A method for automatic correction of drift-distorted SPM images

A method for automatic correction of drift-distorted surface images obtained using a scanning probe microscope is developed. For the case of slowly varying drifts, simple linear transformations describing the observed distortions are constructed. One or two pairs of counter-scanned images (CSIs) are used as initial data. A system of linear equations is solved by finding the coordinate of the same surface feature in each CSI. The solutions obtained, i.e., linear transformation coefficients, are used to correct drift-induced distortions in horizontal and vertical planes. Two nonlinear drift correction methods are proposed, which provide a better accuracy in comparison with the linear correction method. The developed method can be used in feature-oriented scanning of the surface.     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Carleman problem for two pairs of functions in a ring

We consider a particular case of the matrix Carleman problem for two pairs of functions in a ring and find a constructive solution of this problem. In addition, we propose an algorithm for the construction of solutions for two infinite systems of smooth transition and for a system of two singular equations of special type. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 662–671, May, 1997     

On instability of conservative systems with gyroscopic forces

Theorems on equilibrium instability of conservative systems with gyroscopic forces are proved. The theorems obtained are nonlinear analogs of the Kelvin theorem. The equilibrium instability of the Chaplygin nonholonomic systems is considered. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1422–1428, October, 1997.     

Protein Conformation of a Lattice Model Using Tabu Search

We apply tabu search techniques to the problem of determining the optimal configuration of a chain of protein sequences on a cubic lattice. The problem under study is difficult to solve because of the large number of possible conformations and enormous amount of computations required. Tabu search is an iterative heuristic procedure which has been shown to be a remarkably effective method for solving combinatorial optimization problems. In this paper, an algorithm is designed for the cubic lattice model using tabu search. The algorithm has been tested on a chain of 27 monomers. Computational results show that our method outperforms previously reported approaches for the same model.     

U(2, 2) Symmetry as a Common Basis for Quantum Theory and Geometrodynamics

We formulated some criticisms of the Diracequation and its Clifford-algebraic philosophy; inparticular, we show that, within a general-relativisticcontext, they seem to contain hidden action-at-distance concepts. We suggest a new model based on thefour-component Klein-Gordon equation locally invariantunder the U(2,2) gauge group. The usual Dirac equationis then obtained as a certain approximation. The geometrodynamical sector shows reasonablecorrespondence with general relativity.     

Substitution of calcium by strontium within selected calcium phosphates

Sr incorporation in the molecules of amorphous calcium phosphate, apatitic tricalcium phosphate, hydroxyapatite, octacalcium phosphate and dicalcium phosphate dihydrate was investigated. The concentration of Sr ranged from 225 to 1010 μ g / g, i.e. it overlapped with the physiological range of Sr concentrations in human bone. The leading experimental technique was extended X-ray absorption fine structure (EXAFS) at the Sr K edge. Results of these studies demonstrated the following: (1) Sr incorporation in the calcium phosphates is compound-dependent, (2) the coordination of incorporated Sr atoms in the Ca-P molecules is similar to that of Ca atoms, but interatomic distances are ≈0.015 nm larger, (3) in apatitic tricalcium phosphate, hydroxyapatite and octacalcium phosphate lattices Sr atoms may occupy selected Ca sites, which was not the case for dicalcium phosphate dihydrate, (4) in the apatite lattice Sr atoms are coordinated by 6 PO₄ tetrahedrals and (5) EXAFS spectra at the K edge of the incorporated Sr may be used to distinguish the structures of amorphous calcium phosphate, dicalcium phosphate dihydrate as well as apatite and its derivatives (apatitic tricalcium phosphate, octacalcium phosphate).     

X-ray induced fluorescence spectrometry at grazing incidence for quantitative surface and layer analysis

Summary Single layers and layer systems on diverse substrates were measured by Total Reflection X-Ray Fluorescence (TXRF) spectrometry. The angular dependence of the fluorescence intensities at grazing incidence allows the elemental composition, density and thickness of the layers to be evaluated using model calculations.