Table of contents

Preface

The 6^th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Pafos, Cyprus, from Monday, 28^th of August, to Thursday, 31^th of August 2017.

The Conference was attended by more than 120 participants and hosted about 140 oral, poster, and virtual presentations while counted more than 500 pre-registered authors. The 6^th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc.

The scientific program was rather heavy, however, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time.

We would like to thank the hosting Neapolis University of Pafos for providing their excellent infrastructure for the needs of the Conference. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

The Conference Chairman Dimitrios Vlachos University of Peloponnese

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Effective recovery of unconventional oil reserves necessitates development of enhanced oil recovery techniques such as polymer flooding. The study investigated the model of polymer flooding with effects of adsorption and water salinity. The model takes into account six components that include elements of the classic black oil model. These components are polymer, salt, water, dead oil, dry gas and dissolved gas. Solution of the problem is obtained by finite volume method on unstructured Voronoi grid using fully implicit scheme and the Newton's method. To compare several different grid configurations numerical simulation of polymer flooding is performed. The oil rates obtained by a hexagonal locally refined Voronoi grid are shown to be more accurate than the oil rates obtained by a rectangular grid with the same number of cells. The latter effect is caused by high solution accuracy near the wells due to the local grid refinement. Minimization of the grid orientation effect caused by the hexagonal pattern is also demonstrated. However, in the inter-well regions with large Voronoi cells flood front tends to flatten and the water breakthrough moment is smoothed.

In the present study an oxidation behavior of commercially available Ni-base superalloy IN 713C with different surface finishing, namely polished up to 1 μm diamond paste (resulting in R_a = 0.023) and ground by SiC paper with 80 grit (R_a = 1.23), were investigated at 950°C in air. It was found that ground sample developed very thin, protective α-Al₂O₃ scale. Moreover, locally formation of θ-Al₂O₃ in the forms of spikes was observed. For the sample with polished surface formation of outer chromia scale accompanied with internal oxidation of aluminum was observed. Moreover, for specimen which does not form continuous alumina scale or sub-scale, the GD-OES depth profiles showed an enrichment of boron at the oxide scale/alloy interface. It was proposed that the formation of protective alumina scale on ground samples is caused by introducing the defects into the near-surface region of the material, which are an easy diffusion paths for the elements forming a protective oxide scales.

We study the dynamical behavior of a particle flying under the influence of a gravitational field, with dissipation constant λ (Stokes-like), colliding successive times against a rigid surface vibrating harmonically with restitution coefficient α. We define re-scaled dimensionless dynamical variables, such as the relative particle velocity Ω with respect to the surface's velocity; and the real parameter τ accounting for the temporal evolution of the system. At the particle-surface contact point and for the k'th collision, we construct the mapping described by (τ_k; Ω_k) in order to analyze the system's nonlinear dynamical behavior. From the dynamical mapping, the fixed point trajectory is computed and its stability is analyzed. We find the dynamical behavior of the fixed point trajectory to be stable or unstable, depending on the values of the re-scaled vibrating surface amplitude Γ, the restitution coefficient α and the damping constant λ. Other important dynamical aspects such as the phase space volume and the one cycle vibrating surface (decomposed into absorbing and transmitting regions) are also discussed. Furthermore, the model rescues well known results in the limit λ = 0.

The vector potential function ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ for a k-mode and λ-polarization photon, with the quantized amplitude α_0k(ω_k) = ξω_k, satisfies the classical wave propagation equation as well as the Schrodinger's equation with the relativistic massless Hamiltonian $\mathop{H}\limits^{\sim }=-i\hslash c\overrightarrow{\nabla }$ and finally an equivalent quantum equation for the vector potential amplitude operator ${\mathop{\alpha }\limits^{\sim }}_{0}=-i\xi c\overrightarrow{\nabla }$. Thus, ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ behaves as a wave function for the photon within a non-local representation that can be suitably normalized. It is deduced that the probability for detecting a k-mode photon around a point on the propagation axis depends on the square of the angular frequency. Taking into account the left and right circularly polarized states and weighting ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ by ${\omega }_{k}\sqrt{2{\varepsilon }_{0}}$ we define a six components function as a general function for a k-mode photon. The square of the modulus of the defined general function gives the energy density at a given coordinate which depends on the fourth power of the angular frequency. The amplitudes of the electric and magnetic fields of a single k-mode photon free of cavity are also calculated and it is shown that they are proportional to the square of the angular frequency. In this way, the influence of the photon electric and/or magnetic fields on the energy levels of atoms and molecules might be used for a non-destructive photon detection.

We show how the properties of the Mars polar vortex can be understood in the framework of a simple shallow-water type model obtained by vertical averaging of the adiabatic "primitive" equations, and "improved" by inclusion of thermal relaxation and convective fluxes due to the phase transitions of CO₂, the major constituent of the Martian atmosphere. We perform stability analysis of the vortex, show that corresponding mean zonal flow is unstable, and simulate numerically non-linear saturation of the instability. We show in this way that, while non-linear adiabatic saturation of the instability tends to reorganize the vortex, the diabatic effects prevent this, and thus provide an explanation of the vortex form and longevity.

Concentration dependencies of the Helmholtz free energy of mixing for liquid Fe-Co and Fe-Ni alloys are calculated near their melting temperatures in the framework of modified by us earlier the Wills-Harrison model at different values of the probability that not only diagonal couplings between d states in different atoms are possible in transition metal. It is found that an account of non-diagonal d-d couplings leads to an improvement of theoretical results for thermodynamic properties of liquid transition-metal binary alloys.

Diffusion of neutrons in the toroidal nuclear electrogenerator (nuclegen) is investigated. Important conclusion about the practically complete absence of the diffusion of neutrons and charged fission particles through the external boundary under toroidal motion is substantiated by the solution of corresponding equation diffusion with the aid of Fourier's standard division method.

Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury's orbit, Shapiro time delay etc. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable interpolating function (μ) in Milgrom's Law. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which is associated with the interpolating function (μ). In this way, a new relativistic potential is obtained (let us call 2^nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance and for any metric of flat spacetime. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a pure Relativistic Theory of Gravitational Interaction. Then, we pass to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). Thus, we Explain the Rotation Curves in Galaxies (e.g. NGC 3198) and Clusters of them as well as the Solar system, eliminating Dark Matter. This relativistic potential and the corresponding metric of spacetime have been obtained by the light of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metric. Of course, may also be applied by scientists who prefer the hyperbolic geometry of Classic Relativity (CR).

The recombination of plasma charged components, electrons and ions of hydrogen isotopes, on the wall of a fusion reactor is a source of neutral molecules and atoms, recycling back into the plasma volume. Here neutral species participate, in particular, in charge-exchange (c-x) collisions with the plasma ions and, as a result, atoms of high energies with chaotically directed velocities are generated. Some fraction of these hot atoms hit the wall. Statistical Monte Carlo methods normally used to model c-x atoms are too time consuming for reasonably small level of accident errors and extensive parameter studies are problematic. By applying pass method to evaluate integrals from functions, including the ion velocity distribution, an iteration approach to solve one-dimensional kinetic equation [1], being alternative to Monte Carlo procedure, has been tremendously accelerated, at least by a factor of 30-50 [2]. Here this approach is developed further to solve the 2-D kinetic equation, applied to model the transport of c-x atoms in the vicinity of an opening in the wall, e.g., the entrance of the duct guiding to a diagnostic installation. This is necessary to determine firmly the energy spectrum of c-x atoms penetrating into the duct and to assess the erosion of the installation there. The results of kinetic modeling are compared with those obtained with the diffusion description for c-x atoms, being strictly relevant under plasma conditions of low temperature and high density, where the mean free path length between c-x collisions is much smaller than that till the atom ionization by electrons. It is demonstrated that the previous calculations [3], done with the diffusion approximation for c-x atoms, overestimate the erosion rate of Mo mirrors in a reactor by a factor of 3 compared to the result of the present kinetic study.

