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1.
Using certain quadratic forms associated to symplectic endomorphisms which we compare with the Clarke-Ekeland dual action functional, we prove: THEOREM. — Let H be a C2-Hamiltonian defined on R2n, strictly convex, proper and invariant under a certain symplectic rational positive and non-degenerate rotation (this is defined in the introduction); then, every hypersurface of H contains a completely elliptic periodic orbit. This generalizes the result of G. Dell'Antonio, B. D'Onofrio and I. Ekeland contained in [1].  相似文献   

2.
We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the $L_1$ -center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The $L_1$ -center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.  相似文献   

3.
A function f(x) defined on X = X1 × X2 × … × Xn where each Xi is totally ordered satisfying f(xy) f(xy) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on X, is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ??1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications.  相似文献   

4.
5.
Let {γn(V)}n≥1 be the sequence of proper codimensions of some variety V of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence {γn(V)}n≥1 is presented, i.e., the sequence {γn(V)}n≥1 of any such variety V grows as a polynomial of some degree k, but the sequence {γn(W)}n≥1 of any proper subvariety W in V grows as a polynomial of degree strictly less than k.  相似文献   

6.
In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of n-coherent and n-convex conditional previsions, at the varying of n. We investigate which such previsions are the most general one may reasonably consider, suggesting (centered) 2-convex or, if positive homogeneity and conjugacy is needed, 2-coherent lower previsions. Basic properties of these previsions are studied. In particular, we prove that they satisfy the Generalised Bayes Rule and always have a 2-convex or, respectively, 2-coherent natural extension. The role of these extensions is analogous to that of the natural extension for coherent lower previsions. On the contrary, n-convex and n-coherent previsions with n3 either are convex or coherent themselves or have no extension of the same type on large enough sets. Among the uncertainty concepts that can be modelled by 2-convexity, we discuss generalisations of capacities and niveloids to a conditional framework and show that the well-known risk measure Value-at-Risk only guarantees to be centered 2-convex. In the final part, we determine the rationality requirements of 2-convexity and 2-coherence from a desirability perspective, emphasising how they weaken those of (Williams) coherence.  相似文献   

7.
This paper is concerned with the relationship between contexts, closure spaces, and complete lattices. It is shown that, for a unital quantale L, both formal concept lattices and property oriented concept lattices are functorial from the category L-Ctx of L-contexts and infomorphisms to the category L-Sup of complete L-lattices and suprema-preserving maps. Moreover, the formal concept lattice functor can be written as the composition of a right adjoint functor from L-Ctx to the category L-Cls of L-closure spaces and continuous functions and a left adjoint functor from L-Cls to L-Sup.  相似文献   

8.
We prove that determinacy for all Boolean combinations of \({F_{\sigma \delta }}\) (Π 3 0 ) sets implies the consistency of second-order arithmetic and more. Indeed, it is equivalent to the statement saying that for every set X and every number n, there exists a β-model of Π n 1 -comprehension containing X. We prove this result by providing a careful level-by-level analysis of determinacy at the finite level of the difference hierarchy on \({F_{\sigma \delta }}\) (Π 3 0 ) sets in terms of both reverse mathematics, complexity and consistency strength. We show that, for n ≥ 1, determinacy for sets at the nth level in this difference hierarchy lies strictly between (in the reverse mathematical sense of logical implication) the existence of β-models of Π n+2 1 -comprehension containing any given set X, and the existence of β-models of Δ n+2 1 -comprehension containing any given set X. Thus the nth of these determinacy axioms lies strictly between Π n+2 1 -comprehension and Δ n+2 1 -comprehension in terms of consistency strength. The major new technical result on which these proof theoretic ones are based is a complexity theoretic one. The nth determinacy axiom implies closure under the operation taking a set X to the least Σ n+1 admissible containing X (for n = 1; this is due to Welch [9]).  相似文献   

9.
Let {Xk, k?Z} be a stationary Gaussian sequence with EX1 – 0, EX2k = 1 and EX0Xk = rk. Define τx = inf{k: Xk >– βk} the first crossing point of the Gaussian sequence with the function – βt (β > 0). We consider limit distributions of τx as β→0, depending on the correlation function rk. We generalize the results for crossing points τx = inf{k: Xk >β?(k)} with ?(– t)?tγL(t) for t→∞, where γ > 0 and L(t) varies slowly.  相似文献   

10.
In this paper, we study the structure of Turing degrees below 0′ in the theory that is a fragment of Peano arithmetic without Σ1 induction, with special focus on proper d-r.e. degrees and non-r.e. degrees. We prove:
  1. P ? + BΣ1 + Exp ? There is a proper d-r.e. degree.
  2. P ? +BΣ1+ Exp ? IΣ1 ? There is a proper d-r.e. degree below 0′.
  3. P ? + BΣ1 + Exp ? There is a non-r.e. degree below 0′.
  相似文献   

