Complete Functional System Research Articles

Применение модифицированного метода дискретных источников в задаче дифракции импульсной волны на подповерхностном импедансном цилиндре

In contrast to the classical method of auxiliary sources (MAS) with the location of discrete sources (DS) on a closed additional contour, this article investigates the use of a complete system of functions for describing DS fields localized on an open curve in a modified MAS (MMAS). The MMAS was applied to solve a two-dimensional diffraction problem of a broadband electromagnetic impulse on an impedance cylinder located in free space and in the subsurface. The electric thread was a source of external current, excited by an impulse of 1.6 ns duration with a spectrum width from 122 MHz to 726 MHz (at the level of -6 dB). In various combinations, fresh water, thawed and frozen soil, air, and ice were used as the filling medium of the cylinder and the dielectric half-space. The complete system of functions for describing the fields of DS was constructed based on the Hankel functions of the first kind of zero order, the corresponding Green's function for the layered medium problem, and their derivatives in the direction of normal to the curve on which the DS was placed. When compared with the finite difference time domain method (FDTD), it is shown that the MMAS, using Leontovich impedance boundary conditions, can describe impulse fields, scattered by a dielectric cylinder with practically significant accuracy. It has been established that in the case of an elliptical cylinder, the MMAS requires approximately half as many auxiliary DSs compared to the classical MAS while achieving the same accuracy of the solution. In general, this article confirms the possibility of using a complete system of functions to describe the fields of DSs, localized on an open curve for the solving of impulse diffraction problems on subsurface impedance cylinders.

Synthesis of Singular Systems Walsh and Walsh-like Functions of Arbitrary Order

Functionally complete systems of Walsh functions (bases), a particular case of alternating piecewise constant sequential functions, are widely used in various scientific and technological fields. As applied to the tasks of spectral analysis of discrete signals, the most interesting are those Walsh bases that deliver linear coherence of the frequency scales of fast Fourier transform (FFT) processors. By the frequency scales of an FFT processor, we mean the scale on which the normalized frequencies of the input signal are arranged (input scale) and the scale on which the signal's spectral components are arranged (output scale). The frequency scales of the FFT processor are considered linearly coherent if the processor responses with maximum amplitudes and phases of the same sign are located on the bisector of the Cartesian coordinate system formed by the frequency scales of the processor. None of the known Walsh bases ordered by Hadamard, Kaczmage, or Paley provide linear coherence of the frequency scales of the FFT processor. In this study, we develop algorithms to synthesize two systems, called Walsh-Cooley and Walsh-Tukey systems, which turn out to be the only ones in the set of classical Walsh systems and sequents Walsh-like systems, respectively, that deliver linear coherence to the frequency scales of FFT processors.

Analysis of IoT technologies suitable for remote areas in Colombia: Conceptual design of an IoT system for monitoring and managing distributed energy systems

This study presents a conceptual design of an Internet of Things (IoT) communication system for monitoring power generation systems in Colombian Non-Interconnected Zones (NIZs), which lack IoT connectivity due to complex geographical factors. The proposed system aims to ensure the proper operation and energy efficiency of off-grid systems while tracking the variables that influence their performance.The methods used in this study include identifying the needs of such a system, identifying requirements, obtaining technical specifications, and developing a conceptual design. The study also analyses and compares various technologies, including Wi-Fi, Bluetooth, LoRa and ZigBee, to determine which ones are best suited for IoT system design.The conceptual design of the proposed IoT monitoring system considers the geographical, communication and coverage characteristics of the NIZs and the technical characteristics of the energy projects to provide a complete functional system that can connect approximately 2 million people located in these isolated and vulnerable zones. Finally, the defined system can serve as a precedent for building prototypes in various NIZs, and research on IoT technologies suitable for NIZs can help us seek the technologies that are most suitable for these areas. Depending on the application and conditions of the energy project, the most appropriate technology can be determined on a case-by-case basis.