A computational procedure is presented for numerical modeling of the light emitting diode (LED) with top p-electrode designed as a mesh with the strips of rectangular cross section. Isotropic light emission in the LED's active region and light reflection from the bottom electrode are considered. Three-dimensional Laplace equation for electric potential is solved by finite element method. The numerical model incorporates mapped infinite element to account for potential decay far away from the LED structure and finite element model developed for boundary condition at semiconductor-air interface in the mesh opening. Simulation results demonstrate the effect of the mesh's geometrical parameters on the total output power.

We study an angular dependence of EPR spectra of the own defects in topaz (Al₂[SiO₄][F,OH]₂). The topaz crystal structure is built of silicon-oxygen tetrahedral (SiO₄) and octahedral aluminum surrounded by four oxygen ions and fluorine ions or a hydroxyl group. There are two types of substitution defects in topaz, such as octahedral and tetrahedral, depending on the location of the impurity ion. The point defects with octahedral symmetry arise on local substitution of aluminum (Fe³⁺ → Al³⁺), while tetrahedral coordinated centers are formed by substitution of silicon (Fe³⁺→ Si⁴⁺) in the silicon-oxygen tetrahedral (SiO₄). To determine the symmetry of the impurity centers, the angular dependence of the EPR spectrum is calculated. The excited energy states for defects are determined by the magnitude of the g-factor shift. These states equal 1.6 eV and 3.2 eV, respectively. A super-hyperthin structure (SHTS) of the EPR lines of iron has been observed. This SHTS is determined by the magnetic moments of the fluorine nuclei F¹⁹ located in the first coordination sphere of the paramagnetic iron center. The models of the three new paramagnetic centers in topazes are suggested, one of them being of orthorhombic symmetry for aluminum substitution and the two others being of tetragonal symmetry for silicon substitution with oxygen vacancies.

Partial oxidation of natural gas at moderate temperatures below 1500 K has significant interest for a number of industrial applications. But such processes can proceed at different unstable regimes including oscillating modes. Nonlinear phenomena at partial oxidation of methane were observed at different conditions. The investigation of the complex nonlinear system of equations that describes this process is a real method to insure its stability at industrial conditions and, at the same time, is an effective tool for its further enhancement. Numerical analysis of methane oxidation kinetics in the continuous stirred-tank reactor, with the use of detailed kinetic model has shown the possibility of the appearance of oscillating modes in the appropriate range of reaction parameters that characterize the composition, pressure, reagents flow, thermophysical features of the system, and geometry of the reactor. The appearance of oscillating modes is connected both with the reaction kinetics, heat release and sink and reagents introduction and removing. At that, oscillations appear only at a limited range of parameters, but can be accompanied by significant change in the yield of products. We have determined the range of initial temperature and pressure at which oscillations can be observed, if all other parameters remained fixed. The boundaries of existence of oscillations on the phase plane were calculated. It was shown that depending on the position inside the oscillation region the oscillations have different frequency and amplitude. It was reviled the role of heat exchange with the environment: at the absence of heat exchange the oscillating modes are impossible. In the vicinity of the boundary of phase range, where oscillations exist, significant change of concentration of some products were observed, for example, that of CO₂, which in this case one of the principal products is. At that, insignificant increase in pressure not only change the character of CO₂ behaving with time, but as well lead to significant increase of its mole fraction simultaneously twice decreasing the mole fraction of CO.

We propose an agent-based model to theoretically and systematically explore the implications of a new approach to fund science, which has been suggested recently by J. Bollen et al.[?] We introduce various parameters and examine their effects. The concentration of funding is shown by the Lorenz curve and the Gini coefficient. In this model, all scientists are treated equally and follow the well-intended regulations. All scientists give a fixed ratio of their funding to others. The fixed ratio becomes an upper bound for the Gini coefficient. We observe two distinct regimes in the parameter space: valley and plateau. In the valley regime, the fluidity of funding is significant. The Lorenz curve is smooth. The Gini coefficient is well below the upper bound. The funding distribution is the desired result. In the plateau regime, the cumulative advantage is significant. The Lorenz curve has a sharp turn. The Gini coefficient saturates to the upper bound. The undue concentration of funding happens swiftly. The funding distribution is the undesired results, where a minority of scientists take the majority of funding. Phase transitions between these two regimes are discussed.

The technique is presented of restoring the electronic density of states of the valence band from data of X-ray photoelectron spectroscopy. The originality of the technique consists in using a stochastic procedure to solve an integral equation relating the density of states and X-ray photoelectron spectra. The results are presented for bulk metals of gold, silver, and copper. The method can be applied to materials with unknown crystal structure, such as ensembles of nanoclusters.

The method was developed for calculation of electronic properties of an ensemble of nanoclusters with the use of cluster perturbation theory. This method was applied to the ensemble with various geometry of gold nanoclusters with octahedral symmetry. The dependence of the density of electronic states on the mutual spatial arrangement of nanoclusters in the ensemble is obtained. It is shown that the metallic behavior of the ensemble maintains even when strong disorder is present.

The effect of inclusion of higher-order interactions in the XY model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.

The logistic map is commonly used in, for example, chaos based cryptography. However, its properties do not render a safe construction of encryption algorithms. Thus, the scope of the paper is a proposal of generalization of the logistic map by means of a wellrecognized family of chaotic maps. In the next step, an analysis of Lyapunov exponent and the distribution of the iterative variable are studied. The obtained results confirm that the analyzed model can safely and effectively replace a classic logistic map for applications involving chaotic cryptography.

Magnetic field line reconnection (magnetic reconnection) is a phenomenon that occurs in space and laboratory plasma. Magnetic reconnection allows both the change the magnetic topology and the conversion of the magnetic energy into energy of fast particles. The critical point (critical line or plane in higher dimensional cases) of the magnetic field play an important role in process of magnetic reconnection, as in its neighborhood occurs a change of its topology of a magnetic field and redistribution of magnetic field energy. A lot of literature is devoted to the analytical and numerical investigation of the reconnection process. The main result of these investigations as the result of magnetic reconnection the current sheet is formed and the magnetic topology is changed. While the studies of magnetic reconnection in 2D and 3D configurations have a led to several important results, many questions remain open, including the behavior of a magnetic field in the neighborhood of a critical point of high order. The magnetic reconnection problem is closely related to the problem of the structural stability of vector fields. Since the magnetic field topology changes during both spontaneous and induced magnetic reconnection, it is natural to expect that the magnetic field should evolve from a structurally unstable into a structurally stable configuration. Note that, in this case, the phenomenon under analysis is more complicated since, during magnetic reconnection in a highly conducting plasma, we deal with the non-linear interaction between two vector fields: the magnetic field and the field of the plasma velocities. The aim of our article is to consider the process of magnetic reconnection and transformation of the magnetic topology from the viewpoint of catastrophe theory. Bifurcations in similar configurations (2D magnetic configuration with null high order point) with varying parameters were thoroughly discussed in a monograph by Poston and Stewart.

Knowing the ohmic resistance in the materials allow to know in advance its electrical behavior when a potential difference is applied, and therefore the prediction of the electrical performance can be achieved in a most certain manner. Although the Lattice Boltzmann method (LBM) has been applied to solve several physical phenomena in complex geometries, it has only been used to describe the fluid phase, but applicability studies of LBM on the solid-electric-conducting material have not been carried out yet. The purpose of this paper is to demonstrate the accuracy of calculating the equivalent resistor connections using LBM. Several series and parallel resistor connections are effected. All the computations are carried out with 3D models, and the domain materials are designed by the authors.

In the present work an analytic approximation to modified Bessel function of negative fractional order I_−2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

We introduce a gauge invariant Hamiltonian which generalizes one of the Hamiltonian structures of a parametric KdV system, which includes the complex KdV system. The associated canonical field equations have an infinite sequence of conserved quantities which are also gauge invariant. The gauge symmetry relates a wide class of integrable systems to the complex KdV system.

