Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

High-accuracy measurer of complex reflection coefficient of SHF transmission lines

We describe a new method of constructing a device for simultaneous measurement of the relative amplitude and phase difference of microwave signals, using complex phase manipulation of input signals. It is shown that systematic errors of measurement are significantly lower in the proposed amplitude and phase meter. Root-mean-square values are obtained for a system with nonideal elements. A block diagram of the device is presented and its principal characteristics are described. Institute of Radiophysics and Electronics, Armenian Academy of Sciences, Erevan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 9, pp. 1182–1188, September, 1997.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Fast switching anisotropic networks obtained by in situ photopolymerization of liquid crystal molecules

Lightly cross-linked anisotropic networks with uniaxial and π/2 twisted orientations were produced by photopolymerization of monotropic mixtures containing liquid crystal mono and diacrylates. In this way the polymer backbone was immobilized and became decoupled from the motion of the mesogenic side groups. The networks showed very good reversibility and even after becoming isotropic, upon cooling, the initial orientation was recovered. In the same way, in the presence of electric fields the mesogenic groups could be reoriented in the direction of the electric field, reverting back to the initial orientation on removal of the field at a rate comparable with those observed in the monomeric state. Combining viscoelastic measurements with the dielectric behaviour of the monomeric liquid crystal and the anisotropic network, a comparison between the internal and bulk rotational viscosities was also made.     

On the linear relaxation of a one-dimensional bonded fluid model

The linear relaxation of a one-dimensional bonded fluid model is studied in the dynamical mean field approximation at the pair level. The results are compared with simulation data. Relaxation at low temperatures shows a cooperative character that can be understood in terms of a simple diffusion picture.     

Influence of charge distribution on the conformation of neutral polyampholytes

Summary Two polyampholyte copolymers based on sodium-2-acrylamido-2-methylsulfonate (NaAMPS) and methacryloyloxyethyltrimethylammonium chloride (MADQUAT) have been prepared either in homogeneous solution or by an inverse microemulsion polymerization technique. The copolymer microstructure was shown to depend on the method of preparation. The microemulsion polymerization yields copolymers with a monomer sequence distribution not far from random while those obtained by polymerization in solution have a strong tendency to alternation. The aqueous-solution properties of the two samples have been investigated by viscometry. The results show that the charge distribution along the copolymer chain affects considerably its conformation, in good agreement with recent theoretical studies. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994     

Mössbauer studies on some Argentinian soil: Mollisols from Bahia Blanca

Clay fractions of a Mollisol sample as is, treated with ammonium oxalate (AO), with dithionite-citrate-bicarbonate (DCB) and with dithionite-ethilene-diamine-tetraacetic acid (D-EDTA) methods, were studied. Illite-montmorillonites together with hematites, goethites and maghemites, all of the AI-substituted and with a wide range of sizes, were identified. It is found that the AO attack extracts little iron, whereas the other two attacks extract the magnetic signal. Furthermore, the DCB attack facilitates the reduction of the Fe³⁺ ions, while the D-EDTA method does not. Instead, this attack extracts more clay mineral Fe ions. A comparison with large grain soil samples is made.