Solution of nonlinear boundary value problems—X: The false transient method

The solution of a nonlinear boundary value problem may be found by solving a pertinent transient equation until the solution ceases to change significantly (the false transient method). The method is used to get a solution of a strongly nonlinear diffusion problem as well as towards solution of equations arising in the boundary layer theory. If multiple solutions occur the false transient method is not capable of calculating all profiles. For the boundary layer problems it is difficult to construct a reliable false transient equation if it is not based on a physically “sound” transient model.     

Diffractive-optics-based sensor as a tool for detection of biocompatibility of titanium and titanium-doped hydrocarbon samples

Adsorption of the elongated human plasma fibrinogen (HPF) and globular human serum albumin molecules on a titanium-based surface is monitored by analyzing permittivity and optical roughness of protein-modified surfaces by using a diffractive optical element (DOE)-based sensor and variable angle spectro-ellipsometry (VASE). Both DOE and VASE confirmed that fibrinogen forms a thicker and more packed surface adlayer compared to a more porous and weakly adsorbed albumin adlayer. A linear relation of the permittivity (ε(')) and dielectric loss (ε(')) was found for some of the dry titanium-doped hydrocarbon (TDHC) surfaces with excellent HPF adsorption ability. We discuss some aspects of TDHC's aging and its possible effects on fibrinogen adsorption.     

50-nm local anodic oxidation technology of semiconductor heterostructures

A novel approach to local anodic oxidation technique, which leads to approximately equal 50 nm wide line patterns, is described. The technique is utilized to prepare quantum point contact on a low-mobility semiconductor heterostructure. Transport measurements show quantized conductance in zero magnetic field at 4.2 K thanks to very short one-dimensional constriction. The technique is also used for the definition of low-to-room temperature sub-micrometer Hall probes to show its applicability for the room temperature applications. The magnetic-field resolution and the sensitivity of the probes are evaluated in dependence of the probe dimensions, bias current, and temperature. The 200-nm probe shows magnetic-field resolution of 47 microT/(Hz)(1/2) at 140 Hz and at 4.2 K, when it is driven by 5 microA bias current. The novel approach is promising for the development of the future nano-devices operated both at low and room temperatures. To our knowledge, local anodic oxidation technique applied directly to shallow semiconductor heterostructure has been successfully used for the room temperature application for the first time.     

Dynamics of a Q-analogue of the Quantum Harmonic Oscillator

Abstract

We analyse the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the q-analogue of the coherent state. Non-trivial behaviour of the mean values of the q-position operator is observed. The squeezing of the second-order moments of this operator is studied.     

MPC‐based approximate dual controller by information matrix maximization

This paper proposes a method to approximate a dual controller by a computationally feasible algorithm. Dual control that optimally solves the problem of simultaneous control and identification of a system with uncertain parameters is known to be both analytically and computationally unsolvable. This paper proposes a multiple‐step active control algorithm that gives a suboptimal but tractable solution to the original dual control problem. The algorithm is based on model predictive control (MPC) and approximates persistent system excitation in terms of the increase of the lowest eigenvalue of the parameter estimate information matrix. The problem is formulated as a two‐phase optimization problem, where first an MPC solution is found and then the lowest eigenvalue of the information matrix is maximized in the next step within a given permitted input perturbation. Unlike similar methods, the proposed algorithm predicts the information matrix for more than one step of control, which makes it possible to uniformly excite the parameter space. The use of MPC in the first design phase instead of a cautious controller is justified by showing unfavorable properties of cautious control. The advantage of the multiple‐step prediction over single‐step prediction is shown by examples and simulations. The proposed algorithm is analyzed in terms of convergence and complexity, and stability issues are addressed. The formal proofs are included in the Appendix. Copyright © 2012 John Wiley & Sons, Ltd.     

Production of biogenic amines by lactic acid bacteria and bifidobacteria isolated from dairy products and beer

The aim was to monitor production of eight biogenic amines (BAs) (histamine, tyramine (TYR), tryptamine, putrescine, cadaverine (CAD), phenylethylamine, spermine and spermidine) by selected 81 lactic acid bacteria (LAB) strains: Lactobacillus, Lactococcus, Leuconostoc, Enterococcus, Pediococcus, Tetragenococcus and Bifidobacterium. The tested LAB and bifidobacteria were isolated from dairy products and beer. The decarboxylase activity of the micro‐organisms was studied in growth medium after cultivation. The activity was monitored by HPLC after the pre‐column derivatisation with dansylchloride. Fifty LAB showed decarboxylase activity. Thirty‐one strains produced low concentrations of CAD (≤10 mg L^?1). Almost 70% of beer isolates generated higher amounts of TYR (≤3000 mg L^?1). Most of the tested LAB demonstrated decarboxylase activity. The above micro‐organisms can contribute to the increase of content of BAs in dairy products or beer and thereby threaten food safety and health of consumers. Production of BAs even by the representatives of some probiotic strains (Bifidobacterium and Lactobacillus rhamnosus) was detected in this research. This study has also proved that contaminating LAB can act as sources of higher amounts of CAD and TYR in beer.     

A note on Computing simple bifurcation points

A direct method computing simple bifurcation points or isola formation centres is suggested. It is based on an improved implementation of the method published in Computing 35, 277–294 (1985) by G. Pönisch.