Irina Andreeva ^{1}
^{1}Peter the Great St.Petersburg Polytechnic University , Higher Mathematics , Russia
The paper reflects both the original investigating methods and strictly proved mathematical conclusions of some fundamental original study of a special and the same time extended set of polynomial dynamic systems. The present work has been conducted based on classical methods of the qualitative theory of dynamic systems and ODE's, which were sufficiently supplemented with especially developed for the tasks of this work fresh research methods and approach. These methods of a precise mathematical research, together with some new attitudes, have to appear useful for future studies of applied dynamic systems with the different orders of polynomial right parts. Considering the fact, that dynamic systems are constantly used among the main instruments of mathematical modeling in all branches of contemporary science and technology, such as the development of systems of artificial intelligence and neural networks, control systems, as well as in theoretical and practical studies of computing and producing systems, in the mathematical modeling of physical, social, ecological and biological processes etc., this research work has high actuality. The main point of this research work is to outline and strictly describe a pattern of phase trajectories belonging to a set of studied polynomial dynamic systems, as well as to to the enlisted and fully investigated different subsets of a main set of them, in terms of the Poincare sphere and Poincare disk, the same time introducing a series of new notions and invented research attitudes.
Francisco Delgado^{1}
^{1}INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico
Quantum resources are being used to reach improved applications in computing, processing, security, and communications. The switching between classical approaches settled by the traditional electronics and computing in favor of quantum ones is an ongoing task. In this work, the generation via postselection of an entangled resource among three parties is proposed to set a kind of authentication through its characterization coming from a shared agreed processing. Such resource could be used by its entanglement degree as fingerprint in authentication. The robustness and the details of the generation are discussed.
Authors would like to acknowledge to Writinglab, Institute of Future Education, both initiatives ofTecnologico de Monterrey, Mexico, in the development and production of this work.
Jorge Olivares^{1} , Elvis Valero^{2}
^{1}Universidad de Antofagasta, matemáticas, Chile
^{2}Universidad Mayor de San Andrés, matemáticas, Bolivia
In the next paper. We will show the various Geogebra Applets of differential equations of the separable variables type, which served to know the academic performance of the engineering students of the differential equations course of the University of AntofagastaChile, during the year 2021. This work is a continuation and expansion of "Animations and interactive creations in firstorder linear differential equations: the case of Geogebra".
Jorge Olivares^{1} , Elvis Valero^{2}
^{1}Universidad de Antofagasta, matemáticas, Chile
^{2}Universidad Mayor de San Andrés, matemáticas, Bolivia
Next, the Applets used from the Geogebra CAS calculator will be presented, and the effect that occurred in the academic performance in the engineering students of the year 2021, in the learning of nonhomogeneous linear differential equations of the second order. This research comes from a quantitative study and the Geogebra software was used, for its interactivity and dynamism. This work is a continuation and extension of "Solving inhomogeneous linear differential equations by the method of indeterminate coefficients and variation of parameters by GeoGebra". Parameters using GeoGebra".
Fotios Kasolis^{1}
^{1}University of Wuppertal, Chair of Electromagnetic Theory, Germany
A systematic examination of data analysis methods reveals that many of these methods are built on a common algebraic structure. More precisely, the resulting algebraic structure contains a set, a binary relation, and a counting system, where the term counting system refers to a mapping from the set of $N\times N$ Boolean matrices to the set of $N$length vectors, provided that the data sample is of size $N$. Such information tuples are used for obtaining probability mass functions from which various statistics are then computed. Here, after presenting the described framework, some standard data analysis, pattern recognition, and topological inference methods are put in context, while brief computational experiments are employed for illustrating the capacity of the framework and for providing further insights.
