Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

On classification of conformally flat spaces

Classification of conformally flat n-dimensional pseudo-Riemannian spaces via Plebanski's method is discussed. It is based on embedding these spaces into a flat (n + 2)-dimensional space and on finding their minimal isometry groups which are subgroups of the conformal group. In particular, the case n = 4 is given in full detail and compared with incomplete results known in the literature. The found conformally flat spacetimes are identified with the associated solutions of the Einstein equations and with the spacetimes used in various cosmological considerations.     

Homomorphic images of finite subdirectly irreducible unary algebras

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. While working on this paper the first and the third authors were partially supported by the Grant Agency of the Czech Republic, grant #201/02/0594, and by the institutional grant MSM0021620839; the second author was supported by the Ministry of Science, Technologies and Development of Republic of Serbia, grant no. 1227.     

Scattering and bound states of a nonrelativistic neutral spin-1/2 particle in a magnetic field

We have investigated the scattering and bound states of a nonrelativistic spin-1/2 particle in the system ofN magnetic barriers (or magnetic wells) andN magnetic delta functions. We have studied three types of problems: tunnelling with spin, band structure and change of polarization during transmission and reflection.     

A one‐dimensional CdII coordination polymer: catena‐poly[cadmium(II)‐bis(μ‐6‐methylpicolinato)]

In the title compound, [Cd(C₇H₆NO₂)₂]_n, the Cd^II ion has a distorted octahedral geometry. The 6‐methylpyridine‐2‐carboxylate anions are perpendicular to one another and act as bidentate and bridging ligands. Two carboxylate O atoms bridge the Cd^II ions, forming centrosymmetric dinuclear units. These units are further connected via carboxylate O atoms into a one‐dimensional polymeric chain which extends in the [100] direction.     

EPR investigation of cell membrane fluidity upon external oxidative stimulus

The perturbation of the physical state of cell membranes triggered by an external oxidative stimulus has been studied with sperm cells which were chosen as a model system. Electron paramagnetic resonance (EPR) spectroscopy was applied and three different nitroxides bearing a paramagnetic group on the 5th, 7th and 13th carbon of the stearic acid acyl chain were used to probe different regions of the membrane. The theoretical simulations of the experimental spectra indicate distinct domains in the intact cell plasma membrane where local steric constraints impose different degrees of motional averaging experienced by the reporter group. Upon the external oxidative stimulus the spectral changes were proportional to the accumulated oxidation products and were detected only for the reporter group residing close to the lipid-water interface. The EPR spectra reveal that the motion of the reporter group has slowed down in the oxidized cells and that the oxidatively modified membrane shows up as a more rigid structure as compared with the native state. The results also indicate that the oxidation-induced spectral changes are supressed in the presence of gangliosides.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.