Certain results associated with hybrid relatives of the q-Sheffer sequences

The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are also explored using numerical simulations. Finally, the orthogonality condition for the hybrid q-Sheffer polynomials is established.

The Underlying Order Induced by Orthogonality and the Quantum Speed Limit

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

On Riemann problem in weighted Smirnov classes with general weight

Weighted Smirnov classes in bounded and unbounded domains are defined in this work. Nonhomogeneous Riemann problems with a measurable coefficient whose argument is a piecewise continuous function are considered in these classes. A Muckenhoupt type condition is imposed on the weight function and the orthogonality condition is found for the solvability of nonhomogeneous problem in weighted Smirnov classes, and the formula for the index of the problem is derived. Some special cases with power type weight function are also considered,and conditions on degeneration order are found.

Chemotaxis Model for Drug Delivery Using Turing’s Instability and Non-Linear Diffusion

This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated. The proposed mathematical model is governed by a reaction–diffusion system modeling the interaction between the cell density and the concentration of the chemoattractant. We investigate the pattern formation for the model using Turing’s principle and linear stability analysis. An asymptotic expansion is used to linearize the nonlinear diffusive terms. Next, we introduce an implicit finite volume scheme; it is presented on a triangular mesh satisfying the orthogonality condition. Finally, numerical results showing the formation of the spatial pattern for the chemotaxis model are presented and analyzed. The results demonstrate promising progress in understanding the process of controlling and designing targeted drug delivery.

Investigation of the solution relative convergence when calculating step irregularities in the transmission line by the partial domain method using the energy orthogonality condition

The absolute convergence of diffraction problems on stepwise irregularities in transmission lines using the energy orthogonality condition is beyond doubt. In this article, we consider the question of relative convergence and investigate the dependence of the accuracy of the obtained solution on the order of the reduced system, i.e., on the number of waves taken into account in the connected transmission lines. We believe that the most accurate results for a finite number of waves taken into account in the connected waveguides are obtained when the complex powers of the waves propagating in both waveguides are equal. In this case, for the phase constants the relation is valid: β εμjm j j Sk ωεμ β2 k k  kn2   , β εμkn k k Sj ωεμ β2 j j  jm2  where βjm – the phase constant of a wave with maximum number m considered in a waveguide j; βkn – the phase constant of a wave with maximum number n considered in a waveguide k; Sj, Sk – the cross-sectional areas of waveguides j and k, respectively. Using the result of Weyl's spectral theorem, we obtain: N N S Sjk   j k34 , where Nj, Nk – number of considered waves in waveguides j and k, respectively. When calculating step irregularities, when the areas of the connected waveguides differ significantly from each other, the number of waves taken into account in the field expansions must be taken sufficiently large to ensure equality of the tangential components of the field at the interface. The use of the relations obtained in the article allows you to choose this number as optimal, and to achieve the specified accuracy of the solution with a smaller number of waves taken into account, which leads to a reduction in time and computational resources.

Contact Dual Pairs

We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of examples. Among other properties, we prove the characteristic leaf correspondence theorem for contact dual pairs that parallels the analogous result of Weinstein for symplectic dual pairs.

Simulation of echo signals of two-position radar station using matrix of five emitters

The problem of modeling the echo signals of radar systems which use two receiving antennas with spaced phase centers and overlapping beam patterns is considered. To solve it, it is proposed to use a matrix of five emitters. Its configuration is based on the results of the previous work of the authors and meets the conditions of compensation and orthogonality of signals. Independent simulation of targets for each antenna is carried out by two pairs of emitters, while the fifth one is introduced for phase compensation of signals. The orthogonality condition is met by configuring the radiation points. Relations are obtained for calculating the coordinates of the radiation points. It is shown that emitters can be located on one straight line. As an example, a matrix was synthesized for a given input data. It was tested by numerical simulation methods. The results of the experiment confirmed the validity of the results found.

Modal Analysis of Internal Wave Propagation and Scattering over Large-Amplitude Topography

Coupled-mode equations describing the propagation and scattering of internal waves over large-amplitude arbitrary topography in a two-dimensional stratified fluid are derived. They consist of a simple set of ordinary differential equations describing the evolution of modal amplitudes, based on an orthogonality condition that allows one to distinguish leftward- and rightward-propagating modes. The coupling terms expressing exchange of energy between modes are given in an analytical form using perturbation theory. This allows the derivation of a weak-topography approximate solution, generalizing previous linear solutions for a barotropic forcing that were described in 2002 by Llewellyn Smith and Young . In addition, the orthogonality condition derived is valid for a different set of eigenmodes defined on a sloping bottom, which shows a better convergence rate when compared with the standard set of modes. The work presented here provides a useful and simple framework for the investigation of internal wave propagation in an inhomogeneous ocean, along with theoretical insight.

Combined User and Antenna Selection in Massive MIMO Using Precoding Technique

Background and Objectives: We propose here joint semi-orthogonal user selection and antenna selection algorithm based on precoding scheme. Methods: The focus of this proposed algorithm is to increase the system sumrate and decrease the complexity. We select and schedule users from a large number of users based on semi-orthogonality condition among them. Here, we select only the maximum channel gain antennas to maximize the system sumrate. Subsequently, the user selection and antenna selection have been scheduled in an adequate manner in order to obtain maximum system sumrate. We calculate the system sumrate for two scenarios: firstly, by considering the interference and secondly without considering the interference. We achieve maximum system sumrate at MMSE and lowest at without precoding while considering the interference. However, when we do not consider the interference we obtain lowest sumrate at MMSE and maximum at without precoding. Results and Conclusion: Here, we apply the precoding scheme to increase the system sumrate and we obtain approximately 20% to 35% higher system sumrate compared to without precoding, when interference is considered. Thus, we achieve higher sumrate in our proposed algorithms compared to other existing work.

Spectral Lower Bounds for the Orthogonal and Projective Ranks of a Graph

The orthogonal rank of a graph $G=(V,E)$ is the smallest dimension $\xi$ such that there exist non-zero column vectors $x_v\in\mathbb{C}^\xi$ for $v\in V$ satisfying the orthogonality condition $x_v^\dagger x_w=0$ for all $vw\in E$. We prove that many spectral lower bounds for the chromatic number, $\chi$, are also lower bounds for $\xi$. This result complements a previous result by the authors, in which they showed that spectral lower bounds for $\chi$ are also lower bounds for the quantum chromatic number $\chi_q$. It is known that the quantum chromatic number and the orthogonal rank are incomparable. We conclude by proving an inertial lower bound for the projective rank $\xi_f$, and conjecture that a stronger inertial lower bound for $\xi$ is also a lower bound for $\xi_f$.