This work was supported in parts by the Deutsche Forschungsgemeinschaft (DFG) under grant no. CL143/181
Jaykov2 Foukzon^{1}
^{1}Israel Institute of Technology, math, Israel
A new nonArchimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwisedefined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard operatorvalued tempered distribution, but a nonclassical operatorvalued function [1][2]. Then formal expressions containing, e.g., ϕⁿ(x),<ϕⁿ(x)>,etc. can be understood literally, and shown to be well defined as ℝ_{c}^{#}valued functions. In the free field cases, we show that the Wightman functions are explicitly calculated with the pointwise field, without any regularization, e.g., Wick product. We show that some of physicists' naive expressions of Lagrangian λϕⁿ(x) can be rigorously justified. REFERENCES [1] Jaykov Foukzon, Basic Real Analysis on External NonArchimedean Field ℝ_{c}^{#}. Basic Complecs Analysis on External Field ℂ_{c}^{}=ℝ_{c}^{#}+iℝ_{c}^{#}. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3989960 [2] Jaykov Foukzon,The Solution of the Invariant Subspace Problem. Part I. Complex Hilbert space. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4039068
Nikolaos Theodorakatos^{1} , Rohit Babu^{2} , Miltiadis Lytras^{3} , Angelos Moschoudis^{4}
^{1} National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
^{2}Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
^{3}The American College of Greece, School of Business and Economics, Deree, Greece
^{4}National Technical University of Athens , School of Electrical and Computer Engineering, Greece
This paper studies mathematical algorithms for delivery maximum power network observability using synchronized measurements. This problem is an intrinsic extension of the minimization of phasor measurement units (PMUs) by considering the least cost number of these devices around the power network and maximizing the reliability for better performance of power electrical networks. Optimization properties are investigated and used to lie a ΒranchandΒound algorithm (BBA) jointly with Successive Quadratic Programming and Interior Methods to find optimality. Τo evaluate optimal solutions with maximum measurement redundancy, solution algorithms such as BBA, SQP, IPM are used. The nonlinear algorithms mainly rely on local search procedure as the convergence indicator to optimality, whereas BBA is implemented to build a binarytree to find an optimal solution. Thus, it is reasonable and necessary to compare nonlinear algorithms with BBA to show their difference and their efficiency convergence properties towards global optimality whereas the maximum observability is preserved. Moreover the polyhedron being constructed for the implementation of the BBA scheme is transformed into a polytope solved by a SemiDefineProgramming approach to find appropriate optimal solutions for further optimization study. Numerical studies show significant improvement about the maximum observability over existing optimization schemes already published in the recent bibliography.
Nikolaos Theodorakatos^{1} , Rohit Babu^{2} , Miltiadis Lytras^{3} , Angelos Moschoudis^{4}
^{1} National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
^{2}Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
^{3}The American College of Greece, School of Business and Economics, Deree, Greece
^{4}National Technical University of Athens , School of Electrical and Computer Engineering, Greece
The Phasor Measurement Unit (PMU) is a monitoring device capable with highprecision time synchronization that measures magnitudes and phase angle of voltage and current from a specific power network bus. Aiming at achieving the optimal PMU positioning problem (OPP) solving, this study proposes a multiobjective optimization function minimized under a set of 01 Boolean observability inequality constraints whereas a binary restriction is satisfied. Genetic algorithms (GAs) in conjunction with a Binary Particle Swarm Optimization (BPSO) are used to solve the multiobjective constraint linear integer program (mCILP) towards optimality. This GAPSO probabilistic approach aims simultaneously at minimizing the number of PMUs needed and maximizing the measurement redundancy (MR) index. The success of this heuristic approach is proved by comparing its results with those achieved by a BranchandBound (B&B) algorithm which solves the 01 mCILP towards optimality. The minimization models are tested on standard IEEE power networks to show their applicability regarding this multiobjective optimization making problem. The numerical results derived by the GAPSO models in MATLAB language show that the optimal solutions with regard to the maximum MR are achieved with efficiency and at the same time minimizing the whole cost in the optimization process.
Nikolaos Theodorakatos^{1} , Rohit Babu^{2} , Miltiadis Lytras^{3} , Angelos Moschoudis^{4}
^{1} National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
^{2}Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
^{3}The American College of Greece, School of Business and Economics, Deree, Greece
^{4}National Technical University of Athens , School of Electrical and Computer Engineering, Greece
Fault observability is an essential application among intelligent monitoring and outage management system tasks used to understand the selfhealing networks, one of the most important characteristics of power systems. Further, the determination of the location of a faulty transmission line in a power grid is a vital topic to facilitate the selfhealing network and to maintain the continuity of power supply. Selfhealing is an operational aspect of electrical power networks for realtime identification and localization of faulty transmission lines for the whole power network. This paper proposes algorithmic models that determine the optimal number of PMUs and their placement sites to achieve a fault observable system whereas the stateestimation issue is examined. The optimization models discussed herein find a configuration of PMU locations with a least number of devices that locates any fault occurring in a transmission power network. An optimization process is presented within a nonlinear programming model coupling a synchronized phasor as well as conventional measurements. As a comparative reference, a zeroone integer linear program is used that satisfies global optimality. Metaheuristic algorithms such as a binaryparticle swarm optimization and genetic algorithm have been employed to determine a fault observable power system. The algorithm models are illustrated with an IEEE14 bus system. Simulation results are tested on different size power systems to verify the efficacy of the proposed algorithmic approach. The presented results are promising given that they are in complete agreement with those found by the zeroone integer linear programming model.
