Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros

Assume the Riemann hypothesis. On the right-hand side of the critical strip, we obtain an asymptotic formula for the discrete mean square of the Riemann zeta-function over imaginary parts of its zeros.     

Investigation of the electronic structure of the SbSeBr cluster

The energy levels of valence bands (VB) in SbSeBr crystals were calculated for investigation of the photoelectron emission spectra of A⁵B⁶C⁷ — type crystals. The molecular model of this crystal was used for calculation of VB by the Density Functional Theory (DFT) and Unrestricted Hartree — Fock (UHF) methods. The molecular cluster consisting of 20 molecules of SbSeBr was used for calculations of averaged total density of states including atom vibrations. The spectra of averaged total density of states from VB in the SbSeBr cluster were compared with experimental photoelectron emission spectra from VB of A⁵B⁶C⁷ — type crystals. The results of comparison clarify that the atomic vibrations are one of possible reasons for the smoother appearance of the experimental X-ray photoelectron spectrum (XPS).      

On the limit measure for the Laplace transform of the Riemann zeta-function

We identify the limit measures in limit theorems in the space of analytic functions and on the complex plane for the Laplace transform of the square of the Riemann zeta-function. Received: 22 December 2006     

In vitro and in vivo biocompatibility study on laser 3D microstructurable polymers

Films and microstructured scaffolds have been fabricated using direct laser writing out of different polymers: hybrid organic-inorganic ORMOCORE b59, acrylate-based AKRE23, novel organic-inorganic Zr containing hybrid SZ2080, and biodegradable PEG-DA-258. Adult myogenic stem cells were grown on these surfaces in vitro. Their adhesion, growth, and viability test results suggest good potential applicability of the materials in biomedical practice. Pieces of these polymers were implanted in rat’s paravertebral back tissue. Histological examination of the implants and surrounding tissue ex vivo after 3 weeks of implantation was conducted and results show the materials to be at least as biocompatible as surgical clips or sutures. The applied direct laser writing technique seems to offer good future prospects in a polymeric 3D scaffold design for artificial tissue engineering with autologous stem cells.     

A class of test functions for global optimization

We suggest weighted least squares scaling, a basic method in multidimensional scaling, as a class of test functions for global optimization. The functions are easy to code, cheap to calculate, and have important applications in data analysis. For certain data these functions have many local minima. Some characteristic features of the test functions are investigated.This paper was written while the second author was a visiting Professor at Aachen University of Technology, funded by the Deutsche Forschungsgemeinschaft.     

On a Global Optimization Algorithm for Bivariate Smooth Functions

The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.     

Pulsed-laser generation of gold nanoparticles with on-line surface plasmon resonance detection

Size of nanoparticles is an important parameter for their applications. The real-time monitoring is required for reliable and reproducible production of nanoparticles with controllable size. We present results of our research on development of the system for the online nanoparticle characterization during their production by a laser. The laser ablation chamber which allows measurements of surface plasmon resonance spectra during the nanoparticle generation process has been designed and fabricated. The online characterization system was tested by producing and modification of gold nanoparticles. Nanoparticles were generated by nanosecond-laser (wavelength 1064 nm) ablation of gold target in deionized water, and optimal conditions for the highest nanoparticle productivity were estimated. The mean diameter of nanoparticles was determined using their absorption spectra measured in the real-time during the ablation experiments and from the TEM images analysis, and it varied from 20 to 45 nm. The mismatch between nanoparticle diameters, estimated using these two methods, is due to the polydispersity of the generated nanoparticles. The further experiments of laser-induced modification of colloidal gold nanoparticles were carried out using second harmonic (wavelength 532 nm) of nanosecond Nd:YAG laser and alteration in nanoparticle size were acquired by the online measurement system.     

Axiomatic characterization of a global optimization algorithm and investigation of its search strategy

A new axiomatic characterization of a rational algorithm for global minimization based on a statistical model of the objective function is suggested. The globality of the search strategy of such an algorithm is investigated as well as the convergence of the algorithm.     

Effect of H<Subscript>2</Subscript>SeO<Subscript>3</Subscript> on the early stages of nucleation and growth during Cu electrocrystallization in acidic medium on glassy carbon electrode

The early stages of Cu electrodeposition onto a GC electrode were investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] was 1.10⁴ to 2.10². The H₂SeO₃ solution in 0.5 M H₂SO₄ was also used. The electrochemical techniques such as cyclic voltammetry and chronoamperometry and structural investigation using ex situ AFM were applied to study the nucleation and growth of Cu onto a GC electrode. Chronoamperometric results were shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model by Scharifker and Hills. The values of number of Cu nuclei N and average nuclei radius r _av were calculated. It was shown that, in the presence of H₂SeO₃ in amounts of 0.001 to 0.005 mM, N increases and r _av decreases. At higher concentrations of the additive, the changes of these parameters with the deposition potential E _dep were shown to be somewhat more complex. The dependences of N and r _av on the concentration of H₂SeO₃ in different regions of Cu overpotentials were also revealed.