On the condensate values in QCD

Conclusions The sets (3) and (4) of condensates have been compared using the QCD sum rules (2) with indefinite weight functions. A bad matching between both sets of condensates and experimental data has been obtained. The standard values (3) appear to be closer to data but some increase ofQ is necessary to improve the agreement. Only higher values ofm ₀ ² could change the results of this analysis. It is interesting that negative values ofm ₀ ² considerably improve the agreement with data; note that this quantity cannot be determined with a sufficient accuracy. We conclude that the QCD sum rules (2) cannot definitely determine a privileged set of condensates.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Novel liquid crystals based on [1]benzothieno[3,2- b ][1]benzothiophene

Four series of new [1]benzothieno[3,2- b ][1]benzothiophene derivatives have been synthesized. In the non-chiral series a SmA phase occurs, while the chiral series exhibits a rather wide antiferroelectric SmC * A phase just below the SmA phase. The SmA-SmC * A phase transition has been studied using DSC and dielectric spectroscopy. In the SmC * A phase the spontaneous quantities have been measured. The tilt angle shows a typical temperature dependence and the values of spontaneous polarization are rather moderate. The length of the helical pitch increases on increasing the length of the non-chiral alkyl chain.     

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators     

Randomization helps to perform independent tasks reliably

This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

On regularity of a weak solution to the Navier–Stokes equation with generalized impermeability boundary conditions

We consider the 3D Navier–Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution (‘strong’ in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity.     

Scientist up to the highest level

Dr. Miroslav Kyrš, DrSc. passed away prematurely and unexpectedly in August 2006 at age of 75. He was a leading person of the Czech radiochemistry during the second half of the 20th century and his results have of world-wide impact. His diligence, intelligence and permanent activity led him to be at first a laboratory chief and subsequently for about 25 years to be a chief of the Radiochemical Department of Czech Nuclear Research Institute (NRI) at Řež near Prague.     

Parton-hadron duality in event generators

The validity of local parton-hadron duality within the framework of HERWIG and JETSET event generators is investigated. We concentrate one ⁺ e ^– annihilations in LEP 2 energy range as these interactions provide theoretically the cleanest condition for the discussion of this concept. We conclude that the concept of local parton-hadron duality is not valid in either of the two generators considered.