Yuriy Gubarev^{1} , Yang Liu^{2}
^{1}Lavrentyev Institute for Hydrodynamics, Laboratory for Fluid and Gas Vortex Motions, Russian Federation
^{2}Novosibirsk State University, Department for Differential Equations, Russian Federation
The VlasovPoisson model of boundless collisionless electron gas in selfconsistent electric field continues to be one of the basic models for a number of modern physics areas, such as particle physics, electrodynamics, plasma physics, etc. This is due to simplicity, clarity, and obvious effectiveness of the model in describing complicated processes of the micro world. For example, the VlasovPoisson model is successfully used for development and operation of accelerators with colliding beams, which make it possible to accelerate elementary particles additionally by means of hot electron gas. Despite the fact that this model has been intensively studied for a long time, from the point of view of the mathematical stability theory, it was possible to establish only sufficient conditions for the theoretical stability (at semiinfinite time intervals) of a number of dynamic equilibrium states with respect to both small and finite perturbations, but from some incomplete unclosed subclasses. In this report, we consider spatial motions of boundless collisionless electron VlasovPoisson gas in threedimensional Cartesian coordinate system: $$ \frac{\partial f}{\partial t} + v_i\frac{\partial f}{\partial x_i} + \frac{\partial \varphi }{\partial x_i}\frac{\partial f}{\partial v_i} = 0, $$ $$ \frac{\partial ^2\varphi }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f({\bf x}, {\bf v}, t)d{\bf v}; (1) $$ $$ i = 1, 2, 3; f = f({\bf x}, {\bf v}, t) \geq 0; f({\bf x}, {\bf v}, 0) = f_0({\bf x}, {\bf v}). $$ Here $f$ denotes the distribution function of electrons (for reasons of convenience, their charges and masses are assumed to be equal to unity); $t$ is time; ${\bf x} = (x_1, x_2, x_3)$ and ${\bf v} = (v_1, v_2, v_3)$ denote coordinates and velocities of electrons; $\varphi ({\bf x}, t)$ is the potential of selfconsistent electric field; $f_0({\bf x}, {\bf v})$ denotes the initial data for function $f$. We suppose that the distribution function $f$ asymptotically approaches zero as ${\bf v} \rightarrow \infty $, and this function along with the potential $\varphi $ are periodic in argument ${\bf x}$ or asymptotically approach zero as ${\bf x} \rightarrow \infty $ too. It is assumed that the mixed problem (1) has the following exact stationary solutions: $$ f = f^0({\bf x}, {\bf v}) \geq 0, \varphi = \varphi ^0({\bf x}); $$ $$ v_i\frac{\partial f^0}{\partial x_i} =  \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^0}{\partial v_i}, (2) $$ $$ \frac{\partial ^2\varphi ^0}{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^0({\bf x}, {\bf v})d{\bf v}. $$ The aim of this report is to prove the absolute linear instability for the spatial states of dynamic equilibrium (2) of boundless collisionless electron VlasovPoisson gas with respect to small threedimensional perturbations $f^\prime ({\bf x}, {\bf v}, t)$ and $\varphi ^\prime ({\bf x}, t)$: $$ \frac{\partial f^\prime }{\partial t} + v_i\frac{\partial f^\prime }{\partial x_i} + \frac{\partial \varphi ^\prime }{\partial x_i}\frac{\partial f^0}{\partial v_i} + \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^\prime }{\partial v_i} = 0, $$ $$ \frac{\partial ^2\varphi ^\prime }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^\prime ({\bf x}, {\bf v}, t)d{\bf v}; (3) $$ $$ f^\prime ({\bf x}, {\bf v}, 0) = f_0^\prime ({\bf x}, {\bf v}), $$ where $f_0^\prime ({\bf x}, {\bf v})$ denotes the initial data for function $f^\prime $. In the report, a transition from kinetic equations (1) which describe the spatial motions of electron gas under study to an infinite system of relations similar to the equations of isentropic flow of a compressible fluid medium in the “vortex shallow water” and the Boussinesq's approximations was carried out. In the course of instability proof, the wellknown sufficient NewcombGardnerRosenbluth condition for stability of dynamic equilibrium states (2) with respect to one incomplete unclosed subclass of small spatial perturbations was conversed. Also, some linear ordinary differential secondorder inequality with constant coefficients was obtained for the Lyapunov functional. An a priori exponential lower estimate for growth of small threedimensional perturbations (3) follows from this inequality when the sufficient conditions for linear practical instability of the considered dynamic equilibrium states found in this report are satisfied. Since the obtained estimate was deduced without any additional restrictions on the dynamic equilibrium states under study, then the absolute linear instability of the spatial states (2) of dynamic equilibrium of boundless collisionless electron VlasovPoisson gas with respect to small threedimensional perturbations (3) was thereby proved. The report results are fully consistent with the classical Earnshaw instability theorem from electrostatics. At present, the area of applicability for the Earnshaw theorem is expanded from electrostatics to kinetics, namely, to the boundless collisionless electron VlasovPoisson gas. Finally, constructiveness is inherent in the sufficient conditions for linear practical instability established here, which allows them to be used as a testing and control mechanism for conducting physical experiments and performing numerical calculations. In particular, these conditions can be applied to solve the problem of additional acceleration for elementary particles by electron plasma clumps. Specifically, they must be performed during the formation of a bunch of electrons. Due to this, it will take less time to create an electronic clot. On the contrary, after the electron cluster has formed, the conditions should not be fulfilled. Then the electronic clot will last longer. Thus, there is a real opportunity to control the acceleration of elementary particles with the help of electron plasma clumps.
