Abstract. The titanium samples alloyed with molybdenum and aluminum are used to conduct full high-precision X-ray experiments enabling determine the characteristic of atomic interrelations - unit cell dimension, establish phase components doped single crystal. An orthorhombic is found, volume which increases after deformation impact.

Valiant’s theorem from the previous lecture is meaningless for infinite hypothesis classes, or even classes with more than exponential size. In 1968, Vladimir Vapnik and Alexey Chervonenkis wrote a very original and influential paper (in Russian) [5, 6] which allows us to estimate the sample complexity for infinite hypothesis classes too. The idea is that the size of the hypothesis class is a p...

It is shown that in the existing models of solar cell, assumptions were made about ideally smooth surface topography, which had a significant impact on calculation output parameters. proposed to take into account real working area receiving cell improve accuracy, linearity and stability current-voltage characteristics. A geometric model structure has been developed, describes takes changes semi...

Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.

Using Voiculescu’s notion of a matricial microstate we introduce fractal dimensions and entropy for finite sets of self-adjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. We relate the new quantities to free entropy and free entropy dimension and show that a modified version of free Hausdorff dimension is an algebrai...