On the possible mechanisms of the selective effect of a non-equilibrium plasma on healthy and cancer cells in a physiological solution

This paper discusses possible mechanisms for the selective effect of weakly ionized non-equilibrium plasma and currents in electrolyte on healthy and cancerous cells in physiological saline in a Petri dish. The interaction with the plasma source leads to a change in osmotic pressure, which affects the electro-mechanical properties of cell membranes in healthy and cancerous cells in different ways. The currents arising in the electrolyte charge the membranes of healthy and cancerous cells to a different potential difference due to the different values of the membranes' dielectric constant. We hypothesized that the dielectric permeability of cancer cell membranes is lower than that of healthy cells, as is the capacity of a unit of the membrane surface, and therefore, the additional potential difference acquired by the membrane through charging with currents induced in the intercellular electrolyte is greater in cancer cells. This can lead to electroporation of cancer cell membranes, resulting in their apoptosis, but does not effect healthy cells

Surface tension of small bubbles and droplets and the cavitation threshold

In this paper, using an unified approach, estimates are given of the magnitude of the surface tension of water for planar and curved interfaces in the pairwase interaction approximation based on the Lennard-Jones potential. It is shown that the surface tensions of a bubble and droplet have qualitatively different dependences on the curvature of the surface: for the bubble, as the radius of the surface's curvature decreases, the surface tension decreases, whereas it increases on the droplet. The corresponding values of the Tolman corrections are also determined. In addition, it is shown that the dependence of the surface tension on the surface's curvature is important for evaluating the critical negative pressure for the onset of cavitation

On Chow weight structures for cdhcdh-motives with integral coefficients

The main goal of this paper is to define a certain Chow weight structure $w_{Chow}$ on the category $DM_c(S)$ of (constructible) $cdh$-motives over an equicharacteristic scheme $S$. In contrast to the previous papers of D. H\'ebert and the first author on weights for relative motives (with rational coefficients), we can achieve our goal for motives with integral coefficients (if $\operatorname{char}S=0$; if $\operatorname{char}S=p>0$ then we consider motives with $\mathbb{Z}[\frac{1}{p}]$-coefficients). We prove that the properties of the Chow weight structures that were previously established for $\mathbb{Q}$-linear motives can be carried over to this "integral" context (and we generalize some of them using certain new methods). In this paper we mostly study the version of $w_{Chow}$ defined via "gluing from strata"; this enables us to define Chow weight structures for a wide class of base schemes. As a consequence, we certainly obtain certain (Chow)-weight spectral sequences and filtrations for any (co)homology of motives.Comment: To appear in Algebra i Analiz (St. Petersburg Math Journal). arXiv admin note: substantial text overlap with arXiv:1007.454

Inverse dispersion method for calculation of complex photonic band diagram and PT\cal{PT}-symmetry

We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving the eigenvalue problem with a non-Hermitian operator. The analogy with $\cal{PT}$-symmetric Hamiltonians reveals that the operator corresponds to the momentum as a physical quantity and the singularities at the band edges are related to the branch points and responses for the features on the band edges. The method is realized using plane wave expansion technique for two-dimensional periodical structure in the case of TE- and TM-polarization. We illustrate the applicability of the method by calculation of the photonic band diagrams of an infinite two-dimension square lattice composed of dielectric cylinders using the measured frequency dependent dielectric functions of different materials (amorphous hydrogenated carbon, silicon, and chalcogenide glass). We show that the method allows to distinguish unambiguously between Bragg and Mie gaps in the spectra.Comment: 8 pages, 5 figure

Proof of Gal's conjecture for the D series of generalized associahedra

In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture holds for them

De Rham theorem for extended L^2-cohomology

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent (with bounded morphisms and homotopy operators) to a combinatorial complex with the same coefficients. This is established by using the Witten deformation of the de Rham complex. We also prove that the de Rham complex is chain-homotopy equivalent to the spectrally truncated de Rham complex which is also finitely generated.Comment: 16 pages, author-supplied file available at ftp://ftp.math.neu.edu/Pub/faculty/Shubin_Mikhail/papers/DR19.tex This is a slight revision -- some references are added AMSTeX v 2.

An upper bound for the Hales-Jewett number HJ(4,2)

We show that for $n$ at least $10^{11}$, any 2-coloring of the $n$-dimensional grid $[4]^n$ contains a monochromatic combinatorial line. This is a special case of the Hales-Jewett Theorem, to which the best known general upper bound is due to Shelah; Shelah's recursion gives an upper bound between $2 \uparrow \uparrow 7$ and $2 \uparrow \uparrow 8$ for the case we consider, and no better value was previously known

Magnetic behaviour of dirty multiband superconductors near the upper critical field

Magnetic properties of dirty multiband superconductors near the upper critical field are studied. The parameter $\kappa_2$ characterizing magnetization slope is shown to have a significant temperature variation which is quite sensitive to the pairing interactions and relative strengths of intraband impurity scattering. In contrast to single-band superconductors the increase of $\kappa_2$ at low temperatures can be arbitrary large determined by the ratio of minimal and maximal diffusion coefficients in different bands. Temperature dependencies of $\kappa_2(T)$ in two-band MgB$_2$ and iron-based superconductors are shown to be much more sensitive to the multiband effects than the upper critical field $H_{c2}(T)$

Direct and inverse scattering on noncompact star-type quantum graph with Bessel singularity

In this paper we study the noncompact star-type graph with perturbed radial Schrodinger equation on each ray and the matching conditions of some special form at the vertex. The results include the uniqueness theorem and constructive procedure for solution of the inverse scattering problem

On differential polynomial rings over locally nilpotent rings

Let $\delta$ be a derivation of a locally nilpotent ring $R$. Then the differential polynomial ring $R[X; \delta]$ cannot be mapped onto a ring with a non-zero idempotent. This answers a recent question by Greenfeld, Smoktunowicz and Ziembowski