In this paper we discuss how a particles-in-cell computation code can be combined with methods of multicriterion optimization (in particular the Pareto optimal solutions of the multicriterion optimization problem) and a hierarchy of computational models approach to create an efficient tool for solving a wide array of problems related to the laser-plasma interaction. In case of the computational experiment the multicriterion optimization can be applied as follows: the researcher defines the objectives of the experiment - some computable scalar values (i.e. high kinetic energy of the ions leaving the domain, least possible number of electrons leaving domain in the given direction, etc). After that the parameters of the experiment which can be varied to achieve these objectives and the constrains on these parameters are chosen (e.g. amplitude and wave-length of the laser radiation, dimensions of the plasma slab(s)). The Pareto optimality of the vector of the parameters can be seen as this: x⁰ is Pareto optimal if there exists no vector which would improve some criterion without causing a simultaneous degradation in at least one other criterion. These efficient set of parameter and constrains can be selected based on the preliminary calculations in the simplified models (one or two-dimensional) either analytical or numerical. The multistage computation of the Pareto set radically reduces the number of variants which are to be evaluated to achieve the given accuracy. During the final stage we further improve the results by recomputing some of the optimal variants on the finer grids, with more particles and/or in the frame of a more detailed model. As an example we have considered the ion acceleration caused by interaction of very intense and ultra-short laser pulses with plasmas and have calculated the optimal set of experiment parameters for optimizing number and average energy of high energy ions leaving the domain in the given direction and minimizing the expulsion of electrons.

In this paper using a mathematical model of the so-called "space-dynamic" approach we investigate the problem of development and temporal dynamics of different urban population groups. For simplicity we consider an interaction of only two population groups inside a single urban area with axial symmetry. This problem can be described qualitatively by a system of two non-stationary nonlinear differential equations of the diffusion type with boundary conditions of the third type. The results of numerical simulations show that with a suitable choice of the diffusion coefficients and interaction functions between different population groups we can receive different scenarios of population dynamics: from complete displacement of one population group by another (originally more "aggressive") to the "peaceful" situation of co-existence of them together.

A mathematical model was proposed for the frequency distribution of historical inter-event time τ. A basic ingredient was constructed by assuming the significance of a newly occurring historical event depending on the magnitude of a preceding event, the decrease of its significance by oblivion during the successive events, and an independent Poisson process for the occurrence of the event. The frequency distribution of τ was derived by integrating the basic ingredient with respect to all social fields and to all stake holders. The function of such a distribution was revealed as the forms of an exponential type, a power law type or an exponential-with-a-tail type depending on the values of constants appearing in the ingredient. The validity of this model was studied by applying it to the two cases of Modern China and Northern Ireland Troubles, where the τ-distribution varies depending on the different countries interacting with China and on the different stage of history of the Troubles, respectively. This indicates that history is consisted from many components with such different types of τ-distribution, which are the similar situation to the cases of other general human activities.

This paper discusses two-dimensional and three-dimensional solitary electromagnetic waves propagation in Fermi liquid in the framework of ADS/CFT correspondence. The electromagnetic field is classically considered within the framework of Maxwell's equations. The obtained effective equation is numerically analyzed and the state of the electromagnetic field that is localized in two / three spatial dimensions is revealed.

We study a model of irreversible jam formation in congested vehicular traffic on an open segment of a single-lane road. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. Its characteristic features are: (a) the existing clusters of jammed cars cannot break into parts; (b) when the leading vehicle of a cluster hops to the right, the whole cluster follows it deterministically, and (c) any two clusters of vehicles, occupying consecutive positions on the chain, may become nearest-neighbors and merge irreversibly into a single cluster. The above dynamics was used in a one-dimensional model of irreversible aggregation by Bunzarova and Pesheva [Phys. Rev. E 95, 052105 (2017)]. The model has three stationary non-equilibrium phases, depending on the probabilities of injection (α), ejection (β), and hopping (p) of particles: a many-particle one, MP, a completely jammed phase CF, and a mixed MP+CF phase. An exact expression for the stationary probability P(1) of a completely jammed configuration in the mixed MP+CF phase is obtained. The gap distribution between neighboring clusters of jammed cars at large lengths L of the road is studied. Three regimes of evolution of the width of a single gap are found: (i) growing gaps with length of the order O(L) when β > p; (ii) shrinking gaps with length of the order O(1) when β < p; and (iii) critical gaps at β = p, of the order O(L^1/2). These results are supported by extensive Monte Carlo calculations.

The most simple decimation filter is comb filter, which has all coefficients equal to unity. The filter must attenuate aliasing which occur in the bands around the comb zeros, called folding bands. Additionally, it must have flat magnitude characteristic in the passband in order to avoid the deterioration of the decimated signal. However, comb filter has pure attenuation in the folding bands and droop in the passband of interest. The attenuation in the folding bands can be increased by cascading comb filters. Nevertheless, this process increases comb passband droop. We present here a simple method to improve simultaneously comb magnitude characteristic in both: passband and folding bands. The cascade of combs is used to improve the attenuation in the folding bands, and the compensator, cascaded with combs, improve the passband characteristic. Two cases are elaborated depending if the passband of interest is a wideband or narrowband. The comparisons with some methods from the literature confirm the benefit of the proposed method.

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent −1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e⁻³⁰⁰ in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

The paper presents structural characterization of deterministic nano and microfractals using the lacunarity analysis and small-angle scattering technique. We show that for the considered mass-fractal models, the lacunarity spectrum reveals the main structural parameters of the fractal, such as overall size of the system, iteration number, scaling factor and the size of basic units.

Small-angle scattering (of neutrons, x-ray or light; SAS) is a well-established experimental technique for structural analysis of disordered systems at nano and micro scales. For complex systems, such as super-molecular assemblies or protein molecules, analytic solutions of SAS intensity are generally not available. Thus, a frequent approach to simulate the corresponding patterns is to use a CPU-efficient version of the Debye formula. For this purpose, in this paper we implement the well-known DALAI algorithm in Mathematica software. We present calculations for a series of 2D Sierpinski gaskets and respectively of pentaflakes, obtained from chaos game representation.

We approximate a three dimensional version of deterministic Sierpinski gasket (SG), also known as Sierpinski tetrahedron (ST), by using the chaos game representation (CGR). Structural properties of the fractal, generated by both deterministic and CGR algorithms are determined using small-angle scattering (SAS) technique. We calculate the corresponding monodisperse structure factor of ST, using an optimized Debye formula. We show that scattering from CGR of ST recovers basic fractal properties, such as fractal dimension, iteration number, scaling factor, overall size of the system and the number of units composing the fractal.

The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.

In conditions of operation of aggregates on soils with low bearing capacity, the main performance indicators of their operation are determined by the properties of retaining the functional qualities of the propulsor. Therefore, the parameters of the anti-skid device can not be calculated by only one criterion. The equipment of propellers with anti-skid devices, which allow to reduce the compaction effect of the propulsion device on the soil, seems to be a rational solution to the problem of increasing traction and coupling properties of the driving wheels. The mathematical model is based on the study of the interaction of the driving wheel with anti-skid devices and a deformable bearing surface, which takes into account the wheel diameter, skid coefficient, the parameters of the anti-skid device, the physical and mechanical properties of the soil. As a basic mathematical model that determines the dependence of the coupling properties on the wheel parameters, the model obtained as a result of integration and reflecting the process of soil deformation from the shear stress is adopted. The total value of the resistance forces will determine the force of the hitch pressure on the horizontal soil layers, and the value of its deformation is the degree of wheel slippage. When the anti-skid devices interact with the soil, the traction capacity of the wheel is composed of shear forces, soil shear and soil deformation forces with detachable hooks. As a result of the interaction of the hook with the soil, the latter presses against the walls of the hook with the force equal to the sum of the hook load and the resistance to movement. During operation, the linear dimensions of the hook will decrease, which is not taken into account by the safety factor. Abrasive wear of the thickness of the hook is approximately proportional to the work of friction caused by the movement of the hook when inserted into the soil and slipping the wheel.

