In this paper, we studied the fixed points of the Lyapunov operator with degenerate kernel, in which each fixed point of the operator is corresponds to a translationinvariant Gibbs measure with four competing interactions of models with uncountable set of spin values on the Cayley tree of order two. Also, it was proved that Lyapunov operator with degenerate kernel has at most three positive fixed points.

The spectral properties of a photon spontaneously emitted by a material twolevel system, modelling an atom or ion, in a parabolic cavity are investigated. In particular, we concentrate on the special case of a motionless twolevel system positioned exactly at the focus of a parabolic cavity with a dipole moment oriented along the symmetry axis of this cavity. Treating the corresponding atomfield coupling in the dipoleand rotating wave approximation, it is demonstrated that inside the parabolic cavity the position and frequency dependence of the spectrum of the spontaneously emitted photon exhibits interesting interference patterns. These patterns are explored in detail with the help of a photon path representation of the firstorder electric field correlation function. In the radiation, zone the spatial behavior of the spectrum reveals strong interference in particular at distances from the twolevel system of the order of the focal length of the parabola. With increasing distances, these interference patterns decay except for an undepleted component surrounding the symmetry axis at an almost constant radius. Furthermore, the maximum of the frequency dependence of the spectrum exhibits a positiondependent frequency shift with respect to the atomic resonance frequency.

In recent years possible applications of nanoporous materials in biophysics and biomedicine have become a topic of intense scientific interest. One of the main problems in this field is that of transport processes in inhomogeneous nanoporous media. Another one is the reproduction of the specific evolution of the liquid front profile, observed in one medium, in another medium. In this paper, we present a model which simulates twodimensional liquid front propagation in inhomogeneous nanoporous media; we also propose a method to evaluate the parameters of the nanoporous medium required for reproduction of the given liquid front propagation.

The lifetime of magnetic states in single domain micromagnetic islands is calculated within the harmonic approximation to transition state theory. Stable magnetic states, minimum energy paths between them and first order saddle points determining the activation energy are analyzed and visualized on twodimensional energy surfaces. An analytical expression is derived for the preexponential factor in the Arrhenius rate expression for the reversal of the magnetic moment when the external field is directed either along the anisotropy axis or perpendicular to it.

For the first time, nanocomposite colloidosomes of mesoporous silica microspheres decorated with silver nanoparticles have been applied as a highly sensitive vapor phase optical sensors utilizing a semiquantitative analysis of surfaceenhanced Raman spectra (SERS). The material was prepared using soft chemistry approaches and benefits from the intrinsic properties of both components: the mesoporous structure of the silica microspheres allows for capillary condensation of target analytes while the silver nanoparticles favor the great enhancement of Raman fingerprints of thus trapped and preconcentrated analytes. This approach seems to be highly promising for the further development of express gas phase sensors for heterocyclic or polycyclic aromatic hydrocarbon pollutants.

A method for finding a selected region of the minimum energy path between two local minima on an energy surface is presented. It can be used to find the highest saddle point and thereby estimate the activation energy for the corresponding transition when the shape of the path is known reasonably well and a good guess can be made of the approximate location of the saddle point. The computational effort is then reduced significantly as compared with a calculation of the full minimum energy path by focusing the images on the selected part of the path and making one of the images, the climbing image, converge rigorously on the saddle point. Unlike the commonly used implementation where a restraint is used to distribute the images along the path, the present implementation makes use of a constraint where the distance between images is controlled based on a predefined overall length of the path. A relatively even density of images on each side of the climbing image is maintained by allowing images to move from one side to the other. Applications to magnetic skyrmion annihilation and escape through boundary are used to illustrate the savings in computational effort as compared with full minimum energy path calculations.

Energy spectrum of indium antimonide (InSb) quantum dots (QD) was analyzed in this paper. Properties of energy spectrum levels were determined both by calculations and experiments using differential tunneling currentvoltage characteristics (CVC) rated to static conductivity. It was confirmed that relatively large QD (size of about 20–25 nm) exhibit quantum size effects. Critical values of the characteristic parameters of InSb QD are analyzed, in which application of the differential tunneling currentvoltage characteristics method for express analysis of the characteristic sizes of QD leads to significant errors (more than 10 %).