This work was supported partially by China Scholarship Council.
Michel Plaisent^{1}
^{1}universite du quebec a montreal , management, Canada
Technology has radically changed the global landscape as it affects the way people communicate, learn, and think. In the onset of the fourth industrial revolution, many are inspired to find the formula in becoming a global player in this revolution. Hence, this study was intended to explore the explanatory and prediction factors for global players in the fourth industrial revolution. The main data set used was the PISA 2018 results of the seventyseven (77) participating countries along with the Reading, Mathematics, and Science areas. Data mining binary logistic regression were utilized. Results revealed that the global players of the fourth industrial revolution are generally performing above the average in Reading, Mathematics, and Science as opposed to the nonglobal players, the odds of a country to become a global player in the industrial revolution are higher to those who are performing well in the three PISA areas, and the country can be predicted to become a global player if they are highly inclined in Science but less in Reading. The study concluded that the global players in the current industrial revolution considered reading, mathematical, and scientific literacies dire important. But they treated reading as essential and fundamental literacy for them to develop other literacies most especially the scientific literacy. Scientific literate citizens drive the whole country to scientific discoveries and technological glories, which make them stand apart from the rest of the world.
Vaclav Skala^{1}
^{1}University of West Bohemia, DEpt. of Computer Science and Engineering, Czech Republic
A solution of linear systems of equations $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$ is the key part of many computational packages. This paper present a novel formulation based on the projective extension of the Euclidean space using the outer product (extended crossproduct). This enables to solve the both cases, i.e. $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$. The proposed approach actually leads actually to an "analytical" solution of linear systems in the form $\bm{\xi}=\bm{\alpha}_1 \wedge \bm{\alpha}_2 \wedge \ldots \wedge \bm{\alpha}_n,$ on which the other vector operation can be applied before using the numerical evaluation. This contribution also proposes a new approach to the conditionality estimation of matrices applicable also to nonsquared matrices. It splits the conditionality to "structural" conditionality showing matrix property if nearly unlimited precision is used, "numerical" issue which depends on numerical representation with respect to the righthand side influence, if given.
Robert Reynolds^{1}
^{1}York University, Mathematics and Statistics, Canada
In this paper we derive a new multidimensional definite integral whose kernel involves the Hermite polynomial $H_n(x)$. This definite will be used to derive a theorem in terms of a closed form solution represented by the HurwitzLerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.
We wish to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).
Yongzhong Ma^{1}
^{1}Engineering University of PAP, School of Equipment Management & Support, China
In this paper, the fluorescence characteristics of rodamine B essence under different concentration, different solvent, different PH and different excitation time were studied, and the influence of these factors on the fluorescence spectrum of rodamine B essence was analyzed. The results showed that when the concentration of basic rose essence was less than 1×104g/L, the fluorescence intensity was positively correlated with the concentration. When the concentration of basic rose essence was greater than 4×103g/L, the fluorescence intensity increased first and then decreased with the increase of basic rose essence. When the dielectric constant of the solvent increases, the fluorescence intensity of the solution increases. When PH is 1 ~ 2, the fluorescence intensity increases gradually. At 3, the fluorescence intensity remained unchanged.
Yongzhong Ma^{1}
^{1}Engineering University of PAP, School of Equipment Management & Support, China
In order to analyze the safety of detonation bomb, an explosion simulation model of the bomb was established based on LSDYNA simulation platform, the fragmentation distribution and velocity variation were analyzed, and the killing radius of the bomb was evaluated. The results show that the fragmentation size of the projectile is unevenly distributed, and the largemass lowspeed fragment generated in the middle of the explosive is the main source of killing, with a killing radius of about 2.33m. This study provides a scientific basis for the development and application of small highlight detonation bomb, and also provides a useful reference for the research and design of similar ammunition.
Chao Li^{1}
^{1}Jiangsu Automation Research Institute, Department of Computer, China
A nonlinear dynamic model of a 14DOF (degree of freedom) twostage spur gear with timevarying stiffness and flexible gears is developed for the practical problem of nonlinear disturbances in a twostage spur gear system of a model space drive mechanism, the validity of which is demonstrated by motion simulation experiments. The dynamic characteristics of this gear system are analysed. Tooth shape modifications of the twostage gear pair are compared. The variation of dynamic load coefficients and load transfer errors for different modification parameters is analysed. In this paper, tooth profile errors are enhanced in the dynamic model. The effect of tooth profile error and variable load torque on transmission error is analysed. With a linear modification, a modified length of 0.6mm and a tooth profile modification of 0.004mm is the best modification solution, with a 36% reduction in the peak and valley values of the load transfer error. The study of the nonlinear dynamics model of a twostage spur gear and the transmission error of high load loads is enriched, providing an important reference for the practical design of gear systems.