The Wang Landau Monte Carlo algorithm to calculate density of states for the different simple spin lattices was implemented. The energy space was split between the individual threads and balanced according to the expected runtime for the individual processes. Custom spin clustering mechanism, necessary for overcoming of the critical slowdown in the certain energy subspaces, was devised. Stable reconstruction of the density of states was of primary importance. Some data post-processing techniques were involved to produce the expected smooth density of states.

The equation for the natural bending vibrations of an infinite dislocation is written. The long-wavelength limit is considered. The orientation dependence of the vibrational spectrum has been studied. Solutions for two cases (the bending wave velocity along the dislocation line is not equal to the speed of sound waves and the bending wave velocity along the dislocation line is close to the speed of sound waves) are obtained. Local and quasilocal branches of edge and screw dislocations vibrations are found.

Numerical calculation of the generalized susceptibility and the inverse generalized susceptibility matrix elements of the dislocation segment for edge and screw dislocations, different frequencies and different values of the dislocation segment length is performed. Certain regularities have been established. Based on the graphical results of numerical calculations, an approximate calculation of the generalized susceptibility matrix elements was carried out. Expressions for the diagonal and off-diagonal generalized susceptibility matrix elements of the dislocation segment are obtained.

The paper deals with the models of evaluation of performance of both the management company and the individual subsidiaries on the basis of a combination of elements and multi-parameter and target approaches. The article shows that due to the power of multi-dimensional and multi-directional indicators of financial and economic activity it is necessary to assess the degree of achievement of the objectives with the use of multivariate ordinal model as a set of indicators, ordered by growth so that the maintenance of this order on a long interval of time will ensure the effective functioning of the enterprise in the long term. It is shown that these models can be regarded as the monitoring tools of implementation of strategies and guide the justification effectiveness of implementation of management decisions.

In this paper, a triangulated surface model is studied in the context of Finsler geometry (FG) modeling. This FG model is an extended version of a recently reported model for two-component membranes, and it is asymmetric under surface inversion. We show that the definition of the model is independent of how the Finsler length of a bond is defined. This leads us to understand that the canonical (or Euclidean) surface model is obtained from the FG model such that it is uniquely determined as a trivial model from the viewpoint of well definedness.

In network models that take into account growth properties, deletion of old nodes has a serious impact on degree distributions, because old nodes tend to become hub nodes. In this study, we aim to provide a simple explanation for why hubs can exist even in conditions where the number of nodes is stationary due to the deletion of old nodes. We show that an exponential increase in the degree of nodes is a natural consequence of the balance between the deletion and addition of nodes as long as a preferential attachment mechanism holds. As a result, the largest degree is determined by the magnitude relationship between the time scale of the exponential growth of degrees and lifetime of old nodes. The degree distribution exhibits a power-law form ∼ k^−γ with exponent γ = 1 when the lifetime of nodes is constant. However, various values of γ can be realized by introducing distributed lifetime of nodes.

Cosmic rays propagation within the Galaxy is simulated considering a fractallike distribution of matter and magnetic fields. In such an anomalous diffusion process, the sources of ultra-high energy particles were considered to be galactic pulsars. The coordinate and birth times of sources were chosen from SN and pulsar catalogues. From these sources the primary spectrum of cosmic rays (H, He, CNO, Ne-Si, Fe) in energy range EeV and above were reproduced. The resulted spectrum is used to discuss about the change in cosmic ray sources form Galactic to Extragalactic.

The statistical characteristics of light scattering on textured polymer coatings of rolled metal surface are studied on the base screen model with two-dimensional Weierstrass function. In the frame of the Kirchhoff method, the average light scattering and gloss coefficients are numerically calculated for different coating surface calibration (profiles) and falling angles. It is shown; that the scattering is symmetrical relatively to the plane of incidence and it is maximal in the direction θ₃ = 0. The scattering wave is observed in the cone of lateral directions relatively the normal direction θ₂ = 0. For such coatings it is nessesary to develop a special convergence experimental technique allowing identifying a correspondence between the gloss and the texture of the surface.

The influence of the thickness of a ferroelectric film and the depolarizing field on its spontaneous polarization and the order parameter has been investigated by means of the Monte-Carlo method. Dependences of the polarization of thethin ferroelectric film on temperature at different values of its thickness and the potential well depth of the Lennard- Jones potential are calculated. The thickness of the "dead" layer is analyzed depending on the temperature and of the potential well depth.

We study differential equations describing nonlinear processes in dynamical systems (macro-systems) that consist of a large number of components (micro-systems) and allow a synchronization in behavior of these components. In physics, these processes underlie the echo phenomena. An empirical solution of such equations is proposed. A solution is given in the form of power series of power series of the spectra of external of external perturbations acting on a macro-system. Numerical simulations of this solution give a good agreement with a number of experimentally observed echo phenomena.

Dual energy (DE) imaging technique has been applied to many theoretical and experimental studies. The aim of the current study is to evaluate dual energy in breast tomosynthesis using commercial tomosynthesis system in terms of its potential to better visualize microcalcifications (μCs). The system uses a tungsten target X-ray tube and a selenium direct conversion detector. Low-energy (LE) images were acquired at different tube voltages (28, 30, 32 kV), while high-energy images at 49 kV. Fifteen projections, for the low- and high-energy respectively, were acquired without grid while tube scanned continuously. Log-subtraction algorithm was used in order to obtain the DE images with the weighting factor, w, derived empirically. The subtraction was applied to each pair of LE and HE slices after reconstruction. The TORMAM phantom was imaged with the different settings. Four regions-of-interest including μCs were identified in the inhomogeneous part of the phantom. The μCs in DE images were more clearly visible compared to the low-energy images. Initial results showed that DE tomosynthesis imaging is a promising modality, however more work is required.

In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries equations (CMKdVE). Using the Lax pair, we construct a Darboux transformation and namely one-fold and n-fold transformations. The soliton solutions are obtained from the different "seeds" by using this Darboux transformation.

Homogeneity tests are used in high energy physics for the verification of simulated Monte Carlo samples, it means if they have the same distribution as a measured data from particle detector. Kolmogorov-Smirnov, χ², and Anderson-Darling tests are the most used techniques to assess the samples' homogeneity. Since MC generators produce plenty of entries from different models, each entry has to be re-weighted to obtain the same sample size as the measured data has. One way of the homogeneity testing is through the binning. If we do not want to lose any information, we can apply generalized tests based on weighted empirical distribution functions. In this paper, we propose such generalized weighted homogeneity tests and introduce some of their asymptotic properties. We present the results based on numerical analysis which focuses on estimations of the type-I error and power of the test. Finally, we present application of our homogeneity tests to data from the experiment DØ in Fermilab.

This article describes the development and creation of a universal system of data collection to measure the intensity of pulsed signals. As a result of careful analysis of time conditions and operating conditions of software and hardware complex circuit solutions were selected that meet the required specifications: frequency response is optimized in order to obtain the maximum ratio signal/noise; methods and modes of operation of the microcontroller were worked out to implement the objectives of continuous measurement of signal amplitude at the output of amplifier and send the data to a computer; function of control of high voltage source was implemented. The preliminary program has been developed for microcontroller in its simplest form, which works on a particular algorithm.

