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Rugose spiraling whitefly (RSW) is one of the major pests which affects the coconut trees. It feeds on the tree by sucking up the water content as well as the essential nutrients from leaves. It also forms sooty mold in leaves due to which the process of photosynthesis is inhibited. Biocontrol of pest is harmless for trees and crops. The experimental results in literature reveal that Pseudomallada astur is a potential predator for this pest. We investigate the dynamics of predator, Pseudomallada astur’s interaction with rugose spiralling whitefly, Aleurodicus rugioperculatus in coconut trees using a mathematical model. In this system of ordinary differential equation, the pest-predator interaction is modeled using Holling type III functional response. The parametric values are calculated from the experimental results and are tabulated. An approximate analytical solution for the system has been derived. The homotopy analysis method proves to be a suitable method for creating solutions that are valid even for moderate to large parameter values, hence we employ the same to solve this nonlinear model. The $\hbar$-curves, which give the admissible region of $\hbar$, are provided to validate the region of convergence. We have derived the approximate solution at fifth order and stopped at this order since we obtain a more approximate solution in this iteration. Numerical simulation is obtained through MATLAB. The analytical results are compared with numerical simulation and are found to be in good agreement. The biological interpretation of figures implies that the use of a predator reduces the whitefly’s growth to a greater extent.

The main aim, formulated in the first part of article, is to carry out detailed numerical studies of the chemical, ionization, optical, and temperature characteristics of the lower ionosphere perturbed by powerful radio emission. The brief review of the main experimental and theoretical researches of physical phenomena occurring in the ionosphere when it is heated by high-power high-frequency radio waves from heating facilities is given. The decisive role of the $D$-region of the ionosphere in the absorption of radio beam energy is shown. A detailed analysis of kinetic processes in the disturbed $D$-region, which is the most complex in kinetic terms, has been performed. It is shown that for a complete description of the ionization-chemical and optical characteristics of the disturbed region, it is necessary to take into account more than 70 components, which, according to their main physical content, can be conveniently divided into five groups. A kinetic model is presented to describe changes in the concentrations of components interacting (the total number of reactions is 259). The system of kinetic equations was solved using a semi-implicit numerical method specially adapted to such problems. Based on the proposed structure, a software package was developed in which the algorithm scheme allowed changing both the content of individual program blocks and their number, which made it possible to conduct detailed numerical studies of individual processes in the behavior of the parameters of the perturbed region. The complete numerical algorithm is based on the two-temperature approximation, in which the main attention was paid to the calculation of the electron temperature, since its behavior is determined by inelastic kinetic processes involving electrons. The formulation of the problem is of a rather general nature and makes it possible to calculate the parameters of the disturbed ionosphere in a wide range of powers and frequencies of radio emission. Based on the developed numerical technique, it is possible to study a wide range of phenomena both in the natural and disturbed ionosphere.

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple subgradient method with switching along productive and non-productive steps, for which, on a class of problems with Lipschitz functions, it would be possible to guarantee convergence with the rate of geometric progression to the set of exact solutions or its vicinity. It is important that to implement the proposed method there is no need to know the sharp minimum parameter, which is usually difficult to estimate in practice. To overcome this problem, the authors propose to use a step adjustment procedure similar to that previously proposed by B. T. Polyak. However, in this case, in comparison with the class of problems without constraints, it arises the problem of knowing the exact minimal value of the objective function. The paper describes the conditions for the inexactness of this information, which make it possible to preserve convergence with the rate of geometric progression in the vicinity of the set of minimum points of the problem. Two analogs of the concept of a sharp minimum for problems with inequality constraints are considered. In the first one, the problem of approximation to the exact solution arises only to a pre-selected level of accuracy, for this, it is considered the case when the minimal value of the objective function is unknown; instead, it is given some approximation of this value. We describe conditions on the inexact minimal value of the objective function, under which convergence to the vicinity of the desired set of points with a rate of geometric progression is still preserved. The second considered variant of the sharp minimum does not depend on the desired accuracy of the problem. For this, we propose a slightly different way of checking whether the step is productive, which allows us to guarantee the convergence of the method to the exact solution with the rate of geometric progression in the case of exact information. Convergence estimates are proved under conditions of weak convexity of the constraints and some restrictions on the choice of the initial point, and a corollary is formulated for the convex case when the need for an additional assumption on the choice of the initial point disappears. For both approaches, it has been proven that the distance from the current point to the set of solutions decreases with increasing number of iterations. This, in particular, makes it possible to limit the requirements for the properties of the used functions (Lipschitz-continuous, sharp minimum) only for a bounded set. Some computational experiments are performed, including for the truss topology design problem.