DIGITIZATION FUNCTIONS OF MARKETING RESOURCES AT THE ENTERPRISE IN CONDITIONS OF ECONOMIC UNCERTAINTY

The article examines the complex of digitization functions of marketing resources in conditions of economic uncertainty, their interrelationship, and the proven direct impact of the digitization process on the efficiency of enterprise management. It is concluded that modern business structures use digital technologies as a competitive advantage in all areas of their activity: operational processes, business processes, finance, marketing and interaction with market stakeholders. On the basis of the positive correlations summarized by the authors, it can be assumed that the efforts aimed at the digitization of processes can be considered as a managerial innovation that ensures the growth of innovations and increases the efficiency of the functioning of the business structure. On the basis of a systemic approach, the authors substantiated and built a complex functionality of the process of digitization of the company’s marketing resources. In the architecture of complex functionality, the digitization process is determined by the digitization functions of marketing resources, in particular: analytical (data collection and analysis), communication (Internet advertising), sales (sales via the Internet), and the function of regulation and control (regulates and controls the digitization processes of the marketing department). The synthesis of the theory of random processes together with the systemic approach enabled the authors to define marketing resources for enterprise activities as a complete functional dynamic system with a discrete state, in which for each moment of time the economic security of the enterprise in the future depends on the current state of digitization and does not depend on how this state was reached. The prognostic and transformational probabilistic method for determining the effectiveness of digitization of marketing resources of an enterprise’s activities is proposed, which combines the potential of the enterprise’s marketing resources and the functions performed by marketing and allows for taking into account factors of the internal and external environment, the influence of which causes the emergence of risky situations that lead to unjustified losses of the enterprise. The authors have proven the effectiveness of using digital marketing tools within the scope of each marketing function to prevent the occurrence of risky situations in the company’s activities. Within the framework of the analytical function of marketing, a study of the competitive environment has been carried out, the market share of the enterprise has been recognized, an estimate of costs for marketing research has been prepared. Indicators of the communication functionality of marketing activities in the total amount of marketing expenses complement and justify its decisive influence on the general state of not only marketing, but also the entire economic activity of the enterprise. Indicators of the sales function of marketing determine the elasticity of demand for manufactured products, as well as other sales costs. The marketing functionality of regulation and control allows to analyze the relationship between the costs of ensuring the movement of goods and the received income. The markers defined by the authors of each element of the architecture of the process of digitization of the marketing business structure contribute to increasing the efficiency of evaluating the company’s activity in accordance with the main goal and purpose of the company operating in a structured market space and supporting the marketing concept of development, obtaining profit (income) and satisfying the most demanding needs of consumers.

Treatment of Advanced Male Genital Lymphedema With a Complete Functional Lymphatic System Pedicled Transfer

To evaluate the functional efficacy of the superficial circumflex iliac artery perforator (SCIP) -lymphatic pedicled flap in the treatment of advanced male genital lymphedema. From February 2018 to January 2022, we treated 26 male patients with scrotal and penoscrotal advanced lymphedema using reconstructive lymphatic surgery. Isolated scrotal involvement was seen in 15 patients, and 11 patients had penoscrotal involvement. Excision of genital lymphedematous fibrotic tissue was followed by reconstruction utilizing the SCIP-lymphatic flap. Patient characteristics, intraoperative data, and postoperative results were evaluated. The mean patient age was 39 ± 4.6, and the mean follow-up time was 44.9 months. the SCIP-lymphatic flap was used to reconstruct partial (n=11) or total (n=15) scrotum and used to reconstruct total penile skin in 9 cases and partial in 2 cases. The flap survival rate was 100%. Cellulitis rates were dramatically reduced after reconstruction (P value <.001). The mean genital lymphedema score (GLS) after surgery was 0.05, which was significantly lower than the preoperative 1, 6.2 (P < .001). The median Glasgow Benefit Inventory (GBI) total score was +41, all 26 patients (100%) showed a degree of quality of life improvement. The pedicled SCIP lymphatic transfer approach in advanced male genital lymphedema can provide a durable complete functional lymphatic system that improves the appearance and genital lymphatic drainage. This leads to an improvement in quality of life as well as in sexual functions.