The spin-crossover (SCO) phenomenon is related to the ability of a transition metal to change its spin state vs. a given perturbation. For an iron(II) SCO complexes the reversible changes involve the diamagnetic low-spin (S = 0) and the paramagnetic high-spin (HS S = 2) states [1,2,3]. In this contribution we simulate the HS Fraction (n_HS) for different set values of temperature and pressure for a device using two SCO complexes with weak elastic interactions. We improve the calculation given by Linares et al. [4], taking also into account different volume (V_HS, V_LS) changes of the SCO. We perform all the calculation in the frame work of an Ising-like model solved in the mean-field approximation. The two SCO show in the case of "weak elastic interactions", gradual spin transitions such that both temperature and pressure values can be obtained from the optical observation in the light of calculations discussed in this article.

Methodological possibilities of positron annihilation lifetime (PAL) spectroscopy in application to nanostructurized substances treated within three-term fitting procedure are reconsidered to parameterize their atomic-deficient structural arrangement. In contrast to conventional three-term fitting analysis of the detected PAL spectra based on admixed positron trapping and positronium (Ps) decaying, the nanostructurization due to guest nanoparticles embedded in host matrix is considered as producing modified trapping, which involves conversion between these channels. The developed approach referred to as x3-x2-coupling decomposition algorithm allows estimation free volumes of interfacial voids responsible for positron trapping and bulk lifetimes in nanoparticle-embedded substances. This methodology is validated using experimental data of Chakraverty et al. [Phys. Rev. B71 (2005) 024115] on PAL study of composites formed by guest NiFe₂O₄ nanocrystals grown in host SiO₂ matrix.

The mathematical models of degradation-relaxation kinetics are considered for jammed systems composed of screen-printed spinel Cu_0.1Ni_0.1Co_1.6Mn_1.2O₄ and conductive Ag or Ag-Pd alloys. Structurally-intrinsic nanoinhomogeneities due to Ag and Ag-Pd diffusants embedded in spinel phase environment are shown to define governing kinetics of thermally-induced degradation obeying an obvious non-exponential behaviour in the resistance drift. The stretched-to-compressed exponential crossover is detected for degradation-relaxation kinetics in these systems with conductive contacts made of Ag-Pd and Ag alloys. Under essential migration of conductive phase, the resulting kinetics is though to be considerable two-step diffusing process originated from Ag penetration deep into spinel ceramics.

Determination of humidity is one of the most important types of hydrometeorological and glaciological observations performed in agriculture, hydropower and water supply. The work is devoted to the development of physical basis of moisture determination method, based on attenuation of the flux of cosmic-ray muons. The relationship between the intensity of muons registered in the underground room of the Tien Shan mountain research station (Almaty) and relative humidity was studied. The results of studies show that the values of the normalized mutual correlation function between the rows of muon intensity and relative humidity vary from 0.3 to 0.7, depending on the coincidence scheme. The data obtained from the muon telescope located at the the Tien Shan mountain research station was used in the work.

Some six-coordinate iron (II) coordination compounds exhibit thermal-, optical-, electrical-, magnetic- and pressure-induced switching between the diamagnetic low-spin (LS, S=0) and the paramagnetic high-spin (HS; S=2) states [1]. This may lead to potential application of these complexes in molecular devices such as temperature and pressure sensors [2]. An Ising-like model has been proposed to explain the occurrence of the thermal hysteresis behaviour [3,4] of this switchable solids. In this contribution, the local mean field approximation is applied to solve the Hamiltonian modelling interactions pertaining to 2D nanoparticles embedded in a magnetically-inactive matrix.

The physical phenomena underlying crack initiation and hence failures in interconnection alloy is investigated using the ABV model [1] (Metals A and B and void V) focusing on boundary effects at the interface with the device. The Hamiltonian which is expressed as the sum of the interaction energies between A, B and V with interaction parameters E_AA, E_BB, E_AB, E_AV and E_BV and reformulated in terms of fictitious 3 states spins (-1, 0, +1). And new parameters J, K, and U function of the interaction energy parameters between the metal atoms A, B and void V are defined and associated to the different spin combinations of the transformed Hamiltonian. A Monte Carlo (MC) simulation of a 2D microscopic 3 states Ising model taking into account edge effects [2] at the boundary between an active chip in a photovoltaic device or a sensor and nanoparticles of an interconnect alloy is performed. The results are discussed in terms of realistic values of interaction parameters and different algorithms for fixed compositions of A, B and V.

Current fire simulation systems are capable to utilize advantages of high-performance computer (HPC) platforms available and to model fires efficiently in parallel. In this paper, efficiency of a corridor fire simulation on a HPC computer cluster is discussed. The parallel MPI version of Fire Dynamics Simulator is used for testing efficiency of selected strategies of allocation of computational resources of the cluster using a greater number of computational cores. Simulation results indicate that if the number of cores used is not equal to a multiple of the total number of cluster node cores there are allocation strategies which provide more efficient calculations.

In this work, we investigate the role of interactions in the process of thermalization of a weakly interacting Bose gas. The system of kinetic equations based on the 'Fermi's golden rule' is solved numerically using special transformation for calculation efficiency. We study the distribution function for particles in various conditions, including interaction with phonon subsystem, i.e. energy exchange with thermal bath. The possibility to achieve the state of Bose-Einstein condensation with specific values of parameters, is also discussed.

We consider the questions on the decomposition of the initial boundary value problems of elasticity theory and thin bodies for some anisotropic media. In particular, the initial boundary problems of the micropolar (and classical) theory of elasticity are presented, i.e. to introduce tensor-block matrix operators (tensor-operators). In the case of an isotropic micropolar elastic medium (isotropic and transversally isotropic classical media) tensor-block matrix operators (tensor-operators) of cofactors corresponding to the tensor-block matrix operators (tensor-operators) of of the initial boundary value problems are obtained, which are splitting the initial boundary value problems. From three-dimensional decomposed initial boundary value problems the corresponding decomposed initial boundary value problems for the theory of thin bodies are obtained.

The nonlinear effects that appear in test particle (tracer) transport in two-dimensional incompressible velocity fields are discussed. Test particle trajectories show both random and quasi-coherent aspects. The coherent motion is associated with trapping or eddying in the structure of the stochastic field. It generates quasi-coherent trajectory structures. The random motion leads to diffusive transport while the structures determine a micro-confinement process. The strength of each of these aspects depends on the parameters of the turbulence. The transport coefficients and the average size of the quasi-coherent structures are determined as function of the characteristics of the turbulence. The transport process is completely different in the presence of structures in the sense that the dependence on the parameters is different. The quasi-coherence of the motion can also be represented by the generation of flows. We show that tracers flows yield in a stochastic potential with space-dependent amplitude.

Chaos theory has been used to develop several cryptographic methods relying on the pseudo-random properties extracted from simple nonlinear systems such as cellular automata (CA). Cryptographic hash functions (CHF) are commonly used to check data integrity. CHF "compress" arbitrary long messages (input) into much smaller representations called hash values or message digest (output), designed to prevent the ability to reverse the hash values into the original message. This paper proposes a chaos-based CHF inspired on an encryption method based on chaotic CA rule B1357-S2468. Here, we propose an hybrid model that combines CA and networks, called network automata (CNA), whose chaotic spatio-temporal outputs are used to compute a hash value. Following the Merkle and Damgård model of construction, a portion of the message is entered as the initial condition of the network automata, so that the rest parts of messages are iteratively entered to perturb the system. The chaotic network automata shuffles the message using flexible control parameters, so that the generated hash value is highly sensitive to the message. As demonstrated in our experiments, the proposed model has excellent pseudo-randomness and sensitivity properties with acceptable performance when compared to conventional hash functions.

The article deals with the research of modern trends in the development of social entrepreneurship in Russia. The results of the research allow the authors to identify a system of factors that affect the development of entrepreneurship in the modern Russian economy. Moreover, the authors argue the regional specificity of the development of social entrepreneurship. The paper considers specific features and formulates the main limitations of the development of entrepreneurship and the competitive environment in the social sphere. The authors suggest an econometric model for assessing the influence of economic factors on the development of socially-oriented entrepreneurship and present an algorithm for calculating its components. The results of the econometric analysis identify the main factors of the change in the performance indicators of entrepreneurial activity and determine the degree of their impact on social entrepreneurship. The results and conclusions can serve as an estimation of the socioeconomic consequences of the sustainability disruption of the entrepreneurial potential realization in the social sphere.

