Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

Phase state stabilization of ammonium nitrate for creating an oxidizing agent for smokeless gas-generating formulations yielding no toxic combustion products

Methods for phase stabilization of ammonium nitrate were sought for in order to considerably expand the application area of this oxidizing agent in various-purpose self-combustible formulations, including that in a new generation of gas-generating formulations for automobile air bags. New methods for stabilization of ammonium nitrate were studied and, in particular, a search was made for organic compounds that can stabilize ammonium nitrate even at their low content. The mechanism of phase state stabilization of ammonium nitrate by compounds of this kind was examined.     

The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

Gas adsorption in mcm-41 porous silicas dynamic measurements using sans

The European Physical Journal E - The isothermal gas adsorption of two hexane isomers (n-hexane and cyclohexane) in the mesopores of MCM-41 silica have been investigated by small angle neutron...     

Approximate inverse computation using Frobenius inner product

Parallel preconditioners are presented for the solution of general linear systems of equations. The computation of these preconditioners is achieved by orthogonal projections related to the Frobenius inner product. So, min_M∈??∥AM?I∥ _F and matrix M₀∈?? corresponding to this minimum (?? being any vectorial subspace of ??_n(?)) are explicitly computed using accumulative formulae in order to reduce computational cost when subspace ?? is extended to another one containing it. Every step, the computation is carried out taking advantage of the previous one, what considerably reduces the amount of work. These general results are illustrated with the subspace of matrices M such that AM is symmetric. The main application is developed for the subspace of matrices with a given sparsity pattern which may be constructed iteratively by augmenting the set of non‐zero entries in each column. Finally, the effectiveness of the sparse preconditioners is illustrated with some numerical experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.