A New Proof of the Expansion of Iterated Ito Stochastic Integrals with Respect to the Components of a Multidimensional Wiener Process Based on Generalized Multiple Fourier Series and Hermite Polynomials

The article is devoted to a new proof of the expansion for iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process. The above expansion is based on Hermite polynomials and generalized multiple Fourier series in arbitrary complete orthonormal systems of functions in a Hilbert space. In 2006, the author obtained a similar expansion, but with a lesser degree of generality, namely, for the case of continuous or piecewise continuous complete orthonornal systems of functions in a Hilbert space. In this article, the author generalizes the expansion of iterated Ito stochastic integrals obtained by him in 2006 to the case of an arbitrary complete orthonormal systems of functions in a Hilbert space using a new approach based on the Ito formula. The obtained expansion of iterated Ito stochastic integrals is useful for constructing of high-order strong numerical methods for systems of Ito stochastic differential equations with multidimensional non-commutative noise.

Excitation of a rectangular resonator through communication windows in the conveyor installation of microwave heating

Abstract Based on the excitation theory of L.A. Vainstein obtained simple and convenient iterative relations for excitation of a resonator in the form of a rectangular parallelepiped with a dielectric layer through several coupling windows in its walls. Theexpansion of the field in terms of the complete system of solenoidal functions of a rectangular resonator is used. Solenoidality is due to the fact that the electric fields of excitation in the openings of rectangular waveguides on the resonator walls, fed through coaxial-waveguide transitions, are tangent to the boundaries of the heated dielectric layer. Simple formulas for expansion coefficients and calculation of fields are obtained. It is convenient to solve the obtained implicit formulas iteratively; in this case, it is possible to take into account both a linear dielectric and a nonlinear dielectric, the permittivity of which depends on the square of the electric field. The algorithm is implemented to simulate a conveyor installation of microwave heating. It is possible to modify the algorithm by introducing potential basic subsystems of functions for the case of modeling complex dielectric inclusions. The results are suitable for modeling other nonlinear inclusions, as well as in problems when using volumetric given sources instead of surface ones. For given electric fields in the coupling windows, the power entering the resonator is calculated on the basis of the Poynting vector.

Mathematical modeling of snacks drying process from minced fish in a fluidized bed

A mathematical model of snacks drying process from minced fish in a fluidized bed with distributed parameters of the heat exchange process between the surface of an anisotropic body and the environment is proposed. The solution of the problem of non-stationary heat transfer by heat conduction using the Galerkin method is considered. The trial and verification functions of the method used, implemented in the PTC MathCAD engineering calculation environment, are linearly independent, represent the first elements of a complete system of polynomial functions and satisfy the boundary and initial conditions. Theoretical and experimental studies have been carried out, which allow considering the process of drying snacks from minced fish in a fluidized bed and scientifically substantiate options for its improvement. According to the results of experimental studies, the adequacy of the obtained mathematical model is shown. It is proved that with a uniform initial temperature distribution during preheating, the temperature inhomogeneity increases up to the moment of a phase transition on the surface of dried object. The importance of taking into account the preheating phase of wet material is established, since at this stage a temperature profile is formed, which is characterized by significant heterogeneity. This is especially important, since temperature heterogeneity directly affects the quality of the food product. The possibility of taking into account anisotropy in heat transfer processes using a three-dimensional mathematical model of transport with distributed parameters is confirmed. The developed technique allows significantly increasing the accuracy of an anisotropic boundary value problem solving by replacing the operation of integrating the stiffness matrix elements with a system of differential equations by algebraic formulas.

The PxIxIT motif of the RCAN3 inhibits angiogenesis and tumor progression in Triple Negative breast cancer in immunocompetent mice.

