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991.
François Nicoleau 《Journal of Differential Equations》2004,205(2):354-364
We study an inverse scattering problem for a pair of Hamiltonians (H,H0) on L2(Rn), where H0=-Δ and H=H0+V, V being a short- or long-range potential. By an elementary constructive method, we show that the scattering operator S, which is localized near a fixed energy λ>0, determines the asymptotics of the potential V at infinity, in dimension n?3. This is done by studying the action of the scattering operator on suitable wave packets. 相似文献
992.
Starting from any two compactly supported refinable functions in L2(R)
with dilation factor d,we show that it is always possible to construct 2d wavelet functions
with compact support such that they generate a pair of dual d-wavelet frames in L2(R).
Moreover, the number of vanishing moments of each of these wavelet frames is equal
to the approximation order of the dual MRA; this is the highest possible. In particular,
when we consider symmetric refinable functions, the constructed dual wavelets are also
symmetric or antisymmetric. As a consequence, for any compactly supported refinable
function in L2(R), it is possible to construct, explicitly and easily, wavelets that are
finite linear combinations of translates (d · – k), and that generate a wavelet frame with
an arbitrarily preassigned number of vanishing moments.We illustrate the general theory
by examples of such pairs of dual wavelet frames derived from B-spline functions. 相似文献
993.
We proceed with our study of increasing self-described sequences F, beginning with 1 and defined by a functional equation
In [1] we exhibited the simple solution f (t)=Ct, for some (0,1), of the associated functional-differential equation
and we proved that provided <2/(2+d()), where
we have the asymtotic equivalence F(m)~ Cm.In the present paper we show that this last result is optimal, in the sense that the self-described sequence defined by |F–1(m)|=F(m)2, that is
for which the boundary case =2/(2+d())(=1/2) holds, does not satisfy F(m) ~ Cm. We also show that the m-th term F(m) of a sequence F for which the boundary case holds is nevertheless of asymptotic order m.Then we investigate the behaviour of self-described sequences F when lies beyond the boundary case. In [1] we established the estimates
when is the unique fixed point of a certain associated function. We were only able to prove in general that the latter holds when does not lie beyond the boundary case, however. In the present paper we prove that whenever
is the unique fixed point of this function, and in addition we obtain estimates more precise than (*). This applies for instance to the sequence defined by
that is
相似文献
994.
Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution
of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all
Received: 13 June 2003 相似文献
995.
We say that a subset of Cn is hypoconvex if its complement is the union of complex hyperplanes. We say it is strictly hypoconvex if it is smoothly bounded
hypoconvex and at every point of the boundary the real Hessian of its defining function is positive definite on the complex
tangent space at that point. Let Bn be the open unit ball in Cn.Suppose K is a C∞ compact manifold in ∂B1 × Cn, n > 1, diffeomorphic to ∂B1 × ∂Bn, each of whose fibers Kz over ∂B1 bounds a strictly hypoconvex connected open set. Let K be the polynomialhull of K. Then we show that K∖K is the union of
graphs of analytic vector valued functions on B1. This result shows that an unnatural assumption regarding the deformability of K in an earlier version of this result is
unnecessary. Next, we study an H∞ optimization problem. If pis a C∞ real-valued function on ∂B1× Cn, we show that the infimum γρ = infƒ∈H
∞ (B1)n ‖ρ(z, ƒ (z))‖∞ is attained by a unique bounded ƒ provided that the set (z, w) ∈ ∂B1 × C n|ρ(z, w) ≤ γρ has bounded connected strictly hypoconvex fibers over the circle. 相似文献
996.
For a bounded function defined on
, let
be the set of singular values of the (n + 1) x (n + 1) matrix whose (j, k)-entries
are equal to
These matrices can be thought of as variable-coefficient Toeplitz matrices or
generalized Toeplitz matrices. Matrices of the above form can be also thought
of as the discrete analogue of pseudodifferential operators. Under a certain
smoothness assumption on the function , we prove that
where the constant c1 and a part of c2 are shown to have explicit integral
representations. The other part of c2 turns out to have a resemblance to the
Toeplitz case. This asymptotic formula can be viewed as a generalization of
the classical theory on singular values of Toeplitz matrices. 相似文献
997.
An Extended Ant Colony Algorithm and Its Convergence Analysis 总被引:2,自引:0,他引:2
Giovanni?SebastianiEmail author Giovanni?Luca Torrisi 《Methodology and Computing in Applied Probability》2005,7(2):249-263
In this work, we propose a stochastic algorithm for solving
combinatorial optimization problems. The procedure is formulated within the Ant Colony Optimization (ACO) framework, and extends the so-called Graph-based Ant System with time-dependent evaporation factor, (GBAS/tdev) studied in Gutjahr (2002). In particular, we consider an ACO search procedure which also takes into account the objective function value. We provide a rigorous theoretical study on the convergence of the proposed algorithm. Further, for a toy example, we compare by simulation the rate of convergence of the proposed algorithm with those from the Random Search (RS) and from the corresponding procedure in Gutjahr (2002).AMS 2000 Subject Classification: 9OC15, 9OC27 相似文献
998.
We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.Mathematics Subject Classifications (2000) 18C99, 18E05, 08B05. 相似文献
999.
In this paper we define and examine the truncated Witten genus. It is defined as the equivariant index of the Dirac operator on the manifold Map(Cp,M) with its natural Cp-action. Here, Map(Cp,M) is the space of maps from the cyclic group of order p into a closed, connected, spin manifold, M. By applying the Atiyah-Singer index theorem we give a topological formula for the truncated Witten genus which is related to the formula for the Witten genus by truncation of the infinite products. We also show that the equivariant index of the Dirac operator on the projective space Map(Cp,n+1) is closely related to the truncated Witten genus of n. The spaces Map(Cp,n+1) define a filtration of the space Map(S1,n+1) which has been used to study equivariant objects on the smooth loop space of n.Acknowledgement This work was mainly done while the author was studying for a Ph.D. at Warwick University under the supervision of J. D. S. Jones. The author would like to thank John Jones for originally suggesting the problem and for his guidance whilst the author was at Warwick, to thank the EPSRC for funding his Ph.D., and to thank the referee for his detailed comments which helped greatly with the writing of this paper. 相似文献
1000.
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields
, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ‘compact-like’ duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as ‘standard models’ – they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.Mathematics Subject Classiffications (2000). primary: 17C36, 46H70, 17C65; secondary:
17C30, 17C90 相似文献