One key requirement for many cryptograhic schemes is the generation of random numbers. Sequences of random numbers are used at several stages of a standard cryptographic protocol. One simple example is a Vernam cipher, where a string of random numbers is added to message string to generate encrypted code. C = M K. It has been mathematically shown that this simple scheme is unbreakable if key K is as long as M and is used only once. The security of a cryptosystem shall not be based on keeping the algorithm secret but solely on keeping the key secret. The security of a random number generator (RNG) is related to the difficulty of predicting its future sequence values from past values. The quality and unpredictability of secret data is critical to securing communication by modern cryptographic techniques. The generation of such data for cryptographic purposes typically requires an unpredictable physical source of random data. We studied a chaotic circuit which consisted of an inductor, capacitance, diode and thus used for the BB84 protocol. We have studied both pseudo random and true random number generators and evaluated them through various tests like frequency, correlation, NIST etc.

The instability of convection in a Rivlin–Ericksen elasticoviscous nanofluid with vertical throughflow is investigated using the linear stability theory. A modified Brinkman model is employed and singleterm Galerkin method is used to solve the conservation equations. Nine dominating parameters are extracted from the analysis. Due to the combined effect of vertical throughflow, Brownaian motion, and thermophoresis, the Rayleigh number is reduced by a substantial amount. It is found that through flow delays the convection while other nanofluid parameter enhance the convection. The thermal capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern stationary convection. Using the convective component of nanoparticle flux, the critical wave number is a function of nanofluid parameters as well as throughflow parameter. Major trends are investigated briefly by plotting the graphs.

The spatial distribution of the terahertz radiation polarization is experimentally measured from a femtosecond laser twocolor filament in air. Terahertz radiation generation from twocolor plasma filamentation with a  BBO crystal located behind the lens leads to the spatial inhomogeneity of the polarization distribution. Inhomogeneity of the terahertz field polarization is determined by the polarization of the fundamental harmonic of the pump radiation after passing through the  BBO crystal. A spatial inhomogeneity of the fundamental harmonic polarization is observed owing to the  BBO crystal acting as a phase plate illuminated by a spherical front.

Recently, nanotubular hydrosilicates have attracted attention due to numerous possible applications and intriguing formation mechanism. In this study we estimate energy effect of cylindrical and conical (Mg0:5,Ni0:5)3Si2O5(OH)4 nanotube formation depending on their size parameters, cone angle, and Mg–Ni redistribution function. The calculations show that, as we expected, conical morphology is less preferable from an energy perspective than the cylindrical one, and the energy difference between them increases with the cone angle. Nevertheless, Mg and Ni cations redistribution along side length decreases strain energy of conical nanotube. This effect reaches its maximum of 􀀀75 kJ/mol at a cone angle of 5.

Silvercoated WS2 nanotubes (NTWS 2) were successfully synthesized via two wet chemistry techniques. The first employs spontaneous silver nanoparticle growth resulting from an interaction of disulfide nanotubes with AgNO3 in aqueous suspensions at 100 C without any additional reducing agents or stabilizers. The second utilizes [Ag(NH3)2]OH complex to produce silver nanoparticles upon thermal decomposition. Both techniques are capable of producing AgNTWS 2 nanocomposites containing 5–60 nm silver nanoparticles tightly attached to the nanotubes’ surfaces. The hexagonal arrangement of sulfur atoms of the outer WS2 layer was postulated to facilitate crystallization of silver nanocrystals with hexagonal crystallographic system (4H–Ag). The physicalchemical model for spontaneous AgNP formation is proposed.

Modeling approaches based on the density functional theory (DFT): the Kohn–Sham (KS) method and orbitalfree (OF) method are used to for calculation of the binding energies per atom as functions of the diameter of singlewall carbon nanotubes (SWCNTs) with the open ends. It is shown that this energy has a minimum at a diameter of about 1.1 – 1.2 nm. The experiments made by means of Raman spectroscopy have shown that diameters of SWCNTs mainly lie in the range of 1 – 1.5 nm.

The electron structures of two forms of the grafted carbon dimer for the (8, 0) zigzag nanotube were calculated by the semiempirical quantumchemistry method applied to the supercell model. If the dimer adsorbs above the center of the tube’s hexagon (hgrafting), it performs the topochemical transformation of the tube, according to the Stone–Wales scheme of inverse kind. Bgrafting is a chemisorption above tube’s bond, it is energetically lower, than hgrafting. Atomic structure of bgrafting is a splitted diinterstitial. Measuring the electronic density of states in the upper valence bandhas been shown to make it possible to distinguish between pure and grafted nanotubes, as well as between band hgraftings.

