Braid Monodromy Factorization and Diffeomorphism Types

In this manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this and the Chisini conjecture, we obtain that if two discriminant curves (or branch curves in other terminology) of generic projections (to the plane) of surfaces of general type imbedded in a projective space by means of a multiple canonical class have equivalent braid monodromy factorizations, then the surfaces are diffeomorphic (if we consider them as real 4-folds).Comment: 2 files: TEX file of text and file of figures (gzipped

On Symplectic Coverings of the Projective Plane

We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\bar H$ and, maybe, along a line "at infinity" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\"{a}hler symplectic form (assuming that if $\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\bar{H}$ are investigated and applied to the calculation of the first Betti number $b_1(\bar X_n)$ of a resolution $\bar X_n$ of singularities of $n$-sheeted cyclic coverings of $\mathbb C\mathbb P^2$ branched along $\bar H$ and, maybe, along a line "at infinity". We prove that $b_1(\bar X_n)$ is even if $\bar H$ is an irreducible Hurwitz curve but, in contrast to the algebraic case, that it can take any non-negative value in the case when $\bar H$ consists of several irreducible components.Comment: 42 page

Dynamics of abelian subgroups of GL(n, C): a structure's Theorem

In this paper, we characterize the dynamic of every abelian subgroups $\mathcal{G}$ of GL($n$, $\mathbb{K}$), $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$. We show that there exists a $\mathcal{G}$-invariant, dense open set $U$ in $\mathbb{K}^{n}$ saturated by minimal orbits with $\mathbb{K}^{n}- U$ a union of at most $n$ $\mathcal{G}$-invariant vectorial subspaces of $\mathbb{K}^{n}$ of dimension $n-1$ or $n-2$ on $\mathbb{K}$. As a consequence, $\mathcal{G}$ has height at most $n$ and in particular it admits a minimal set in $\mathbb{K}^{n}-\{0\}$.Comment: 16 page

Thermodynamic modeling and analysis of the structure of a heat-resistant alloy of the Fe-Cr-Ni system

There has been carried out thermodynamic modeling of phase transformations of the Fe-Cr Ni alloy alloyed with titanium and niobium in order to predict the phase composition and to substantiate the concentration of alloying elements of the experimental alloy for parts of metallurgical equipment. The results of microstructural analysis and phase composition of an experimental heat-resistant alloy are presented

Thermodynamic modeling and analysis of the structure of a heat-resistant alloy of the Fe-Cr-Ni system

There has been carried out thermodynamic modeling of phase transformations of the Fe-Cr Ni alloy alloyed with titanium and niobium in order to predict the phase composition and to substantiate the concentration of alloying elements of the experimental alloy for parts of metallurgical equipment. The results of microstructural analysis and phase composition of an experimental heat-resistant alloy are presented

Multilevel Parallelization: Grid Methods for Solving Direct and Inverse Problems

In this paper we present grid methods which we have developed for solving direct and inverse problems, and their realization with different levels of optimization. We have focused on solving systems of hyperbolic equations using finite difference and finite volume numerical methods on multicore architectures. Several levels of parallelism have been applied: geometric decomposition of the calculative domain, workload distribution over threads within OpenMP directives, and vectorization. The run-time efficiency of these methods has been investigated. These developments have been tested using the astrophysics code AstroPhi on a hybrid cluster Polytechnic RSC PetaStream (consisting of Intel Xeon Phi accelerators) and a geophysics (seismic wave) code on an Intel Core i7-3930K multicore processor. We present the results of the calculations and study MPI run-time energy efficiency

The Geometry and Moduli of K3 Surfaces

These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of polarized K3 surfaces, studying their moduli, degenerations and the compactification problem. This theory is then further enhanced to a discussion of lattice polarized K3 surfaces, which provide a rich source of explicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3 surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.