Olga Sidorova^{1}
^{1}Joint Institute for Nuclear Research, Laboratory of Neutron Physics, Russia
PFN emission of 235U(n,f) reaction are under investigation in JINR for last 20 year. The recent achievements in experimental apparatus simulation are the subject of this presentation. The object of simulation is prompt fission neutron (PFN) detector used for resonance neutron induced fission of U235. The neutron source was IREN facility and double ionization chamber (DIC) with Frisch grids was used for fission fragment spectroscopy. The PFN detector was multi detector system consisted of 32 BC501 scintillation liquid filled modules from the Sionix (Netherlands) company. Detectors were located on the sphere surface with 50 cm radius. Double Frisch gridded ionization chamber, used as fission spectrometer at the same time generated trigger signal for PFN registration apparatus. For each fission event the following simulated information was recorded: correlated fission fragments time mark, emission angle in respect to the selected coordinate frames along with the pulse heights and shapes of neutron detector signals. Multiple neutron scattering and the crosstalks were taken into account in order to evaluate contribution of those effects in the final results.
Shakir Zeynalov^{1}
^{1}JINR, FLNP, Russia
Autors: Shakir Zeynalov1 and Olga Sidorova1,2 1JINR, Frank Laboratory of Neutron Physics, Dubna, Moscow region,141980 2Dubna State University, Dubna, Moscow region Investigations of prompt fission neutron emission are important in understanding the fission process in the sharing of excitation energy among the fission fragments. Experimental activities at JINR on prompt fission neutron (PFN) emission are underway for more than 20 years. Main focus lied on investigations of prompt neutron emission from the reactions 252Cf (sf) and 235U(n,f) [210] in the region of the resolved resonances. Resonance neutron energy region is interesting in the testing of nuclear scission model []. For the 235U(n,f) reaction strong fluctuations of fission fragment mass and the mean total kinetic energy distributions have been observed as a function of incident neutron energy [16, 37]. In addition fluctuations of prompt neutron multiplicities were also observed in [44]. The goal of the present study is to verify the current knowledge of prompt neutron multiplicity fluctuations and study the correlations with fission fragment properties. Recent measurement of PFN multiplicity in resonance neutron induced fission of 235U(n,f) reaction [27] reveal surprising result, stimulated us to investigate the PFN multiplicity at IREN with new high efficiency experimental setup.
Ivan Sudakow^{1} , Dubrava Kirievskaya^{2} , Ekaterina Cherniavskaia^{3}
^{1}University of Dayton, Physics, United States
^{2}University of Dayton, Geology, United States
^{3}AARI, Oceanography, Russian Federation
We consider a simple model of a resource competition ecosystem. We investigate as that ecosystem biodiversity evolves under temperature changes, which could include slow climate trends, extreme phenomena, and a combination of those both effects. The model also includes the formation of new species. We show that slow trends can lead to total species extinctions, but if new species appear at a sufficiently large rate then biodiversity conserves, or, at least extinction rate diminishes. Extreme phenomena essentially increase the extinction rate. In the most sophisticated model, where temperature oscillations are determined by a random dynamical system with a strange attractor, we can observe a catastrophic bifurcation when the growth of temperature oscillations leads to a sharp increase in the extinction rate.
Samson Ayanlade^{1} , Abdulrasaq Jimoh^{2} , Emmanuel Ogunwole^{3} , Abdulsamad Jimoh^{4} , Sunday Ezekiel^{5}
^{1}Lead City University, Electrical and Electronic Engineering, Nigeria
^{2}Obafemi Awolowo University, Electronic and Electrical Engineering, Nigeria
^{3}Cape Peninsula University of Technology , Electrical, Electronic and Computer Engineering, South Africa
^{4}University of Ilorin, Electrical and Electronic Engineering, Nigeria
^{5}Olabisi Onabanjo University, Electrical and Electronic Engineering, Nigeria
The status of a power network, as well as the techniques for estimating it, are important in assessing the power network’s operation and control, as well as determining its future expansion. Power flow analysis, which estimates the magnitudes of the bus voltages as well as the power flowing through the system’s lines, may be utilized to identify the state of any distribution network. Power flow analysis of distribution networks necessitates proper mathematical modeling of network components, particularly distribution lines. Typically, singlephase mathematical modeling is used. However, because this mathematical modeling does not reflect the underlying features of the distribution networks, the power flow calculations are insufficiently accurate. In this study, threephase mathematical modeling was used to analyze the power flow of a practical Nigerian distribution network, and the results were compared to those of a singlephase equivalent. Modified Carson’s equations were used to accurately model the lines of the three phases while accounting for mutual inductances between the phases to compute the line impedances. Thereafter, the threephase bus admittance matrix of the network under study was developed. The threephase power flow equations of the distribution network were formulated in the phase frame. The NewtonRaphson power flow technique was adopted to solve the network threephase power flow problems formulated. A MATLAB program was developed to implement the method. The results revealed that the voltage magnitudes, as well as the active and reactive power losses, were not equal in all the three phases. This contradicts the results of the power flow simulation using singlephase mathematical modeling. Therefore, threephase power flow analysis better matched the actual distribution network operating circumstances than singlephase power flow analysis.
