Completeness of coherent states associated with self-similar potentials and Ramanujan's integral extension of the beta function

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.

On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

FUNCTIONAL ALPHA-TROPOMYOSIN PRODUCED IN ESCHERICHIA-COLI - A DIPEPTIDE EXTENSION CAN SUBSTITUTE THE AMINO-TERMINAL ACETYL GROUP

Unlike the muscle protein, alpha-tropomyosin expressed in Escherichia coli does not bind actin, does not exhibit head-to-tail polymerization, and does not inhibit actomyosin ATPase activity in the absence of troponin. The only chemical difference between recombinant and muscle tropomyosins is that the first methionine is not acetylated in the recombinant protein (Hitchcock-DeGregori, S. E., and Heald, R. W. (1987) J. Biol. Chem. 262, 9730-9735). We expressed three fusion tropomyosins in E. coli with 2, 3, and 17 amino acids fused to its amino terminus. Ah three fusions restored actin binding, head-to-tail polymerization, and the capacity to inhibit the actomyosin ATPase to these unacetylated tropomyosins. Unlike larger fusions, the small fusions of 2 and 3 amino acids do not interfere with regulatory function. Therefore the presence of a fused dipeptide at the amino terminus of unacetylated tropomyosin is sufficient to replace the function of the N-acetyl group present in muscle tropomyosin. A structural interpretation for the function of the acetyl group, based on our results and the coiled coil structure of tropomyosin, is presented.

The high-eccentricity asymmetric expansion of the disturbing function for non-planar resonant problems

In this paper we present an extension to the nonplanar case of the asymmetric expansion of the averaged resonant disturbing function of Ferraz-Mello & Sato (1989, A&A 225, 541-547). Comparions with the exact averaged disturbing function are also presented. The expansion gives a good approximation of the exact function in a wide region around the center of expansion.

Electromyographic behaviour of the gastrocnemius muscle during knee extension and flexion performed on the leg press

The gastrocnemius was analysed in 10 male volunteers during knee flexion and extension with the foot in normal, plantar flexion and dorsal flexion positions. Hewlett-Packard surface electrodes, an electromyographic signal amplifier, a computer equipped with an AID conversion plaque (Model CAD 10/26), a software specially designed to record and analyse the signals, a horizontal leg press, and electrogoniometers were used. The gastrocnemius muscle showed strong potentials at the end of knee extension and beginning of knee flexion. The muscle presented a similar activity both in the zipper and lower platforms. As to bilateral action, the right gastrocnemius presented stronger potentials on the upper platforms, whereas the potentials were bilaterally similar on the lower platforms. As for foot position, the gastrocnemius presented strong potentials when the foot was in plantar flexion. The remaining positions had no effect on the work of the muscle.

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.