We show that in the Horava theory at the kinetic-conformal point there are more solutions of the field equations in the Hamiltonian formalism than in the original Lagrangian formalism. To hold this we add all the constraints, primary and secondary, to the Hamiltonian. There are certain configurations for the Lagrange multipliers associated to the secondary constraints that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. Here we relax one condition on one Lagrange multiplier, showing the existence of more special solutions on the Hamiltonian side.

In the framework of the Ising-like model, the thermal and pressure effects on the spin crossover systems are evaluated through two-states fictitious spin operators σ with eigenvalues 𝜎 = −1 and 𝜎 = +1 respectively associated with the low-spin (LS) and highspin (HS) states of each spin-crossover (SCO) molecule. Based on each configurational state, the macroscopic SCO system, is described by the following variables: m=Σ σ_i, s=Σ σ_i σ_j and c=Σ σ_k standing respectively for the total magnetization, the short-range correlations and surface magnetization. To solve this problem, we first determine the density of macrostates d[m][s][c], giving the number of microscopic configurations with the same m, s and c values. In this contribution, two different ways have been performed to calculate this important quantity: (i) the entropic sampling method, based on Monte Carlo simulations and (ii) a new algorithm based on specific dynamic programming. These two methods were tested on the 2D SCO nanoparticles for which, we calculated the average magnetization < σ> taking into account for short-, long-range interactions as well as for the interaction between surface molecules with their surrounding matrix. We monitored the effect of the pressure, temperature and size on the properties of the SCO nanoparticles.

The expression for the generalized susceptibility of the dislocation obtained earlier was used. The electronic drag mechanism of dislocations is considered. The study of small dislocation oscillations was limited. The contribution of the attenuation of low-frequency bending dislocation vibrations to the overall coefficient of dynamic dislocation drag in the long-wave and short-wave limits is calculated. The damping of short-wave bending dislocation vibrations caused by an external action of an arbitrary frequency has been investigated. The contribution of long-wave bending dislocation vibrations damping in total drag coefficient at an arbitrary frequency is found.

We introduce a new data based approach to homogeneity testing and variable selection carried out in high energy physics experiments, where one of the basic tasks is to test the homogeneity of weighted samples, mainly the Monte Carlo simulations (weighted) and real data measurements (unweighted). This technique is called 'data re-arranging' and it enables variable selection performed by means of the classical statistical homogeneity tests such as Kolmogorov-Smirnov, Anderson-Darling, or Pearson's chi-square divergence test. P-values of our variants of homogeneity tests are investigated and the empirical verification through 46 dimensional high energy particle physics data sets is accomplished under newly proposed (equiprobable) quantile binning. Particularly, the procedure of homogeneity testing is applied to re-arranged Monte Carlo samples and real DATA sets measured at the particle accelerator Tevatron in Fermilab at DØ experiment originating from top-antitop quark pair production in two decay channels (electron, muon) with 2, 3, or 4+ jets detected. Finally, the variable selections in the electron and muon channels induced by the re-arranging procedure for homogeneity testing are provided for Tevatron top-antitop quark data sets.

This work presents a discussion related to the teaching and learning of mathematical contents related to the study of exponential functions in a freshman students group enrolled in the first semester of the Science and Technology Bachelor's (STB of the Federal University of Jequitinhonha and Mucuri Valleys (UFVJM). As a contextualization tool strongly mentioned in the literature, the modelling approach was used as an educational teaching tool to produce contextualization in the teaching-learning process of exponential functions to these students. In this sense, were used some simple models elaborated with the GeoGebra software and, to have a qualitative evaluation of the investigation and the results, was used Didactic Engineering as a methodology research. As a consequence of this detailed research, some interesting details about the teaching and learning process were observed, discussed and described.

In this paper we consider the possibility to study hydrodynamic instabilities (HDI) in a specific type of a decay flow existing at a rise of a nematic liquid crystal (NLC) in the flat capillary of a variable gap. In this case the capillary can be replaced by a number of parallel channels of different gaps with different instant values of a pressure gradient, which induces a flow. The last feature makes such flow to be different from the previously studied decay flow [1] with a constant value of a pressure gradient, applied to the channels of different thickness.

In the conditions of the modern economy, in connection with the development of production, the expansion of the market for goods and services, its differentiation, active use of marketing tools in the sphere of sales, changes occur in the system of values and consumer needs. Motives that drive the consumer are transformed, stimulating it to activity. The article presents a model of personal consumption that takes into account modern trends in consumer behavior. The consumer, making a choice, seeks to maximize the overall utility from consumption, physiological and socio-psychological satisfaction, in accordance with his expectations, preferences and conditions of consumption. The system of his preferences is formed under the influence of factors of a different nature. It is also shown that the structure of consumer spending allows us to characterize and predict its further behavior in the market. Based on the proposed model and analysis of current trends in consumer behavior, conclusions and recommendations have been made that can be used by legislative and executive government bodies, business organizations, research centres and other structures to form a methodological and analytical tool for preparing a forecast model of consumption.

In this study a similarity in changes of frequencies dynamics for semantically related words was analyzed using word statistics extracted from more than 4.5 million books written over a period of 205 years. The approach is based on the correlation analysis of 1-grams frequency dynamics. We analyzed the frequencies correlation of synonym pairs, their corresponding antonymous groups and random words pairs. Also, we compared several metrics to find the most effective for assessing the degree of similarity in the dynamics of use of different words. Comparing differences between logarithmic rank variations in pairs of synonyms and random word pairs, significant differences are found, though they are smaller than it could be expected.

The teaching and learning of Mathematics contents have been challenging along the history of the education, both for the teacher, in his dedicated task of teaching, as for the student, in his arduous and constant task of learning. One of the topics that are most discussed in these contents is the difference between the concepts of proof and demonstration. This work presents an interesting discussion about such concepts considering the use of the mathematical modeling approach for teaching, applied to some examples developed in the classroom with a group of students enrolled in the discipline of Geometry of the Mathematics curse of UFVJM.

In the face of the reality of teaching Mathematics in Basic Education in Brazil, specially relating teach functions focusing their relevance to the student's academic development in Basic and Superior Education, this work proposes the use of educational software to help the teaching of functions in Basic Education since the computers and software show as an outstanding option to help the teaching and learning processes. On the other hand, the study also proposes the use of Didactic Transposition as a methodology investigation and research. Along with this survey, some teaching interventions were applied to detect the main difficulties in the teaching process of functions in the Basic Education, analyzing the results obtained along the interventions in a qualitative form. Considering the discussion of the results at the end of the didactic interventions, it was verified that the results obtained were satisfactory.

Quantum information is an emergent area merging physics, mathematics, computer science and engineering. To reach its technological goals, it is requiring adequate approaches to understand how to combine physical restrictions, computational approaches and technological requirements to get functional universal quantum information processing. This work presents the modeling and the analysis of certain general type of Hamiltonian representing several physical systems used in quantum information and establishing a dynamics reduction in a natural grammar for bipartite processing based on entangled states.

The energy levels of methane molecule trapped, at low temperature, in small (s) and large (l) nano-cages of cubic sI clathrates are calculated in the Born-Oppenheimer approximation using the Extended Lakhlifi-Dahoo model based on pairwise atom-atom effective interaction potentials. In the s cage, the center of mass of CH₄ exhibits a slightly asymmetrical 3D oscillation motion with small amplitude around the cage center. Two methods were used to calculate the frequencies of such a motion: a 3D harmonic treatment and a 1D Discrete Variable Representation (DVR) treatment in the X, Y and Z directions. They give approximately the same values of, respectively, 133 cm^-1, 108 cm^-1 and 120 cm^-1. In the l cage, the oscillations are anharmonic and characterized by large amplitude motions with frequencies of 63 cm^-1, 52 cm^-1 and 47 cm^-1. In the s and l nano-cages, the molecule exhibits strongly perturbed rotational motion. The rotational level schemes are quite different from that of the molecular free rotational motion, and for each nano-cage, the obtained levels are described as combination of the free rotation levels.