Yuriy Gubarev^{1} , Jingyue Luo^{2}
^{1}Lavrentyev Institute for Hydrodynamics, Laboratory for Fluid and Gas Vortex Motions, Russian Federation
^{2}Novosibirsk State University, Department for Differential Equations, Russian Federation
In the electrostatic approximation, when the electric field of electrons and ions is selfconsistent, the plasma dynamics is described by the kinetic VlasovPoisson equations. In this case, such equations are used to study the collisionless motion of electrons, which interact with each other through the Coulomb repulsive forces, against the background of a homogeneous distribution of ions in the whole physical continuum. In threedimensional statement, the mathematical model for the twocomponent VlasovPoisson plasma is written in the form: $$ \begin{array}{c} f_{t}+\vec{v} \nabla_{\vec{x}} f\nabla_{\vec{x}} \varphi \nabla_{\vec{v}} f=0 \end{array} $$ $$ \Delta_{\vec{x}} \varphi=4 \pi(1 \int \limits_{\Re^{3}} f(\vec{x}, \vec{v}, t) d \vec{v}) \quad (1) $$ $$ \begin{array}{c} f=f(\vec{x}, \vec{v}, t) \geq 0 ; \quad f(\vec{x}, \vec{v}, 0)=f_{0}(\vec{x}, \vec{v}) \end{array} $$ Here $f$ is the distribution function of electrons; $t$ is time; $\vec{x}, \vec{v}$ are electron coordinates and velocities; $\varphi$ is the potential of selfconsistent electric field; $\pi $ is the known constant value; $\Re^{3}$ is physical space or continuum of velocities; $f_{0}$  the initial data. It is assumed that $f$ and $\varphi$ are the smooth functions, and the integral from the right side of the Poisson equation exists. The mathematical model (1) of a boundless electrically neutral collisionless fully ionized plasma of electrons and ions in the electrostatic approximation (the twocomponent VlasovPoisson plasma) is considered further in index form: $$ \begin{array}{c} \frac{\partial f}{\partial t}+{v}_{i}\frac{\partial f}{\partial x_{i}} \frac{\partial \varphi}{\partial x_{i}}\frac{\partial f}{\partial {v}_{i}}=0 \end{array} $$ $$ \frac{\partial^2 \varphi}{\partial x^2_{i}} =4 \pi(1 \int \limits_{\Re^{3}} f(x_i, v_i, t)d\vec{v}) \quad (2) $$ $$ \begin{array}{c} f=f(x_i, v_i, t) \geq 0 ; \quad f(x_i, v_i, 0)=f_{0}(x_i, v_i) \end{array} $$ where $\vec{v} = (v_1, v_2, v_3), \vec{x} = (x_1, x_2, x_3), d\vec{v} = d v_1 d v_2 d v_3; i = 1, 2, 3$. The mathematical model (2) of the twocomponent VlasovPoisson plasma has the following exact stationary solutions: $$ f=f^0(x_i, v_i), \quad \varphi = \varphi ^0(x_i) \quad (3) $$ $$ {v}_{i}\frac{\partial f^0}{\partial x_{i}} =\frac{\partial \varphi^0}{\partial x_{i}}\frac{\partial f^0}{\partial {v}_{i}}, \quad \frac{\partial^2 \varphi^0}{\partial x^2_{i}} =4 \pi(1 \int \limits_{\Re^{3}} f^0(x_i, v_i) d v_1 d v_2 d v_3) $$ The aim of this research is to prove the absolute instability for exact stationary solutions (3) to the mathematical model (2) by the direct Lyapunov method with respect to small threedimensional perturbations. The results of the study are important for solving the problem of controlled thermonuclear fusion. To achieve this goal, the hydrodynamic substitution of independent variables is performed so that the VlasovPoisson equations (2) are transformed to the previously known infinite system of threedimensional equations similar to the equations of isentropic flows of a compressible fluid medium in the vortex shallow water and the Boussinesq approximations. The new defining equations have exact stationary solutions that are equivalent to exact stationary solutions (3). Then these defining equations are linearized in the vicinity of their stationary solutions. A priori exponential estimate from below is constructed for a subclass of small threedimensional perturbations of exact stationary solutions to the new defining equations, which grow over time and are described by the field of Lagrangian displacements. Since the estimate is obtained for any exact stationary solutions, it proves precisely the absolute linear instability of the latter regarding threedimensional perturbations. Thus, the NewcombGardnerRosenbluth sufficient condition $$ \begin{array}{c} \frac{d f^{0}}{d\left(\frac{\vec{v}^{2}}{2}+\varphi^{0}\right)} \leq 