RCAN proteins are endogenous regulators of the calcineurin-cytosolic nuclear factor of activated T cells (CN-NFATc) pathway that bind CN through similar conserved motifs PxIxIT and LxVP of the NFATc family. RCAN1 and RCAN3 protein levels were reported to correlate with overall survival of breast cancer patients. We additionally provided supporting results about RCAN3 role on cancer showing that overexpression of the native PxIxIT sequence of RCAN3-derived R3 peptide (PSVVVH, EGFP-R3178-210) dramatically inhibits tumor growth and tumor angiogenesis in an orthotopic mouse model of Triple Negative Breast Cancer (TNBC) in nude mice. On the other hand, RCAN3 protein and its derived peptide EGFP-R3178-210 bind to CN and inhibit NFAT-mediated cytokine gene expression without affecting CN phosphatase activity suggesting that RCAN3 and EGFP-R3178-210 peptide have tumor suppressor and immunosuppressant activity. Due to the known relationship between tumor development and immune system, as well as the relevance of CN-NFATc in the regulation of the immune system, in the present study we decided to assess the effect of EGFP-R3178-210 peptide in an orthotopic syngeneic TNBC mouse model, in order to ensure that the role of RCAN3 as immunosuppressant do not override its tumor suppressor activity. Our results evidence that EGFP-R3178-210 peptide displays an inhibitory potential on tumor growth and tumor angiogenesis similar to those obtained in the previous orthotopic TNBC model. These results highlight the importance of the RCAN3 peptide as a tumor suppressor protein and totally complement our previous results, indicating that this antitumor activity role is maintained in the presence of a complete functional immune system.

Trefftz numerical functions for solving inverse heat conduction problems

This paper presents a concept of solving the inverse heat conduction problem with the use of a linear combination of functions satisfying the differential equation in terms of identity, that is Trefftz functions. Characteristic feature of Trefftz functions applied for solving the heat equation is lack of their analytical form. It is known that these functions satisfy the differential equation with known boundary conditions. It was proved that so defined Trefftz functions create a complete system of functions to develop the solution to the heat conduction equation. It means that solving the inverse problem is reduced to determining unknown coefficients of the linear combination of basis functions, obtained from the solution of the direct problem. Two examples of inverse problems were solved: using the conjugate gradient method and using the Tikhonov regularization. As the first example, the inverse heat conduction problem was solved in the rectangle domain with known analytical solution to this problem and with verified stability of this solution. The second example concerns determination of temperature distribution on internal boundaries of the multiply-connected domain for the material, the heat conduction coefficient of which is the function of temperature.

Computational method for solving boundary value problems of mechanics deformable body using non-orthogonal functions

In this paper a complete system of non-orthogonal functions was built on the basis of orthogonal sines and cosines. It is shown that the known orthogonal systems of functions are a degenerate case of non-orthogonal systems of functions. It has been proven that the continuous function can be approximated non-orthogonal functions in such a way that one selected nonorthogonal function will not included in this amount. The boundary value problem of the elasticity theory has been considered for an inhomogeneous plate. A new method for solving the boundary value problem is developed for the fourth-order equation with variable coefficients. The proposed method is based on separating of the stress state of the plate, use of complete systems of nonorthogonal functions and a generalized quadratic form. Criteria have been established under which the constructed approximate solution coincides with the exact solution. This method has been adapted to solving a boundary value problem for high-order differential equations. The high accuracy of the method has been confirmed by numerical calculations.

The Evaluation of Electric Power by Separate Analysis of Fourier Transform Components

This paper presents a substantiation of an approach for the evaluation of components of apparent power and intended to simplify the computational procedures which usually should be implemented in order to process the preliminary sampled waveform of instantaneous power. The results of carried out studies have shown that both active and reactive power can be calculated by the analysis of calculated components of sine and cosine Fourier transforms. This paper also presents the discussion of restrictions, which should be imposed on the duration of the analyzed signal and on frequencies of the auxiliary trigonometric functions, which are applied in order to calculate components of Fourier transform which are used for the evaluation of active and reactive power. The compliance with these restrictions allows us to eliminate the undesirable bias of active and reactive power estimation caused by the refusal from the decomposition of the analyzed waveform of the instantaneous power by applying the complete system of orthogonal trigonometric functions, as the evaluation of components of the apparent power is attained based on separate analysis of sine and cosine Fourier transforms calculated for the analyzed signal. The results of carried out simulations illustrate the frequency dependencies of sine Fourier transform calculated for the case of compliance with the restrictions, which allow to attain the highest accuracy of estimation and for the case when the duration of analyzed signal does not fit these restrictions.