The ordinary Bondi—Metzner—Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space—times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). Strongly continuous unitary irreducible representations (IRs) of B(2, 1), the analogue of B in three space—time dimensions, are analysed in the Hilbert topology. It is proved that all IRs of B(2, 1) are induced from IRs of compact 'little groups', which are the closed subgroups of SO(2). It is proved that all IRs of B(2, 1) are obtained by Wigner—Mackey's inducing construction notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.

We design oscillator networks to generate a signal with a prescribed power spectrum. We consider networks of identical sin-wave oscillators and the Kuramoto order parameter as an output signal of the system. We use the Kullback-Leibler entropy as a measure of the distance between the power spectrum of the output signal and those of desired one. By optimizing the connection network through the Markov chain Monte Carlo method with replica exchange, we found that even oscillator network with a small number of elements can be generate a variety of time signals. The output signals include periodic and quasi-periodic signals with prescribed periods, and aperiodic signals with prescribed power spectrums.

This paper describes methods of the power law verification using different empirical data. We do not analyse the value of deviations from the model but try to found out whether these deviations are regular or random. The suggested approach is based on the idea of finding local power approximation of the considered series for each range of ranks, after which one or another trend criterion is applied to the obtained series of local exponents. Application of the runs test is also discussed. The suggested methods were tested using 10 sets of empirical data, which are available for free. It was shown that compliance with the power law is satisfactory only in one case.

The time evolution of the rotational distribution of diatomic molecules induced by a train of broadband optical pulses can be modeled as a class of continuous-time quantum walk (CTQW) on a half line. As the transition moments asymptotically decrease to zero like Gaussian distribution, the rotational distribution cannot reach infinity far from the initial state and exhibits a localization-like behavior where the upper limit of the distribution is not trivial. We investigated a time evolution of the density distribution with the transition moments of the Gaussian distribution peaked at the boundary of the half line for the initial state of J=0. Even though the time evolution exhibited oscillatory motion inside a certain region repeatedly, we observed a clear time-averaged distribution that is well fitted to the stretched exponential distribution with parameters close to the Gaussian distribution by numerical simulation. By varying the coefficients of the Gaussian distribution of the transition moments, the coefficients of the stretched exponential distribution can be determined by regression.

In this work the problem of recognition is studied using SAR images. The algorithm of recognition is based on the computation of conjugation indices with vectors of class. The support subspaces for each class are constructed by exception of the most and the less correlated vectors in a class. In the study we examine the ability of a significant feature vector size reduce that leads to recognition time decrease. The images of targets form the feature vectors that are transformed using pre-trained convolutional neural network (CNN).

Increase in the number of small businesses and the lack of effectiveness of existing support at local and regional level have led to curb the development of entrepreneurial activity. The article presents the methodological tools for assessing the effectiveness, which allows to identify existing municipalities in the advantages and disadvantages for the implementation of entrepreneurial potential, including the effectiveness of state and municipal support measures, as well as calculate the degree of progress in the implementation of entrepreneurial potential. In order to evaluate the implementation of the business potential of the Republic of Tatarstan and the impact of their public support at the regional level was calculated indexes of business activity in the municipal districts (MD) of the republic. It should be noted that a major breakthrough in share of small and medium-sized businesses is important to the whole ecosystem. The method of evaluation of the implementation of entrepreneurial potential which is presented in this paper can be used by every competent organization to analyze and form the effective programs of the economic and finance development.

We analyze baryogenesis using a Bohr-type rotating neutrino model in which the strong force is modeled as the gravitational force between ultrarelativistic neutrinos. The kinetic energy plus rest energy of these neutrinos constitutes the rest energy of the gravitationally confined composite neutrino structure. In this work we derive a simple expression for the gravitational mass of the rotating neutrinos in terms of their rest mass and their total energy. It is found, both analytically and graphically, that when the gravitational mass reaches the Planck mass, then the relativistic mass of the neutrinos equals the effective mass of u and d quarks. The model contains no adjustable parameters and leads to semiquantitative (within 1%) agreement with the masses of baryons. It also shows that hadronization is easier to achieve with light particles such as neutrinos rather than with heavier particles. The model can also be extended by considering ultrarelavivistic rotating positron or electron-neutrino pairs, triplets or quartets whose mass is found to match within 2% those of W^±, Z° and H° bosons.

The dynamics of the concentration of nanofluids placed in a light field with a Gaussian intensity profile is studied theoretically. The investigation is based on the analytical and numerical solutions of the system of linearized heat conduction and convection-diffusion equations. The convection-diffusion equation contains terms that correspond both to the Soret effect and to the transfer of nanoparticles, caused by the action of a light field on them (electrostriction). The dependence of the coefficient of thermal conductivity of the medium on the concentration is taken into account. It is shown that under these conditions single travelling waves appear in the medium, the velocity of which depends not only on the thermal physical parameters of the medium, but also on the polarization of the particles. Conditions under which the stratification of the medium is possible are found.

The paper takes on the issue of assessment of remaining useful life (RUL). The goal of the paper was to develop a method, which would enable use of diagnostic information in the task of reducing the uncertainty related to technical risk. Prediction of the remaining useful life (RUL) of the system is a very important task for maintenance strategy. In the literature RUL of an engineering system is defined as the first future time instant in which thresholds of conditions (safety, operational quality, maintenance cost, etc) are violated. Knowledge of RUL offers the possibility of planning the testing and repair activities. Building models of damage development is important in this task. In the presented work, logistic function will be used to model fatigue crack development. It should be remembered that modeling of every phase of damage development is very difficult, yet modeling of every phase of damage separately, especially including on-line diagnostic information is more effective. Particular attention was paid to the possibility of forecasting the occurrence of damage due to fatigue while relying on the analysis of the structure of a vibroacoustic signal.

The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. The clustered order parameter is proposed for the description of the magnetic transition in spin systems regardless of the sign of the exchange integral and the number of neighbors. The method of calculation of critical field to change the magnetic states was presented. For diluted 1D antiferromagnetic model two plateaus in magnetization behavior are observed, and explained. Influence of length of interaction plays critical role for phase transition of dipoles system. Dipoles on hexagonal lattice show the phase transition only in model of long range interaction, and there isn't critical behavior for short range. The approach to calculation of spin system in Heisenberg model is proposed.

To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, df/dx = −f − f². It is satisfied with the stationary solution, f(x) = 1/(e^{x + μ} − 1), of the Kompaneets equation, where μ is the constant chemical potential. Setting R = 1/f, we obtain a linear differential equation for R. Then, the Caputo fractional derivative of order p (p > 0) is introduced in place of the derivative of x, and fractional BE distribution is obtained, where function e^x is replaced by the Mittag–Leffler (ML) function Ep(x^p). Using the integral representation of the ML function, we obtain a new formula. Based on the analysis of the NASA COBE monopole data, an identity p ≃ e^−μ is found.

Quantum information processing should be generated through control of quantum evolution for physical systems being used as resources, such as superconducting circuits, spinspin couplings in ions and artificial anyons in electronic gases. They have a quantum dynamics which should be translated into more natural languages for quantum information processing. On this terrain, this language should let to establish manipulation operations on the associated quantum information states as classical information processing does. This work shows how a kind of processing operations can be settled and implemented for quantum states design and quantum processing for systems fulfilling a SU(2) reduction in their dynamics.