In the paper we construct the model of phase change. Process of hydriding / dehydriding is taken as an example. A single powder particle is considered under the assumption about its symmetry. A ball, a cylinder, and a flat plate are examples of such symmetrical shapes. The model desribes both the "shrinking core"(when the skin of the new phase appears on the surface of the particle) and the "nucleation and growth"(when the skin does not appear till complete vanishing of the old phase) scenarios. The model is the non-classical boundary-value problem with the free boundary and nonlinear Neumann boundary condition. The symmetry assumptions allow to reduce the problem to the single spatial variable. The model was tested on the series of experimental data. We show that the particle shape’s influence on the kinetics is insignificant. We also show that a set of particles of different shapes with size distribution can be approxomated by the single particle of the "average" size and of a simple shape; this justifies using single particle approximation and simple shapes in mathematical models.

The paper develops a new mathematical method of the joint signal and noise calculation at the Rice statistical distribution based on combing the maximum likelihood method and the method of moments. The calculation of the sough-for values of signal and noise is implemented by processing the sampled measurements of the analyzed Rician signal’s amplitude. The explicit equations’ system has been obtained for required signal and noise parameters and the results of its numerical solution are provided confirming the efficiency of the proposed technique. It has been shown that solving the two-parameter task by means of the proposed technique does not lead to the increase of the volume of demanded calculative resources if compared with solving the task in one-parameter approximation. An analytical solution of the task has been obtained for the particular case of small value of the signal-to-noise ratio. The paper presents the investigation of the dependence of the sought for parameters estimation accuracy and dispersion on the quantity of measurements in experimental sample. According to the results of numerical experiments, the dispersion values of the estimated sought-for signal and noise parameters calculated by means of the proposed technique change in inverse proportion to the quantity of measurements in a sample. There has been implemented a comparison of the accuracy of the soughtfor Rician parameters’ estimation by means of the proposed technique and by earlier developed version of the method of moments. The problem having been considered in the paper is meaningful for the purposes of Rician data processing, in particular, at the systems of magnetic-resonance visualization, in devices of ultrasonic visualization, at optical signals’ analysis in range-measuring systems, at radar signals’ analysis, as well as at solving many other scientific and applied tasks that are adequately described by the Rice statistical model.

The functioning of DNA regulatory regions rely primarily on their physicochemical and structural properties but not on nucleotide sequences, i.e. ‘genetic text’. The formers are responsible for coding of DNA-protein interactions that govern various regulatory events. One of the characteristics is SIDD (Stress-Induced Duplex Destabilization) that quantify DNA duplex region propensity to melt under the imposed superhelical stress. The duplex property has been shown to participate in activity of various regulatory regions. Here we employ the SIDD model to calculate melting probability profiles for T7 bacteriophage promoter sequences. The genome is characterized by small size (approximately 40 thousand nucleotides) and temporal organization of expression: at the first stage of infection early T7 DNA region is transcribed by the host cell RNA polymerase, later on in life cycle phage-specific RNA polymerase performs transcription of class II and class III genes regions. Differential recognition of a particular group of promoters by the enzyme cannot be solely explained by their nucleotide sequences, because of, among other reasons, it is fairly similar among most the promoters. At the same time SIDD profiles obtained vary significantly and are clearly separated into groups corresponding to functional promoter classes of T7 DNA. For example, early promoters are affected by the same maximally destabilized DNA duplex region located at the varying region of a particular promoter. class II promoters lack substantially destabilized regions close to transcription start sites. Class III promoters, in contrast, demonstrate characteristic melting probability maxima located in the near-downstream region in all cases. Therefore, the apparent differences among the promoter groups with exceptional textual similarity (class II and class III differ by only few singular substitutions) were established. This confirms the major impact of DNA primary structure on the duplex parameter as well as a need for a broad genetic context consideration. The differences in melting probability profiles obtained using SIDD model alongside with other DNA physicochemical properties appears to be involved in differential promoter recognition by RNA polymerases.

In this paper, we discuss the procedure for finding nominal trajectories of the planar five-link bipedal robot with point contact. To this end we use a virtual constraints method that transforms robot’s dynamics to a lowdimensional zero manifold; we also use a nonlinear optimization algorithms to find virtual constraints parameters that minimize robot’s cost of transportation. We analyzed the effect of the degree of Bezier polynomials that approximate the virtual constraints and continuity of the torques on the cost of transportation. Based on numerical results we found that it is sufficient to consider polynomials with degrees between five and six, as further increase in the degree of polynomial results in increased computation time while it does not guarantee reduction of the cost of transportation. Moreover, it was shown that introduction of torque continuity constraints does not lead to significant increase of the objective function and makes the gait more implementable on a real robot.

