Chirality of Real Non-singular Cubic Fourfolds and Their Pure Deformation Classification

In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.Comment: 21 pages, 12 Figures, Journal reference added, no changes in the tex

Apparent contours of nonsingular real cubic surfaces

We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of these sextics.Comment: 61 pages, 8 figures, Revised version to be published in Transactions AMS: some minor corrections, a missing lemma is include

DEFORMATION CLASSES OF REAL FOUR-DIMENSIONAL CUBIC HYPERSURFACES

We study real nonsingular cubic hypersurfaces X subset of P-5 up to deformation equivalence combined with projective equivalence and prove that, they, are classified by the conjugacy classes of involutions induced by the complex conjugation in H-4(X). Moreover, we provide a graph Gamma(K4) whose vertices represent the equivalence classes of such cubics and whose edges represent their adjacency. It turns out that the graph Gamma(K4) essentially coincides with the graph Gamma(K3) characterizing a certain adjacency of real nonpolarized K3-surfaces

On Affine Real Cubic Surfaces

We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other via wall-crossing.Comment: 12 pages, 3 figures, 2 tables; added: Theorem 1.3.2 (on walls extended by cuspidal strata), Section 4 with a proof of this theorem, and Section 5 with a few remarks including an enumeration of ordinary wall

Abundance of 3-planes on real projective hypersurfaces

We show that a generic real projective $n$-dimensional hypersurface of odd degree $d$, such that $4(n-2)=\binom{d+3}3$, contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, $d^3\log d$, as the number of complex 3-planes. This estimate is based on the interpretation of a suitable signed count of the 3-planes as the Euler number of an appropriate bundle.Comment: 25 pages, minor typos corrected after proofreadin

Study of the electrodes length influence on the trajectories of water droplets dispersed in oil and affected by non-uniform electric field

The paper presents the results of numerical modelling of the processes accompanying movement of drop viscous media (water) in oil under the influence of exterior forces of the electric and dynamic nature. Systematic calculations of influence on the electric field heterogeneity drops, created by a symmetric and asymmetrical configuration of electrodes are carried out both in inter electrode and behind electrode areas taking into account a complex operation of dielectrophoresis forces, buoyancies and drag, as well as the variability of electrode sizes. The analysis of drop movement trajectories shows that the asymmetrical configuration of electrodes can be applied for an electro-coalescence intensification of water-in-oil emulsion. Correctness of calculations of the mathematical model and numerical methods are confirmed by good results if compared with the available data of the other authors