Automorphism subgroups for designs with $$\lambda =1$$ λ = 1

Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order,  if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there...     

Automorphism groups of designs with λ=1

If $G$ is a finite group and $k=q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a 2-$(v,k,1)$-design $\mathbf{D}$ for which $\mathrm{Aut}\mathbf{D}?G$.     

Velocity Addition Theorem and Einstein-Dopfleh Effect

The Einstein velocity addition theorem can be derived from the Einstein-Doppler expression in contrast to Pauli's assertion that the one has nothing to do with the other.     

Computer simulation of interactions in the NH3-CO2-H2O system

Computer simulation of interactions in the NH₃-CO₂-H₂O system was performed using a quantum-chemical method B3LYP/6-31G(d,p) for the simulation of the possible routes of the reactions and the estimation of the energy parameters: interaction energy between molecules in complexes, activation energy of forward and reverse reactions, and the heat of the reaction. A new version of termolecular reaction mechanism is proposed and investigated. The probability of realization of various paths of interaction in the NH₃-CO₂-H₂O system was shown to be determined by the temperature: at low temperatures the termolecular mechanism is more probable, while at the temperatures close to the standard conditions carbamate and bimolecular mechanisms are preferable.     

Monitoring and Statistical Analysis of Formation of Organochlorine and Organobromine Compounds in Drinking Water of Different Water Intakes

The main drawback of drinking water chlorination involves the formation of quite hazardous disinfection by-products (DBPs), represented mainly by halogenated species. Based on the authors’ monitoring data since 2002, the prevalence of chlorine over bromine in the composition of volatile DBPs was shown for the drinking water in Ufa (Russia). However, the situation was completely reversed in the case of semi-volatile DBPs. The principal goal of the present study involved rationalization of the results of the long-term monitoring. Gas chromatography–mass spectrometry (GC-MS) was used for the qualitative and quantitative analysis of volatile DBPs. Identification of semi-volatile compounds was carried out with GC-MS, while gas chromatography with an atomic emission detector (GC-AED) was used for their quantification. A significant contribution of oxygen to the composition of semi-volatile compounds proves the decisive role of the dissolved organic matter oxidative destructive processes. Statistical analysis revealed notable linear correlations for trihalomethane and haloacetic acid formation vs. chlorine dose. On the contrary, halogenated semi-volatile products do not demonstrate any correlations with the water quality parameters or chlorine dose. Principal component analysis (PCA) placed them into separate groups. The results allow for proposing that formation of the organohalogenated species involved the fast penetration of bromine into the humic matter molecules and, further, their oxidative destruction by active chlorine.     

A problem for a micropolar rectangular region in the fifth approximation

An isotropic micropolar two-dimensional region is considered. Several equations of the fifth approximation for displacements and rotations are derived in terms of moments with respect to the Legendre polynomials. Based on these equations, the solutions obtained in the framework of the micropolar theory are compared with the solutions obtained in the framework of the classical theory of elasticity.     

Improved rigorous bounds on the effective elastic moduli of a composite material

A new method for deriving rigorous bounds on the effective elastic constants of a composite material is presented and used to derive a number of known as well as some new bounds. The new approach is based on a presentation of those constants as a sum of simple poles. The locations and strengths of the poles are treated as variational parameters, while different kinds of available information are translated into constraints on these parameters. Our new results include an extension of the range of validity of the Hashin-Shtrikman bounds to the case of composites made of isotropic materials but with an arbitrary microgeometry. We also use information on the effective elastic constants of one composite in order to obtain improved bounds on the effective elastic constants of another composite with the same or a similar microgeometry.     

Loops in one-dimensional random walks

Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate numerically and analytically loops in several types of RWs, including RWs with continuous step-length distribution. We show that for long walks the probability density of the longest loop becomes independent of the details of the walks and definition of the loops. We investigate crossovers and convergence of probability densities to the limiting behavior, and obtain some of the analytical properties of the universal probability density. Received 8 January 1999     

Rationale Zerlegung der birationalen Transformationen in ihre Primfactoren

Ohne Zusammenfassung     

Theorie der Transformationen ImR 3, welche keine Fundamentalcurven 1. Art besitzen und ihrer endlichen gruppen

Ohne Zusammenfassung “We have first raised a dust and them complain, that we cannot see”.Berkeley