Varying glycine to nitrate ratio in the initial solution the powders based on nanocrystalline LaFeO3 were synthesized by solution combustion synthesis. The powders were studied by Xray diffractometry, scanning electron microscopy, adsorption analysis and helium pycnometry. The average crystallite size of the synthesized LaFeO3 nanocrystals ranged from 182 to 859 nm, and the specific surface area of the nanopowders based on them ranged from 8 to 33 m2/g. Based on the results, the influence of redox composition of the reaction solution on the nature of the combustion processes, as well as the composition, structure and properties of LaFeO3 nanocrystals were analyzed. Here, it was shown, that the nanopowders have specific microstructure in terms of monocrystalline nanoscale layers of lanthanum orthoferrite, therefore it is allowed to consider them as a promising base for catalytically and magnetically functional materials.

Nonlinear light absorption and its time evolution at high optical excitation levels in GaSe and InSe layered crystals have been experimentally investigated. It is shown that the nonlinear absorption observed in InSe in the region of exciton resonance is due to the excitonexciton interaction. The effect of filling the zones detected in GaSe at high excitation intensities leads to a change in the absorption coefficient and the refractive index. For InSe nanoparticles obtained by the chemical deposition method, a quantadimensional effect was observed; the width of the forbidden band was dependent upon the dimensions of the nanoparticles.

We prepared SnO2 quantum dots embedded in polyvinylpyrrolidone (PVP) matrix and report its operation as a Nano Light emitting device. The samples have been prepared via quenching technique where bulk ZnO powder is sintered at a very high temperature of 1000 C and then quenched into ice cold polyvinylpyrrolidone solution. The specimen was then characterized using UV/VIS spectroscopy, Xray diffraction study and high resolution transmission electron microscopy (HRTEM). These studies indicate the sizes of quantum dots to be within 9 nm. The prepared quantum dot samples have been evaluated as nano light emitting devices by exploring the variation of electroluminescence (light emission phenomenon) with supply voltage at room temperature.

Current and surface topographies of composite based on polystyrene with reduced graphene oxide were investigated using atomic force microscopy. Different substrates such as gold, silicon and graphite were used for this purpose. The strong influence of the substrate’s nature on the current distribution map I(x; y) and the currentvoltage characteristics was observed. This effect can be related to different adhesion of composite on the investigated substrates.

For the first time, a systematic study of a background noise to signal ratio is given for various preparation histories of consolidated silver nanoparticles and artificially prepared nanostructures to rate the best and the worst routes of deposition of surfaceenhanced Raman spectroscopy (SERS) active layers. It is shown that most of common preparation schemes face with a high intensity of extra peaks in the ca. 900–1100 and 1400–1700 cm􀀀1 range as related to residual adsorbed / chemosorbed nitrate, nitrite ions and organic oxidation products of various pollutants formed in the course of Ag+ redox reactions. Finally, Leopold–Lendl and the original USR (Ultrasonic Silver Rain) methods would be recommended for the highly sensitive SERS analysis of diluted solutions and impurities.

A universal mechanism of tetrahedral metal cluster formation in crystal with geometrically frustrated pyrochlore sublattices is pr oposed. It has been shown that the critical irreducible representation , which generated the formation of metal clusters in noncentrosymmetrical F4 3mphases from high symmetry phases with Fd3 m space group, is a one dimensional irreducible representation 11(4(A2u)) (in Kovalev notation). The structural theory of metal cluster formation based on group theoretical calculations was published earlier for the case of Aordered spinel. In this work, the theory is generalized in the case of any high symmetry Fd3 m structures that include pyrochlore sublattices. We presented a brief review of such structures and mechanisms of the tetrahedral metal cluster formation. The existence of so called “breathing” pyrochlore sublattices in ordered phases is predicted theoretically. The groups of atoms, between which bond clusters, are found. These groups of atoms define electron correlation effects. Examples of tetrahedral metal cluster formation in ordered spinels, ordered lacunar spinels, ordered Laves phases (MgCu4Sn structural type) and ordered pyrochlore are considered. The theoretical results are confirmed by the known experimental facts.