Optimization of Growth Conditions for Test Fungus Cultures used in Direct Bioautographic TLC Detection. 3. Test Fungus: Candida albicans

JPC – Journal of Planar Chromatography – Modern TLC - Optimum conditions have been established for culture of the fungus Candida albicans (ATCC 90028) for microbial detection of zones...     

Circularity of numerical ranges and block-shift matrices

Let A be a square complex matrix. Several characterizations are found for A to be permutationally similar to a block-shift matrix. One interesting equivalent condition is that the numerical range of every matrix with the same zero pattern as A is a circular disk. Equivalent conditions for the characteristic polynomial of the hermitian part of the matrix e^iθA to be the same for all real values θ are also obtained.Complex matrices of order four that are unitarily similar to a block-shift matrix are identified. A result of Marcus and Pesce [6] is extended, and an open question of Li and Tsing [4] is also answered partially.     

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140. Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan. Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028     

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

Optical and acoustic study of nucleation and growth of bubbles at a liquid-solid interface induced by nanosecond-pulsed-laser heating

The dynamics of liquid-vapor phase-change in the nanosecond time-scale induced by pulsed-laser heating of a liquid on a solid sample is studied by means of optical reflectance and scattering measurements, and the piezoelectric detection technique. The liquids studied include water, ethanol, methanol, IsoproPropyl Alcohol (IPA), and mixtures of water and IPA. The threshold fluence for nucleation is determined with high accuracy using the optical and acoustic signals. Heat diffusion calculations performed for the threshold fluences indicate that the liquids are sufficiently superheated before nucleation sets on. The transient optical reflectance signal is analyzed by an effective-medium theory to provide bubble-growth kinetics, so that the bubble-growth velocity for the test liquids could be estimated. In addition, it is observed that, following the thermally induced nucleation, repetitive acoustic cavitation at the surface of the solid sample occurs, with a time interval related to the speed of sound in the liquid.     

Some Global Optimization Problems on Stiefel Manifolds

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem.     

A Smoothing Newton Method for Semi-Infinite Programming

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer–Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically.     

Fluorescence feedback control of a diode pumped solid state laser

We implement active feedback control in a Q-switched diode-pumped Nd:YVO₄ laser by monitoring the fluorescence intensity from the laser crystal. When the initial inversion level indicated by the detected fluorescence has reached a predetermined value, Q-switching is initiated. The Q-switched pulse energy is stabler with our feedback scheme based on the fluorescence intensity than that with the conventional Q-switching when pumping source is not stable.