152,642 research outputs found
Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
We introduce new fractional operators of variable order on isolated time
scales with Mittag-Leffler kernels. This allows a general formulation of a
class of fractional variational problems involving variable-order difference
operators. Main results give fractional integration by parts formulas and
necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with
Springe
Second-order discrete Kalman filtering equations for control-structure interaction simulations
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix
Universal Rashba Spin Precession of Two-Dimensional Electrons and Holes
We study spin precession due to Rashba spin splitting of electrons and holes
in semiconductor quantum wells. Based on a simple analytical expression that we
derive for the current modulation in a broad class of experimental situations
of ferromagnet/nonmagnetic semiconductor/ferromagnet hybrid structures, we
conclude that the Datta-Das spin transistor (i) is feasible with holes and (ii)
its functionality is not affected by integration over injection angles. The
current modulation shows a universal oscillation period, irrespective of the
different forms of the Rashba Hamiltonian for electrons and holes. The analytic
formulas approximate extremely well exact numerical calculations of a more
elaborate Kohn--Luttinger model.Comment: 7 pages, 2 eps figures included, minor change
Deformation Quantization of Poisson Structures Associated to Lie Algebroids
In the present paper we explicitly construct deformation quantizations of
certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although
the considered Poisson structures in general are far from being regular or even
symplectic, our construction gets along without Kontsevich's formality theorem
but is based on a generalized Fedosov construction. As the whole construction
merely uses geometric structures of E we also succeed in determining the
dependence of the resulting star products on these data in finding appropriate
equivalence transformations between them. Finally, the concreteness of the
construction allows to obtain explicit formulas even for a wide class of
derivations and self-equivalences of the products. Moreover, we can show that
some of our products are in direct relation to the universal enveloping algebra
associated to the Lie algebroid. Finally, we show that for a certain class of
star products on E^* the integration with respect to a density with vanishing
modular vector field defines a trace functional
Numerical integration formulas of degree two,
Abstract Numerical integration formulas in n-dimensional nonsymmetric Euclidean space of degree two, consisting of n + 1 equally weighted points, are discussed, for a class of integrals often encountered in statistics. This is an extension of Stroud's theory [A.H. Stroud, Remarks on the disposition of points in numerical integration formulas, Math. Comput. 11 (60) (1957) 257-261; A.H. Stroud, Numerical integration formulas of degree two, Math. Comput. 14 (69) (1960) 21-26]. Explicit formulas are given for integrals with nonsymmetric weights. These appear to be new results and include the Stroud's degree two formula as a special case
On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
In this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods
Modified Runge-Kutta methods for solving ODES
A class of Runge-Kutta formulas is examined which permit the calculation of an accurate solution anywhere in the interval of integration. This is used in a code which seldom has to reject a step; rather it takes a reduced step if the estimated error is too large. The absolute stability implications of this are examined
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