We propose a two step procedure for finding minimum of the considered optimization problem with objective function in the form of cost of transportation and with high number of constraints. During the first step we solve a feasibility problem: remove cost function (set it to zero) and search for feasible solution in the parameter space. During the second step we introduce the objective function and use the solution found in the first step as initial guess. For the first step we put forward an algorithm for finding initial guess that considerably reduced optimization time of the first step (down to 3–4 seconds) compared to random initialization. Comparison of the objective function of the solutions found during the first and second steps showed that on average during the second step objective function was reduced twofold, even though overall computation time increased significantly.

Despite numerous achievements of modern science the problem of lightning initiation in an electrodeless thundercloud, the maximum electric field strength inside which is approximately an order of magnitude lower than the dielectric strength of air, remains unsolved. Although there is no doubt that discharge activity begins with the appearance of positive streamers, which can develop under approximately half the threshold electric field as compared to negative ones, it remains unexplored how cold weakly conducting streamer systems unite in a joint hot well-conducting leader channel capable of self-propagation due to effective polarization in a relatively small external field. In this study, we present a self-organizing transport model which is applied to the case of electric discharge tree formation in a thundercloud. So, the model is aimed at numerical simulation of the initial stage of lightning discharge development. Among the innovative features of the model are the absence of grid spacing, high spatiotemporal resolution, and consideration of temporal evolution of electrical parameters of transport channels. The model takes into account the widely known asymmetry between threshold fields needed for positive and negative streamers development. In our model, the resulting well-conducting leader channel forms due to collective effect of combining the currents of tens of thousands of interacting streamer channels each of which initially has negligible conductivity and temperature that does not differ from the ambient one. The model bipolar tree is a directed graph (it has both positive and negative parts). It has morphological and electrodynamic characteristics which are intermediate between laboratory long spark and developed lightning. The model has universal character which allows to use it in other tasks related to the study of transport (in the broad sense of the word) networks.

A simple model based on a kinetic-type equation is proposed to describe the spread of a virus in space through the migration of virus carriers from a certain center. The consideration is carried out on the example of three countries for which such a one-dimensional model is applicable: Russia, Italy and Chile. The geographical location of these countries and their elongation in the direction from the centers of infection (Moscow, Milan and Lombardia in general, as well as Santiago, respectively) makes it possible to use such an approximation. The aim is to determine the dynamic density of the infected in time and space. The model is two-parameter. The first parameter is the value of the average spreading rate associated with the transfer of infected moving by transport vehicles. The second parameter is the frequency of the decrease of the infected as they move through the country, which is associated with the passengers reaching their destination, as well as with quarantine measures. The parameters are determined from the actual known data for the first days of the spatial spread of the epidemic. An analytical solution is being built; simple numerical methods are also used to obtain a series of calculations. The geographical spread of the disease is a factor taken into account in the model, the second important factor is that contact infection in the field is not taken into account. Therefore, the comparison of the calculated values with the actual data in the initial period of infection coincides with the real data, then these data become higher than the model data. Those no less model calculations allow us to make some predictions. In addition to the speed of infection, a similar “speed of recovery” is possible. When such a speed is found for the majority of the country's population, a conclusion is made about the beginning of a global recovery, which coincides with real data.

In this paper, the system of equations of magnetic hydrodynamics (MHD) is considered. The exact solutions found describe fluid flows in a porous medium and are related to the development of a core simulator and are aimed at creating a domestic technology «digital deposit» and the tasks of controlling the parameters of incompressible fluid. The central problem associated with the use of computer technology is large-dimensional grid approximations and high-performance supercomputers with a large number of parallel microprocessors. Kinetic methods for solving differential equations and methods for «gluing» exact solutions on coarse grids are being developed as possible alternatives to large-dimensional grid approximations. A comparative analysis of the efficiency of computing systems allows us to conclude that it is necessary to develop the organization of calculations based on integer arithmetic in combination with universal approximate methods. A class of exact solutions of the Navier – Stokes system is proposed, describing three-dimensional flows for an incompressible fluid, as well as exact solutions of nonstationary three-dimensional magnetic hydrodynamics. These solutions are important for practical problems of controlled dynamics of mineralized fluids, as well as for creating test libraries for verification of approximate methods. A number of phenomena associated with the formation of macroscopic structures due to the high intensity of interaction of elements of spatially homogeneous systems, as well as their occurrence due to linear spatial transfer in spatially inhomogeneous systems, are highlighted. It is fundamental that the emergence of structures is a consequence of the discontinuity of operators in the norms of conservation laws. The most developed and universal is the theory of computational methods for linear problems. Therefore, from this point of view, the procedures of «immersion» of nonlinear problems into general linear classes by changing the initial dimension of the description and expanding the functional spaces are important. Identification of functional solutions with functions makes it possible to calculate integral averages of an unknown, but at the same time its nonlinear superpositions, generally speaking, are not weak limits of nonlinear superpositions of approximations of the method, i.e. there are functional solutions that are not generalized in the sense of S. L. Sobolev.