Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function

This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.

The arrowhead-Jacobsthal sequence

In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix. Also, we give connections between Fibonacci, Jacobsthal, Pell and arrowhead-Jacobsthal numbers.

Electron scattering cross-sections for particle transport modeling in a weakly ionized air plasma

Data on processes of electron scattering on ions and neutral atoms are required in fundamental studies and in applied research in such fields as astro- and laser physics, low density plasma simulations, kinetic modeling etc. Experimental and computational data on elastic and inelastic electron scattering in a wide range of electron energies is available mostly for the electron interaction with neutral atoms, but are very limited for the scattering on ions, notably for elastic processes. In present work the calculational approaches for the cross-section computation of electron elastic and inelastic scattering on neutral atoms and ions are considered. The atomic and ion properties obtained in quantum-statistical Hartree-Fock-Slater model are used in the direct computation of electron elastic scattering and ionization cross-sections by a partial waves method, semiclassical and distorted-wave approximations. Calculated cross-sections for elastic scattering on nitrogen and oxygen atoms and ions, and electron ionisation cross-sections are compared with the available experimental data and widely used approximations and propose consistent results. Considering applicability of Hartree-Fock-Slater model in wide scope of temperatures and densities, such approach to the cross-section calculation can be used in a broad range of energies and ion charges.

On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.

Factor generalized BE-semigroups through deductive systems

In this paper, we investigate some properties of homomorphisms and deductive systems of generalized BE-semigroups. In particular, we show that through every deductive system, we may get factor generalized BE-semigroup.

Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration

In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spherical derivatives. Special attention is paid to the boundary properties of annular holomorphic functions. The behavior of annular holomorphic functions on the boundary of the unit circle is considered. It is shown that Gavrilov's P-sequences play an important role in the study of the boundary properties of holomorphic and meromorphic functions.

Modified Fourier transform and its properties

In this manuscript we recommend a new description of the modified Fourier transform for a function which is absolutely integrable, having finite number of maxima and minima and finite number of discontinuities which further takes the form of simple Fourier transform for substituting α = e where α > 0 and α ≠ 1. Moreover we prove various results of the modified Fourier transform and also we show that the set that consists of whole modified Fourier transformable functions under the convolution operation is a commutative semi group as well as form an abelian group under the operation of addition

On the mathematical model of combined rarefaction and compression waves in condensed matter

Two waves model where shock wave is combined with rarefaction wave appearing in laser ablation due to metal-nonmetal transition effect is investigated using conservation laws for mass and momentum fluxes for the steady-state regime of the process. This approach permits to obtain the relation between front velocities of the waves which shows that the rarefaction wave can be rather slow compared with the generated shock wave.

Weakly chain separated sets in a topological space

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness.

Some aspects of Neyman triangles and Delannoy arrays

This note considers some number theoretic properties of the orthonormal Neyman polynomials which are related to Delannoy numbers and certain complex Delannoy numbers.