0 \end{array} $$ for linear stability of exact stationary solutions (3) is reversed and its formal character is revealed. Also, the sufficient conditions for linear practical instability of exact stationary solutions (3) to the mathematical model (2) are found and their constructive nature is discovered. At last, the results of this research are consistent with the wellknown Earnshaw theorem on instability in electrostatics and extend the scope of its applicability from classical mechanics to statistical one. As for the significance of these results, they can be used to study the adequacy of mathematical models for plasma to the physical phenomena which the models describe. Furthermore, the results obtained here can be applied to the development and subsequent operation of devices designed to perform the controlled thermonuclear fusion. In order for a plasma confinement device to operate reliably, it needs for us to ensure the practical stability of its dynamic equilibrium states with respect to all acceptable perturbations. In particular, these equilibrium states should be robust in a practical sense for small threedimensional perturbations. This can be achieved by creation of numerical and physical models, which correspond to the linearized initialboundary value problem under investigation, with control the sufficient conditions for linear practical instability at some reference time points. In constructing these models, the main focus should be on ensuring that the sufficient conditions for linear practical instability are not met at the expense of those or other known external influences on small threedimensional perturbations growing with time (for example, by virtue of violation of initial conditions). In consequence, the operation reliability of the device for plasma confinement in working mode will be guaranteed.
This work was supported partially by China Scholarship Council.
Cristia Vacacela Gomez^{1}
^{1}Istituto Nazionale di Fisica Nucleare , Laboratori Nazionali di Frascati, Italy
Quantum tunneling (QT), at first approximation, is a microscopic phenomenon where a particle can penetrate and pass through a potential barrier, which is assumed to be higher than the kinetic energy of the particle. This effect, nonpredicted by the laws of classical mechanics, plays an essential role in different physical phenomena, such as nuclear fusion in stars, radioactive decay, quantum biology, cold emission, tunnel junction, quantumdot cellular automata, tunnel diode, tunnel fieldeffect transistor, quantum conductivity, kinetic isotope effect, scanning tunneling microscope, and more recently, water quantum tunneling. With this in mind and based on the relevant solutions to the Schrodinger equation, we present a simple derivation of onedimensional quantum tunneling through 𝑛successive potential barriers, separated by intermediate free and nonfree regions. In particular, we show that the transmission coefficient depends strictly on the number (𝑛) of barriers. This finding has never been discussed previously and can be used in future experiments. Our results are expected to be of immediate help for students and educators.
The authors would like to thank Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia  CEDIA for the financial support given to the present research, development, and innovation work through its CEPRA program, especially for the “Proyecto 18Tecnologias Inmersivas” fund.
Osama Ogilat^{1}
^{1}AlAhliyya Amman University, Basic sciences, Jordan
In this article, a novel technique depends on Fitting the CloughTocher approach (CT) and the multiquadric radial basis function (RBF) associated through a linear polynomial (RBFL) is applied to recreate threedimensional leaf surface from the data. Since modeling leaf surface is essential for improving plant model, the exactness of the solution is established by applying the CloughTocher multiquadric radial basis function enhanced with a linear polynomial approach (CTRBFL) to real 3D leaf data. It is shown that the (CTRBFL) method generates an exact representation of the leaf surface.
