Abstract:
Super-microscopic techniques like scanning tunnelling microscopy, atomic force microscopy or scanning near-field optical microscopy allows investigate micro- and/or nano-scale surfaces and structures. In this paper, both Environmental scanning electron microscope (ESEM) and Scanning near field optical microscope (SNOM) have been applied to more closely study of biomaterials. The results of visualization of human osteo-sarcoma cell line (U2OS) are compared. SNOM and ESEM yield different, however, comparable and complementary information on studied biological samples.

For the first time, this paper describes the concentration
dependence of the relative dynamic viscosity coefficient of rubber suspensions
and the initial viscoelastic modulus of 3D cross-linked elastomers on the
maximum volume filling with solidpolydisperse particles. It allows to predict
the rheological and mechanical properties of thepolymer compositions
being developed now. In this paper, we present the first experimental study of
the pole of the concurrent lines of the concentration dependence in the
coordinates of the linear form. The pole validates the invariant value of the
constant of the developed equation and allows the experimental determination of
the maximumvolume filling of polymer binders filledwith separate
fractions orpolydisperse mixtures. The results of the study are recommended for
use in developing new polymer composite materials.

Abstract:
This publication is a revised version of the previous article. Seismic rigidity method despite its widespread use is the object of harsh criticism from scientists who oppose it to the methodology and results of seismological registration of earthquakes and microseisms. The article substantiates the original approach based on the solution of the direct problem of seismic microzonation for the model of real soil thickness. A new formula of the seismic rigidity method is proposed, taking into account the lithological, hydrogeological and spectral features of the soil mass, as well as the position of the new seismic scale of the SSI. The formula was tested on the example of the correct description of the features of macroseismic effects on the territory of Leninakan at the Spitak earthquake in 1988. Linear estimates according to the formula of seismic rigidity in the seismic microzoning area represent changes in seismic intensity in the most contrast way. It is shown that the real estimates of seismic intensity under strong seismic effects (by I > VII degree) will not exceed those given by the formula of the seismic rigidity method.

Abstract:
We compute the characteristic Cartan connection associated with a system of third order ODEs. Our connection is different from Tanaka normal one, but still is uniquely associated with the system of third order ODEs. This allows us to find all fundamental invariants of a system of third order ODEs and, in particular, determine when a system of third order ODEs is trivializable. As application differential invariants of equations on circles in R^n are computed.

Abstract:
We present the concept-oriented model (COM) and demonstrate how its three main structural principles — duality, inclusion and partial order — naturally account for various typical data modeling issues. We argue that elements should be modeled as identity-entity couples and describe how a novel data modeling construct, called concept, can be used to model simultaneously two orthogonal branches: identity modeling and entity modeling. We show that it is enough to have one relation, called inclusion, to model value extension, hierarchical address spaces (via reference extension), inheritance and containment. We also demonstrate how partial order relation represented by references can be used for modeling multidimensional schemas, containment and do main-specific relationships.

Abstract:
The wetting and filling properties of a fluid adsorbed on a solid grooved substrate are studied by means of a microscopic density functional theory. The grooved substrates are modelled using a solid slab, interacting with the fluid particles via long-range dispersion forces, to which a one-dimensional array of infinitely long rectangular grooves is sculpted. By investigating the effect of the groove periodicity and the width of the grooves and the ridges, a rich variety of different wetting morphologies is found. In particular, we show that for a saturated ambient gas, the adsorbent can occur in one of four wetting states characterised by i) empty grooves, ii) filled grooves, iii) a formation of mesoscopic hemispherical caps iv) a macroscopically wet surface. The character of the transition between particular regimes, that also extend off-coexistence, sensitively depends on the model geometry. A temperature at which the system becomes completely wet is considerably higher than that for a flat wall.

Abstract:
We investigate the effective interactions between two nanoparticles (or colloids) immersed in a solvent exhibiting two-phase separation. Using a non-local density functional theory, we determine the dependence of the effective potential on the separation of the nanoparticles when the solvent is near bulk two-phase coexistence. If identical nanoparticles preferentially adsorbing phase $\alpha$ are inserted into phase $\beta$, thick wetting layers of the preferable phase $\alpha$ develop at their surfaces. At some particular separation $h_b$ of the nanoparticles, the wetting layers connect to form a single bridge, and the induced effective potential becomes strongly attractive for all distances $h

Abstract:
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by constructing self-adjoint extensions of the corresponding Hamiltonians. Two particularly interesting examples of this kind are nonrelativistic spin zero particles in $\delta$-function potential and Dirac particles in Aharonov-Bohm magnetic background. In this paper we show that by extending the corresponding Schr\"odinger and Dirac equations onto the flat noncommutative space a well-defined quantum theory can be obtained. Using a star product and Fock space formalisms we construct the complete sets of eigenfunctions and eigenvalues in both cases which turn out to be finite.

Abstract:
A simple fluid, in a microscopic capillary capped at one end, is studied by means of fundamental measure density functional. The model represents a single, infinitely long nanogroove with long-range wall-fluid attractive (dispersion) forces. It is shown that the presence or absence of hysteresis in adsorption isotherms is determined by wetting properties of the wall as follows: Above wetting temperature, $T_w$, appropriate to a single wall of the groove, the adsorption is a continuous process corresponding to a rise of a meniscus from the capped to the open end of the groove. For a sufficiently deep capillary the meniscus rise is shown to be a steep, yet continuous process taking place near the capillary condensation of a corresponding slit. However, for temperatures lower than $T_w$ the condensation exhibits a first-order transition accompanied by hysteresis of the adsorption isotherm. Finally, it is shown that hysteresis may occur even for $T>T_w$ as a consequence of prewetting on the side and bottom walls of the groove.