On zeta-functions associated to certain cusp forms. I

In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained. Partially supported by Lithuanian Foundation of Studies and Science     

Generalized Relative Entropies as Contrast Functionals on Density Matrices

We use a class of generalized relative entropies on density matrices to obtain one-parameter families of torsion-free affine connections.     

Repetition rate multipliers for efficient implementation of multiphoton and pump-probe fluorescence microscopy

With the advances in pulsed laser systems, microscopic imaging techniques such as multiphoton and pump-probe fluorescence microscopy have developed into effective tools for investigating intensity and time-resolved phenomena inside biological systems. However, pulsed lasers used in these techniques usually are commercial systems with repetition frequencies of around 80 MHz. While these systems have proven to be adequate for multiphoton and pump-probe microscopic imaging applications, the temporal separation of the laser pulse train (around 12.5 ns) is long compared to the fluorescence lifetimes of many common fluorescence species. In this work, we present the designs of repetition rate multipliers based on passive optical components that can be used to increase the efficiency in multiphoton and pump-probe fluorescence microscopy. Depending on the lifetime of fluorescence molecules under investigation, the passive repetition rate multiplier can increase the duty cycle of multiphoton or pump-probe microscopy up to fourfold.     

Lanthanum nitrate decomposition by both temperature programmed heating and citrate gel combustion

Thermal decomposition of lanthanum nitrate to lanthanum oxide was carried out by both temperature programmed heating (TPH) and citrate-gel combustion. The temperature programmed heating was carried out under flow of oxidizing (air), neutral (nitrogen) and reducing (25 vol.% hydrogen+argone mixture) gases, and the processes were controlled by simultaneous thermogravimetry and differential thermal analysis. It was shown that hydrogen atmosphere helps to reduce temperatures of all decomposition steps. The results of TPH were utilized to check the nature of residues in the products of lanthanum nitrate-to-oxide conversion performed via citrate-gel combustion technique.     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.     

Colour intransparency and the cross sections for colour-singlet and colour-octet hadrons in the Low-Nussinov model

The dependence of cross sections on the colour state of the colliding hadrons is investigated within the Low-Nussinov model of two-gluon exchange. The total cross sections for colour-octet hadrons are practically constant as functions of the hadronic radii, while they tend to zero when the radii of the colour-singlet hadrons approach zero. The slope parameter of the differential clastic cross sections for small momentum transfers is rather insensitive to the colour structure of the colliding hadrons. The integrated colour exchange cross section is calculated.