Norm of iegnfunction of one-dimension photonic crystal

Relevance. In recent decades (about the 90-s ХХ century) there has been rapid development of photonic. Thus, to arise scientific interest to optic range of electromagnetic radiation. Currently, the diffraction problem about scattering electromagnetic waves on such object as photonic crystal is impotent problem. As well known, this problem can be reduced to a solution of wave equation. The need to calculate the norm iegnfunction spectral iegnfunction Sturm-Liouville problem, however, to arise in the transition from one complete orthogonal system to another complete orthogonal system of functions by separating variables method, correspondingly, for a wave equation solving. The purpose of the work. We indicate a direct approach to calculating of the norm of iegnfunction of spectral Sturm-Liouville problem for the tow-layer infinite one-dimension photonic crystal (a direct approach to calculating of the norm that is presuppose a direct integration); and propose a methodologically different approach, which is based on the marginal transition in the scalar product, which accordingly sets this norm. Materials and methods. Taking the limit in calculation the norm of the iegnfunction of spectral Sturm-Liouville problem for the tow-layer infinite one-dimension photonic crystal encounters difficulties, associated with the emergence of species uncertainty . Such infinitive investigates by the Lopital's rule. In turn, Lopital's rule entails the need to find a derivative of solution of spectral equation by a spectral param. In this way we have to face the solution a linear inhomogeneous differential equation 2-nd order. Results. We propose a methodic of calculating of norm of iegnfunction of spectral Sturm-Liouville problem for the tow-layer infinite one-dimension photonic crystal. Conclusion. Unlike the direct approach, proposed methodic to make it possible to understand the character of dependencies the required norm of iegnfunction itself (ending expression containing the iegnfunction itself). Further work in this direction of development of this approach may be aimed at simplifying the final expression for the norm.

Комп’ютерний метод розв’язання крайових задач теорії пружності з використанням неортогональних систем функцій

A complete system of functions based on non-orthogonal sinuses and cosine was constructed. It has been proven that the continuous function can be approximated by a finite number of non-orthogonal functions in such a way that this amount does not enter the selected function of the non-orthogonal base. The numerical experiment confirmed the high accuracy of approximations of continuous functions by a small number of non-orthogonal functions. The flat problem of the theory of elasticity for the plate with variable elastic characteristics is considered. This equation is simplified when the characteristics of the material change insignificantly depending on the spatial coordinates. A new method of solving a boundary value problem has been developed for the fourth-order equation with variable coefficients. The proposed method is based on the separation of the stress state of the plate from an inhomogeneous material to the main and indignant state, the use of complete systems of non-orthogonal functions and a generalized quadratic form. A criterion under which the constructed approximate decision coincides with the exact solution was found.

A canonical basis of a pair of compatible Poisson brackets on a matrix algebra

Given an arbitrary complex matrix and a generic matrix we find a canonical basis for the Kronecker part of the bi-Lagrangian subspace with respect to the corresponding Poisson brackets on the Lie algebra , and also find a system of functions in bi-involution corresponding to this basis. In particular, for nilpotent matrices we prove that all nonzero functions obtained by applying the Mishchenko-Fomenko argument shift method to the coefficients of the characteristic polynomial form the Kronecker part of the complete system of functions in bi-involution. Bibliography: 9 titles.

From flames to ashes. A functional fire management system in the neolithic hut of Lugo di Romagna (Fiorano Culture)

The excavations carried out on the Neolithic site of Lugo di Romagna (Ravenna, Culture of Fiorano) have allowed to document, in addition to a complex village fence system, a whole hut destroyed by fire and in primary collapse. The structure consisted of two distinct rooms, equipped with combustion structures, accessory elements, an entire pottery set and stored foodstuffs. The house was equipped with a central hearth, an oven leaning against a perimeter wall and a series of pits excavated in the floor and filled with ashes, that were interpreted as accessory structures for the preservation of the embers. Regardless of the specific characteristics of the different combustion structures, the case of Lugo di Romagna offers the rare opportunity to study its complementarity, outlining a complete functional system for the management of fire as a source of heat, lighting and as a means of food cooking.

