Quantum Interference, Quantum Theory of Measurement, and (In)completeness of Quantum Mechanics

The new techniques and ideas in quantum interferometry with neutrons, photons, atoms, electrons, and Bose condensates that fluorished in the last two decades have influenced in a decisive way the thinking and the research in the foundations and interpretation of quantum mechanics. The controversies existing among different schools on the reality of matter waves of quantum theory, the postulates of quantum measurement theory, and the (in)completeness of quantum mechanics have to be approached now in a new way. Our argumentation follows the spirit of the Paris school.     

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.     

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.     

The silicon effect on the regioselectivity of the Tsuji-Trost reaction. Experimental and theoretical approaches

Regioselectivity of the Tsuji-Trost reaction on allyl acetates and carbonates substituted with silyl groups at the olefinic moiety has been analyzed. Silicon atom in the central carbon atom increases the stability of the intermediate π-allylpalladium cation with respect to the isomeric π-allylpalladium cation featuring the silicon in a terminal carbon atom.     

On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.     

On the Rees algebra of certain codimension two perfect ideals

 Suppose ? is a set of arbitrary number of smooth points in ℙ² its defining ideal. In this paper, we study the Rees algebras of the ideals generated by I _t , t ≥α. When the points of ? are general, we give a set of defining equations for the Rees algebra . When the points of ? are arbitrary, we show that for all t≫ 0, the Rees algebra is Cohen-Macaulay and its defining ideal is generated by quadratics. A cohomological characterization for arithmetic Cohen-Macaulayness of subvarieties of a product space is also given. Received 4 April 2001     

IR finite one-loop box scalar integral with massless internal lines

The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments. Received: 31 January 2002 / Published online: 26 April 2002     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.