such that (1) every interior vertex of P E k or E k is exposed and (2) there is a fixed set C E, C k k , such that every monotone-interior point of D belonging to F k has its monotone concealment in the set C. In addition, we show that if P 1 =(N k , 1),..., P r =(N k , r ) is any sequence of posets, then we can find E,D, and F so that the properties (1) and (2) described above hold simultaneously for each P i . We note that the main point of (2) is that the bound k k depends only on the dimension of the lattice and not on the poset P. Statement (1) is derived from classical Ramsey theory while (2) is derived from a recent powerful extension of Ramsey theory due to H. Friedman and shown by Friedman to be independent of ZFC, the usual axioms of set theory. The fact that our result is proved as a corollary to a combinatorial theorem that is known to be independent of the usual axioms of mathematics does not, of course, mean that it cannot be proved using ZFC (we just couldn"t find such a proof). This puts our geometrically natural combinatorial result in a somewhat unusual position with regard to the axioms of mathematics.  相似文献   

11.
Summary It is proved that the operatorP: L 1 (0, ) L 1(0, ), given byPg(z) = z/c [g(x)/cx]dx, is completely mixing, i.e.,P n g 1 0 forg L 1(0, ) with g dx = 0. This implies that, forc (0, 1), each continuous and bounded solution of the equationf(x)= 0 cx f(t)dt/(cx) (x (0, 1]) is constant.  相似文献   

12.
Summary LetG be a separable locally compact group with dual space. consists of all equivalence classes of irreducible unitary representations ofG, and is endowed with the Fell-topology. We study the topological properties in of the square-integrable representations ofG. [ is square-integrable provided there is a coordinate functiong((g)v, v),gG, for which is inL 2(G) w.r.t. left Haar measure onG.]SupposeG contains an open normal subgroupN of the formeKN n e whereK is compact. (All groups with a compact invariant neighborhood of the identity, [IN] groups, satisfy this condition.) In this case we show that if is square-integrable then {} is an open point of.Finally, our techniques are used to prove this result for arbitrary (non connected) nilpotent Lie groups.  相似文献   

13.
Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv , , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim t t –1(E(X t )2–(EX t )2) and findD=(p–q)()–1((1–)+(1)) as conjectured by Spohn (1991). We show that in the scale the position ofX t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.  相似文献   

14.
It is well known that the homogeneous orthochronous proper Lorentzgroup is isomorphic to the proper motion group of the hyperbolic space. To each Lorentz boost \ {id} there corresponds in the hyperbolic space exactly one lineL such that fixes each of the two ends ofL . Furthermore has no fixed points but each plane containingL is fixed by . If we fix a pointo, then to each other pointa there is exactly one boosta + such thatL a+ is the line joiningo anda anda +(o)=a. The set P of points of the hyperbolic space is turned in a K-loop (P, +) bya+b:=a +(b). Each line of the hyperbolic space has the representationa+Z(b) wherea, b P,b 0 andZ(b):= {x P |x+b=b+x}.Dedicated to H. Salzmann on the occasion of his 65th birthdaySupported by the NATO Scientific Affairs Division grant CRG 900103.  相似文献   

15.
LetR be a commutative ring with 1 andM anR-module. If:M R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM *, where the isomorphism is given by the adjoint of.  相似文献   

16.
Summary Let {x t :t0} be the solution of a stochastic differential equation (SDE) in d which fixes 0, and let denote the Lyapunov exponent for the linear SDE obtained by linearizing the original SDE at 0. It is known that, under appropriate conditions, the sign of controls the stability/instability of 0 and the transience/recurrence of {x t :t0} on d \{0}. In particular if the coefficients in the SDE depend on some parameterz which is varied in such a way that the corresponding Lyapunov exponent z changes sign from negative to positive the (almost-surely) stable fixed point at 0 is replaced by an (almost-surely) unstable fixed point at 0 together with an attracting invariant probability measure z on d \{0}. In this paper we investigate the limiting behavior of z as z converges to 0 from above. The main result is that the rescaled measures (1/ z ) z converge (in an appropriate weak sense) to a non-trivial -finite measure on d \{0}.Research supported in part by Office of Naval Research contract N00014-91-J-1526  相似文献   

17.
Summary We investigate classes of conditioned super-Brownian motions, namely H-transformsP H with non-negative finitely-based space-time harmonic functionsH(t, ). We prove thatH H is the unique solution of a martingale problem with interaction and is a weak limit of a sequence of rescaled interacting branching Brownian motions. We identify the limit behaviour of H-transforms with functionsH(t, )=h(t, (1)) depending only on the total mass (1). Using the Palm measures of the super-Brownian motion we describe for an additive spacetime harmonic functionH(t, )=h(t, x) (dx) theH-transformP H as a conditioned super-Brownian motion in which an immortal particle moves like an h-transform of Brownian motion.  相似文献   

18.
Let {X(t); 0t1} be a real-valued continuous Gaussian Markov process with mean zero and covariance (s, t) = EX(s) X(t) 0 for 0<s, t<1. It is known that we can write (s, t) = G(min(s, t)) H(max(s, t)) with G>0, H>0 and G/H nondecreasing on the interval (0, 1). We show that
In the critical case, i.e. this integral is infinite, we provide the correct rate (up to a constant) for log P(sup0<t1 |X(t)|<) as 0 under regularity conditions.  相似文献   

19.
In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder (rd) where (r, , z) denotes the cylindrical co-ordinates in 3 is considered. The motion is with swirl (i.e. the -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. [9] that for the problem without swirl (f q = 0 in (f)) in the whole space, as the flux constant k tends to 1) dist(0z, A) = O(k 1/2); diam A = O(exp(–c 0 k 3/2));2) k1/2)k converges to a vortex cylinder U m (see (1.2)).We show that for the problem with swirl, as k , 1) holds; if m q + 2 then 2) holds and if m > q + 2 it holds with U q+2 instead of U m. Moreover, these results are independent of f 0, f q and d > 0.  相似文献   

20.
Summary In this article we continue our study of the following problem posed by Lawrence Zalcman in 1972. LetS be the closed unit square. For eachz in the interior,S 0, ofS letS(z) be the largest closed square inS with centroidz, and for each in the interval (0, 1] letS (z) be the square homothetic toS(z) with linear ratio . Iff is a continuous function such that its integral overS (z) vanishes for allz in S0, is f =0? We show that the answer is yes if 3/4 < 1.  相似文献   

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