Analytical solutions to the optimization of a quadratic cost function subject to linear and quadratic equality constraints

In the area of broad-band antenna array signal processing, the global minimum of a quadratic equality constrained quadratic cost minimization problem is often required. The problem posed is usually characterized by a large optimization space (around 50–90 tuples), a large number of linear equality constraints, and a few quadratic equality constraints each having very low rank quadratic constraint matrices. Two main difficulties arise in this class of problem. Firstly, the feasibility region is nonconvex and multiple local minima abound. This makes conventional numerical search techniques unattractive as they are unable to locate the global optimum consistently (unless a finite search area is specified). Secondly, the large optimization space makes the use of decision-method algorithms for the theory of the reals unattractive. This is because these algorithms involve the solution of the roots of univariate polynomials of order to the square of the optimization space. In this paper we present a new algorithm which exploits the structure of the constraints to reduce the optimization space to a more manageable size. The new algorithm relies on linear-algebra concepts, basic optimization theory, and a multivariate polynomial root-solving tool often used by decision-method algorithms.This research was supported by the Australian Research Council and the Corporative Research Centre for Broadband Telecommunications and Networking.     

A novel SRN1 substitution: the reaction between the anion of 2-nitropropane and 3-bromo-1-nitrocyclohex-1-ene

X-Ray crystallography has been used to determine the unusual cyclopropyl structure for the product of the S_RNl reaction between the anion of 2-nitropropane and 3-bromo-1-nitrocyclohex-1-ene.     

Equilibrium charge-state fractions for 2.7–31 keV deuterium atoms and ions in strontium vapor

Equilibrium charge-state fractions of 2.7–31 keV deuterium in strontium vapor are reported. The energy dependence of the D^- equilibrium yield is discussed. The results are compared with the D^- yield in cesium and magnesium vapors.     

Mass Scaling of Permanent Magnet Line Cusp Plasma Leaks

Plasma leaks to permanent magnetic produced "full line cusps" are shown to depend on ion mass as (mj?). This result is consistent with hybrid gyroradius (i.e., geometric mean of ion and electron gyroradii) leaks but not with ion gyroradius leaks.     

Nonlocal effects in the optical response of composite materials with metallic nanoparticles

A phenomenological model for the optical response of composite materials with metallic nanoparticles is presented. This model applies the conventional effective medium theories (EMT) but takes into account the spatial dispersion effects in the dielectric response of the metallic nanoparticles. This leads to an EMT that depends on the size of the particles. Numerical results from a model computation shows that this effect due to the nonlocal optical response of the nanoparticles can increase the resonant absorption frequency of the composite significantly for particles of very small sizes; and can lead to resonant absorption even in the Bruggeman symmetric EMT—a feature which is believed to be absent in the conventional treatment where local response for the metal particles has been assumed.     

Pulsed NMR observation of ultradrawn polypropylene

Proton spin-spin relaxation times have been measured as a function of temperature for ultradrawn polypropylene with draw ratios λ up to 24. The three relaxation times T_2a (the longest), T_2i (intermediate), and T_2c (the shortest), observed for all the samples, have been ascribed to the relaxations of the amorphous, constrained amorphous, and crystalline components, respectively. T_2i and T_2a, which reflect the changes in structure and mobility in the noncrystalline regions, decrease with increasing λ; T_2i becomes saturated at λ > 9, whereas T_2a shows a substantial decrease up to λ = 24. The continued decrease in T_2a indicates that the constraint on the amorphous segments keeps increasing up to the highest λ. The associated mass fractions F_a, F_i, and F_c also change with λ. At λ < 9, the increasc in F_i with increasing λ is accompanied by a decrease in F_a, with F_c remaining unchanged. At higher λ, however, F_a is almost constant, and stepwise rises in F_c at about λ = 12 and 24 are accompanied by corresponding drops in F_i. It seems that, in this high draw ratio range, some of the taut molecules are fully extended and are in sufficiently good lateral register to transform into crystalline bridges. This conjecture is supported by the similarity in the λ dependence of F_c and the mass-fraction crystallinity obtained from the heat of fusion.     

Partial spin depolarization of muonium in ice

Muon spin precession signals arising from both muonium and a diamagnetic muon species have been studied in single crystal of ice over the temperature range 90–263 K. Conversion of initial signal amplitudes to fractions of muon polarization reveals that for temperatures above 200 K part of the original muon polarization is unaccounted for. Such a missing fraction is well known for liquid water. but was not found in earlier work on polycrystalline ice. Muonium signals in Polycrystalline ice were reanalyzed using a non-exponential decay function appropriate to the powder pattern spectrum. Smaller muonium fractions were found. consistent with those determined for single crystall, thus confirming the existence of the missing fraction. The origin of the missing fraction is discussed, and it is proposed that non-reactive spin exchange encounters between muonium and hydrogen atoms may be the cause.     

Subject index to volume 26

The reflectivity of picosecond pulses from a Nd: glass laser on Ge has been measured. A marked increase (∽ 20%) has been found at excitation intensities just below the damage threshold. The effect is discussed in terms of the contribution to the dielectric constant of the crystal, arising from direct intraband transitions within the branches of the valence band. The relevance of these transitions to explain the “plateau” observed in the transmission experiment, is also briefly pointed out.     

Dynamic analysis of periodic structures

The natural vibration analysis of a periodic structure with repeated identical substructures may be simplified by using some symmetrical properties of the substructure dynamic matrices, resulting in a set of linear difference equations in the displacements. These equations are readily solved for cyclic symmetric systems, simply supported systems and infinite systems. The order of the overall frequency equations is at most equal to one half of the total number of degrees of freedom retained for a single substructure regardless of the number of substructures in the system. With these natural modes, the system with general boundary conditions at end stations is analyzed by a fast converging method.