The model of magnetic deformable system was developed. The modelling of magnetic elastomer deformation and magnetization dependence on external magnetic field was calculated within the method of movable cellular automata (MCA). It was shown that ordering of magnetic particles substantially effects on elastomer saturation deformation. The maximum orderly elastomer saturation deformation is twice higher the saturation deformation of system with chaotic ordering of magnetic particles.

We measure the stomatic plasticity at Ctenanthe oppenheimiana leaves based on distance between stomata pairs in microscopic images. Theoretical graphs were built according with distance thresholds as connectivity parameter. The theoretical networks based at distances between stomata depends on how the connectivity can vary according with the threshold distances. Plants exposed to extreme light irradiation times from 24 to 4 hours per day, presented discernible relations between stomatic distances. The graphs related to average distances between stomata pairs revealed a powerful tool to predict changes of the geometric distribution of stomata at live Ctenanthe openheimiana plants.

One-way quantum key distribution (QKD) optical schemes require active stabilization algorithms for continuous operation. To achieve this a mathematical model for a new optical scheme has been developed. The model uses Jones calculus to describe the polarization state evolution within the optical scheme. The developed algorithms have been successfully tested experimentally.

Pulsed electron beam ablation (PEBA) has recently emerged as a very promising technique for the deposition of thin films with superior properties. Interaction of the pulsed electron beam with the target material is a complex process, which consists of heating, phase transition, and erosion of a small portion from the target surface. Ablation can be significantly affected by the nature of thermal phenomena taking place at the target surface, with subsequent bearing on the properties, stoichiometry and structure of deposited thin films. A two stage, one-dimensional heat conduction model is presented to describe two different thermal phenomena accounting for interaction of a graphite target with a polyenergetic electron beam. In the first instance, the thermal phenomena are comprised of heating, melting and vaporization of the target surface, while in the second instance the thermal phenomena are described in terms of heating and sublimation of the graphite surface. In this work, the electron beam delivers intense electron pulses of ∼100 ns with energies up to 16 keV and an electric current of ∼400 A to a graphite target. The temperature distribution, surface recession velocity, ablated mass per unit area, and ablation depth for the graphite target are numerically simulated by the finite element method for each case. Based on calculation findings and available experimental data, ablation appears to occur mainly in the regime of melting and vaporization from the surface.

Realistic modeling of the complicated phenomena as Forbush decrease of the galactic cosmic ray intensity is a quite challenging task. One aspect is a numerical solution of the Fokker-Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The second difficulty arises from a lack of detailed knowledge about the spatial and time profiles of the parameters responsible for the creation of the Forbush decrease. Among these parameters, the central role plays a diffusion coefficient. Assessment of the correctness of the proposed model can be done only by comparison of the model output with the experimental observations of the galactic cosmic ray intensity. We apply the Approximate Bayesian Computation (ABC) methodology to match the Forbush decrease model to experimental data. The ABC method is becoming increasing exploited for dynamic complex problems in which the likelihood function is costly to compute. The main idea of all ABC methods is to accept samples as an approximate posterior draw if its associated modeled data are close enough to the observed one. In this paper, we present application of the Sequential Monte Carlo Approximate Bayesian Computation algorithm scanning the space of the diffusion coefficient parameters. The proposed algorithm is adopted to create the model of the Forbush decrease observed by the neutron monitors at the Earth in March 2002. The model of the Forbush decrease is based on the stochastic approach to the solution of the Fokker-Planck equation.

The paper presents the results of the research on the application of the new analytical models of multilayer adsorption on heterogeneous surfaces with the unique fast multivariant identification procedure, together called LBET method, as a tool for analysing the microporous structure of the activated carbon fibres obtained from polyacrylonitrile by chemical activation using potassium and sodium hydroxides. The novel LBET method was employed particularly to evaluate the impact of the used activator and the hydroxide to polyacrylonitrile ratio on the obtained microporous structure of the activated carbon fibres.

The paper presents the results on the application of the LBET numerical method as a tool for analysis of the microporous structure of activated carbons obtained from a bituminous coal. The LBET method was employed particularly to evaluate the impact of the burn-off on the obtained microporous structure parameters of activated carbons.

Wireless mobile technologies have caused a tendency to use mobile devices in the learning process. However, delivery mode should be changed. This paper describes a method of uploadable semantic structures for students' personal mobile devices that would ensure interdisciplinarity.

The information model of interdisciplinary links (Gnitetskaya T., 2016) allows to reach the interdisciplinary in the process of training physics. Presenting the fundamental physical term with semantic structure we can see that structure's node(s) where interdisciplinary link(s) from physics to chemistry and vice versa could be established. Method of optimization the interdisciplinary content was described in this paper. Method based on quantity estimation of the information – an entropy, as characteristic of semantic structure graph. Results of entropy calculation for interdisciplinary content of term "atom structure", corresponded to school physics' level, were discussed.

The article is devoted to the study of the impact of the information economy on the formation of the middle class. The paper identifies factors contributing to the increase in the share of the middle class in the transition to the information economy. The positive synergetic influence of telecommunication technologies on the formation of the middle class is considered through a possibility of using virtual spaces for labor and educational activities, a possibility of obtaining high returns in the form of dividends on intellectual capital, a qualitative change in the structure of needs, an access to new types of information services, etc. Authors develop a complex model of research of the middle class in the information economy, differing from those available using an expanded list of criteria. In addition to such widely used criteria as income level, level of education and self-identification, the criterion "degree of involvement in the information society" was introduced. The study substantiates that the transition to the information economy made an access to information and communication technologies one of the most significant criteria for social differentiation of society. On the basis of the model, an econometric estimate of the middle class has been carried out, which makes it possible to reveal the share of the middle class in modern society, dynamics of its development, as well as multicollinearity between spending on education, the Gini coefficient, access to information and telecommunication technologies and the size of the middle class.

We measure the stomatal plasticity at Ctenanthe oppenheimiana leaves based on distance between stomata pairs in microscopic images. The distance measurements revealed that the plasticity induced by environmental adaptations are measurable using the distance between neighbor stomata. Plants exposed to extreme light irradiation times from 24 to 4 hours per day, presented discernible relations between stomatal distances. The average distances between stomata pairs revealed a powerful tool to predict changes of plasticity of stomata according with different light acclimation conditions at Ctenanthe openheimiana plants.

In this paper, we consider modular multiplicative inverse operators (MMIO)'s of the form:

$$\begin{eqnarray}&&{{\mathscr{J}}}_{(m+n)}:{({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }\to {\mathbb{Z}}/(m+n){\mathbb{Z}},\text\,{{\mathscr{J}}}_{(m+n)}(a)={a}^{-1}.\end{eqnarray}$$

${{\mathscr{J}}}_{(m+n)}(.)$

${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$

${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$

${({\mathbb{Z}}/\varrho {\mathbb{Z}})}^{* }$

Small amplitude bending vibrations of a screw dislocation with arbitrary slip plane in an uniaxial ferroelectric is considered, the dislocation line is along the ferroelectric axis. To solve this problem the system of equations was made up. Fourier transform of the Peach- Koehler forces projection on the dislocation slip plane is obtained and a linear response function of a screw dislocation in a ferroelectric to an external force is found. The estimates of the additive to the dislocation effective mass and effective rigidity, the additional contribution to the damping of the dislocation vibrations are obtained.

We study the asymptotic behavior of the solution u(x, t) of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients (as t → ∞) in which the initial data are zero, and the right-hand side of the equation has the form f(x) exp(−iωt), where ω is real.

It is known that conservation law plays an important role in the study of nonlinear evolution equations and namely to integrability and constants of motion. In this paper, we construct infinitely many conservation laws for the Hirota-Maxwell-Bloch system and its reductions with symbolic computation from the Riccati form of the Lax pair.

This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity and very strict passivity (i.e. joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, it is discussed how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain.

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I₀(x), where I₀(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.