NANODEVICES WITH PROGRAMMABLE LOGIC

The paper describes the computer-aided design of nanoelectronic circuits with programmable logic on quantum majority components is implemented. The single-electronic component base has the greatest influence on such basic parameters of modern computer systems as performance exceeding 10 THz, power consumption less than 1 nW and submicron dimensions. Methods of constructing arithmeticological computing devices of combinational and sequential types, which realize almost complete system of logical functions both in majority and in Boolean bases, are offered. The design of reliable nanoelectronic circuits with programmable logic based on the technology of quantum automata has been described. While constructing majority circuits the interaction of Colomb forces using. The order of syntesis and programming of various types of arithmetic-logic nanodevices has been analyzed.

Identifying heat source intensity in treatment of cancerous tumor using therapy based on local hyperthermia - The Trefftz method approachs.

The presented study considers the equation of hyperbolic conduction of heat with perfusion in order to identify such intensity of spatial heat source that will lead to hyperthermia of a cancerous tumor placed in healthy tissue. The tumor is assumed to be in the form of a sphere with a small radius. In order that the determined intensity of the heat source does not damage healthy tissue, different temperature distributions as a function of time are anticipated at the tumor's border. The mathematical tools used are based on the Trefftz method. The results are presented in the form of numbers and graphs illustrating the intensity of the identified heat source and matching the obtained temperature distributions in the tumor to the predicted ones.

СТОХАСТИЧЕСКАЯ МОДЕЛЬ ПРОЦЕССА РАЗДЕЛЕНИЯ СЛОЖНЫХ ГЕТЕРОГЕННЫХ ДИСПЕРСНЫХ СИСТЕМ В ЦЕНТРИФУГАХ С РАДИАЛЬНО-ОСЕВЫМ ПОТОКОМ

The article describes separation processes in apparatus with complex hydrodynamic conditions. The new approach to the theoretical study consists in taking into account the action of the centrifugal field and the field of random forces, as it was implemented earlier for the simplest structures, but also in a detailed examination of the radial and axial flows. The movement of particles is investigated in the cramped conditions of precipitation during their interaction with each other. The processes of separation in centrifugal devices of various types have been identified, subject to stochasticity, constrained movement of a set of real particles and the possibility of their dispersion and coagulation. The combined deterministic and stochastic effects on the dispersed phase in a centrifugal field are described by means of a differential equation, the solution of which makes it possible to calculate the fractional and total centrifugation efficiency with high accuracy. A semi-analytical method has been developed and implemented for one-and two-dimensional stochastic models for the approximate solution of non-stationary centrifugal boundary value problems. Compared to difference schemes Faedo-Galerkin method gives the solution of equation systems with a smaller number of unknowns defined in all values of the arguments. The use of the method is possible only in the case of homogeneous boundary conditions and is limited by the possibility of selecting a complete system of functions that would satisfy them. The proposed approach to identification of refining fuels and lubricants is preferable since it fully reflects the essence of the processes occurring in centrifuges with a radial-axial flow. Generalization of stochastic effects on centrifugation, taking into account the hydrodynamic features of the flow of shared media in a centrifugal field, allows calculating all indicators of cleaning fuels and oils from mechanical impurities without model experiments, predicting the total and fractional efficiency of fuel oil filters and oil filters of the internal combustion engines. The developed identification method of separating complex dispersed systems is aimed at the synthesis of systems and devices for oil purification and fuel oil preparation of increased efficiency with predetermined parameters of purification quality in operating conditions.

Integral relations associated with the semi-infinite Hilbert transform and applications to singular integral equations

Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of the Hermite polynomials, including their Hilbert and Fourier transforms and connections to the Laguerre polynomials. The relations discovered give rise to complete systems of new orthogonal functions. Free of singular integrals, exact and approximate solutions to the characteristic and complete singular integral equations in a semi-infinite interval are proposed. Another set of the Hilbert transforms in a semi-axis are deduced from integral relations with the Cauchy kernel in a finite segment for the Jacobi polynomials and the Jacobi functions of the second kind by letting some parameters involved go to infinity. These formulas lead to integral relations for the Bessel functions. Their application to a model problem of contact mechanics is given. A new quadrature formula for the Cauchy integral in a semi-axis based on an integral relation for the Laguerre polynomials and the confluent hypergeometric function is derived and tested numerically. Bounds for the remainder are found.