11.
We perform the rounding-error analysis of the conjugate-gradient algorithms for the solution of a large system of linear equations Ax=b where Ais an hermitian and positive definite matrix. We propose a new class of conjugate-gradient algorithms and prove that in the spectral norm the relative error of the computed sequence {xk} (in floating-point arithmetic) depends at worst on ζк32, where ζ is the relative computer precision and к is the condition number of A. We show that the residual vectors rk=Axk-b are at worst of order ζк?vA?v ?vxk?v. We p oint out that with iterative refinement these algorithms are numerically stable. If ζк 2 is at most of order unity, then they are also well behaved.  相似文献   

12.
One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained.  相似文献   

13.
Let L be a positive Z-lattice with level N = cd, (c, d) = 1. Then the Fourier expansion at cusp 1d of the theta function associated to L is a theta function associated to L1, where a lattice L1 is defined by ZpL1 = ZpL for p?c, ZpL1 = the dual of ZpL for p | c.  相似文献   

14.
Given a sequence X=(Xk)k?1 of random variables taking values in {?v,…,0,…,+u}, let's define the local score of the sequence by Hn=max1?i?j?n(∑k=ijXk). The local score is used to analyze biological sequences pointing out regions of the sequences with interesting biological properties. In order to separate randomly events from really interesting segments, we establish here the distribution of the local score of Hn when the sequence X is a Markov chain of order 1. To cite this article: S. Mercier, C. Hassenforder, C. R. Acad. Sci. Paris, Ser. I 336 (2003).  相似文献   

15.
We consider n messages of N blocks each, where each block is encoded by some antinoise coding method. The method can correct no more than one error. We assume that the number of errors in the ith message belongs to some finite random subset of nonnegative integer numbers. Let A stand for the event that all errors are corrected; we study the probability P(A) and calculate it in terms of conditional probabilities. We prove that under certain moment conditions probabilities P(A) converge almost sure as n and N tend to infinity so that the value n/N has a finite limit. We calculate this limit explicitly.  相似文献   

16.
《Journal of Complexity》1997,13(2):195-207
A model of computation over thep-adic numbers, for odd primesp, is defined following the approach of Blum, Shub, and Smale. This model employs branching on the property of being a square inQpand unit height. The feasibility of systems of quadratic polynomials is shown to be NP-complete in this model. A polynomial time algorithm is given for feasibility of a single quadratic polynomial overQp.  相似文献   

17.
This Note is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [7]. The paper [7] derives, by means of a three-scale matched asymptotic expansion, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis number – i.e., the ratio between thermal and molecular diffusion – to be strictly less than unity. In this Note, we give the main ideas of a rigorous proof of the validity of this model, under the additional restriction that the Lewis number is close to 1. To cite this article: C. Lederman et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 569–574.  相似文献   

18.
Let A be an n×n matrix with eigenvalues λ1,λ2,…,λn, and let m be an integer satisfying rank(A)?m?n. If A is real, the best possible lower bound for its spectral radius in terms of m, trA and trA2 is obtained. If A is any complex matrix, two lower bounds for are compared, and furthermore a new lower bound for the spectral radius is given only in terms of trA,trA2,‖A‖,‖AA-AA‖,n and m.  相似文献   

19.
Consider the free group Γ = {A,B} generated by matrices A, B in SL2(Z). We can construct a ternary form Φ(x,y,z) whose GL3(Z) equivalence class is invariant, as it depends on Γ and not the choice of generators. If Γ is the commutator of SL2(Z), then the generating matrices have fixed points corresponding to different fields and inequivalent Markoff forms, but they are all biuniquely determined by Φ = -z2+ y(2x+y+z) to within equivalence. When referred to transformations A, B of the upper half plane, this phenomenon is interpreted in terms of inequivalent homotopy elements which are primitive for the perforated torus.  相似文献   

20.
The pair (P, p) is a (partial) (n, b)-PBD if (P, p) isa (partial) pairwise balanced design with the property that |P| = n and each block in p has exactly b elements. The following theorems are proved.Theorem. If (P, p) is an (n, b)-PBD and n > b ? 4, then (P, p) has an isomorphic disjoint mate. (Theorem 2.3)Theorem. Suppose k and b are positive integers and b ? 5. There is a constant C(k, b) such that if (P, p) is an (n, b)-PBD and n > C(k, b), then there exist k mutually disjoint isomorphic mates of (P, p). (Theorem 2.2)Theorem. Suppose k and b are positive integers, k ? 2 and b ? 5. If (P, p1, (P, p2),…, (P, pk) is a collection of partial (|P|, b)-PBD's, there exist k (n, b)-PBD's (X, x1), (X, x2), …, (X, xk) such that (P, p1) is embedded in (X, x1) and for ij, p1p1 = x1x1. Additionally the existence of certain collections valuable in embedding is explored. (Theorem 4.10)  相似文献   

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