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961.
The influence of spreading, in wavepacket transmission across a potential barrier has been analyzed, by considering several collisions between a wavepacket and a potential barrier, in which the initial distance between the packet and the barrier—the launching distance, is changed. An effective total potential (Bohm’s quantum potential plus classical potential), has been used, to show that, for suitable classical barrier widths and heights, light masses, as well as mean collision energies, one should expect an increase of the quantum transmission factor as the initial wavepacket—barrier distance is decreased. Numerically converged time-dependent wavepacket propagation calculations confirm that trend, leading to an increase as high as 20% per ?, in thin square and Eckart barrier problems. Possibilities of experimentally measuring this effect are also analyzed.  相似文献   
962.
963.
We give an explicit formula for the exterior powers ∧ k π 1 of the defining representation π 1 of the simple Lie algebra ?ο(2n + 1, ?). We use the technique of family algebras. All representations in question are children of the spinor representation σ of g2ο(2n + 1, ?). We also give a survey of main results on family algebras.  相似文献   
964.
We give a new, somewhat elementary method for proving parity results about Iwasawa-theoretic Selmer groups and apply our method to certain Galois representations which are not self-dual. The main result is essentially that Iwasawa's λ-invariants for these representations over dihedral -extensions are even. Our approach is a specialization argument and does not make use of Neková?'s deformation-theoretic Cassels pairing, though Neková?'s theory implies our results. Examples of the representations we consider arise naturally in the study of CM abelian varieties defined over the totally real subfield of the reflex field of the CM type. We also discuss connections with “large Selmer rank” in the sense of Mazur-Rubin and give several examples in the context of abelian varieties and modular forms.  相似文献   
965.
We establish that each lattice bimorphism from the Cartesian product of two vector lattices into a universally complete vector lattice is representable as the product of two lattice homomorphisms defined on the factors. This fact makes it possible to reduce the problem to the linear case and obtain some results on representation of an order bounded disjointness preserving bilinear operator as a strongly disjoint sum of weighted shift or multiplicative operators.  相似文献   
966.
In this paper we prove a stochastic representation for solutions of the evolution equation
where L  ∗  is the formal adjoint of a second order elliptic differential operator L, with smooth coefficients, corresponding to the infinitesimal generator of a finite dimensional diffusion (X t ). Given ψ 0 = ψ, a distribution with compact support, this representation has the form ψ t  = E(Y t (ψ)) where the process (Y t (ψ)) is the solution of a stochastic partial differential equation connected with the stochastic differential equation for (X t ) via Ito’s formula.   相似文献   
967.
We obtain some integral representations of the form f(x) = P(f) + K(?f) on the Carnot groups, where P(f) is a polynomial and K is an integral operator with a specific singularity. These representations are employed to prove the weak Poincaré inequality.  相似文献   
968.
We present an extension of a version of Naimark's dilation theorem which states that complete systems in a Hilbert space are projections of -linearly independent systems of elements of an ambient Hilbert space. This result is presented in the context of other known extensions of Naimark's theorem.

  相似文献   

969.
We study the kernels in the remainder terms of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at , when the weight is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel attains its maximum on the real axis (positive real semi-axis) for each . It was stated as a conjecture in [Math. Comp. 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes in the corresponding Gauss-Turán quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each . Numerical examples are included.

  相似文献   

970.
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n . We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.   相似文献   
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