Paola Lecca^{1}
^{1}Free University of BozenBolzano, Faculty of Computer Science, Italy
In most mathematical models and their practical applications, a network represented by a graph is a finite metric space where distance is defined by the number of edges of the shortest path between two nodes. However, as recent studies are already stating, this is not the only geometry of a network [1, 2, 3]. There is in fact the geometry of the latent metric space underlying the organisation of the network structure and the geometry of the metric space induced by the network dynamics [1]. Often, in modelling processes, one geometry is imposed on the network, without considering that the network may have a different one defined by the properties of the nodes and edges representing, respectively the actors and the relationships between actors involved in the physical processes of which the network is a model. It is therefore of great importance to be able to uncover the real geometry of a network and then build a realistic model of its static and dynamic properties based on this real geometry. With this motivation, I present a method to determine the latent geometry of a network and the geometry induced by its dynamics. There are countless benefits that knowledge of network geometry can have in the biological and medical fields. Such networks underlie several biochemical processes, molecular dynamics, and signal generation. These include the understanding of the molecular mechanisms underlying biological processes and the identification of drug targets. I show the practical applications of this research on protein interaction map of SARSCov2 based on previous studies [4, 5]. [1] Boguñá M., Bonamassa I., De Domenico M. et al. Network geometry. Nat Rev Phys 3, 114–135 (2021). https://doi.org/10.1038/s42254020002644 [2] Mulder D., Bianconi, G. Network Geometry and Complexity. J Stat Phys 173, 783–805 (2018). https://doi.org/10.1007/s1095501821159 [3] Fernanda S. Tonin, Helena H. Borba, Antonio M. Mendes, Astrid Wiens, Fernando FernandezLlimos, Roberto Pontarolo, Description of network metaanalysis geometry: A metrics design study, PLoS ONE, 14(2): e0212650, 2019, https://doi.org/10.1371/journal.pone.0212650 [4] Lecca P. , Carpentieri B., Sylos Labini P., Vella F., Troiani E., Cavezzi A., Analysis of SARSCoV2 protein interactome map, IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2021)  Workshop on Integrative Data Analysis in Systems Biology (IDASB 2021), 912 December 2021  Virtual online conference, pp. 24292436, doi: https://doi.org/10.1109/BIBM52615.2021.9669641 [5] Gordon D.E., Jang G.M., Bouhaddou M. et al. A SARSCoV2 protein interaction map reveals targets for drug repurposing. Nature 583, 459–468 (2020). https://doi.org/10.1038/s4158602022869
This study is supported by the project SABLE (Computational methods to simulate the SARSCoV2 attack to red blood cells), RTD 2021 nr. 5744, funded by the Free University of BozenBolzano, Italy.
Armen Kuzanyan^{1} , Astghik Kuzanyan^{2} , Vahan Nikoghosyan^{3}
^{1}Institute for Physical Research, National Academy of Sciences of Armenia, Material Science Lab., Armenia
^{2}Institute for Physical Research, National Academy of Science of Armenia, Material science , Armenia
^{3}Institute for Physical Research, National Academy of Sciences of Armenia, , Armenia
We present the results of modeling of heat propagation processes in the $SiO_2/W/FeSb_2/W/Al_2O_3$ fivelayer detection pixel of thermoelectric singlephoton detector after absorption of one photon, simultaneous absorption of more than one photon, as well as photons absorption with optical delay in the definite or given by the random number generator areas. We have considered the absorption of photons with an energy of 0.95 eV in the detection pixel with a surface area of $10 × 10 μm^2$ and various thicknesses of the antireflection layer ($SiO_2$), absorber ($W$), thermoelectric sensor ($FeSb_2$), heat sink ($W$), and substrate ($Al_2O_3$). The threedimensional matrix method for partial differential equations was used in calculations. The cases of simultaneous absorption of several photons on a length of 1 μm of the absorber surface as well as absorption of photons following with optical delay 30 – 5 fs are investigated. It is shown that the decay time of the detector signal to the background substantially depends on the number of simultaneously absorbed photons; therefore, the number of absorbed photons up to eight photons can be determined. $SiO_2/W/FeSb_2/W/Al_2O_3$ detection pixel can also detect photons with optical delay of 5 fs, which corresponds to the count rate of $2×10^{14}$ Hz. The fivelayer detection pixel of the thermoelectric singlephoton detector with $FeSb_2$ sensor can also detect photons absorbed with an optical delay of 5 fs independently of photons absorption areas location in the absorber. A detector with such characteristics is highly demanded in many fields of quantum electronics.
The authors are grateful to A.M. Gulian for his interest in the work and useful discussions. This work was supported by the Science Committee of RA, in the frames of the research project №21T1C088 “Sensor development of the thermoelectric singlephoton detector for UV radiation taking into account thermal noise”.
Naoyuki Iwata^{1} , Hiroki Suzuki^{2} , Shinsuke Mochizuki^{3}
^{1}Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
^{2}Okayama University, Graduate School of Natural Science and Technology, Japan
^{3}Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
This study presents a numerical analysis of SGS model validation using the Reynolds number dependence of unsteady turbulence fields. The Smagorinsky model, a typical SGS model for largeeddy simulation (LES), usually needs to be corrected for a value of the model constant in wall turbulence. To examine the necessity of reducing the model constant value of the Smagorinsky model in the low Reynolds number region observed near the wall of the unsteady flow field, a comparison was performed with other SGS models without the need for model constant value correction. As a result, the Smagorinsky model was found to be effective in the low Reynolds number region. For this unsteady turbulence, the period and amplitude of the external forcing term were changed as computational conditions. Also, the Reynolds number was changed to examine the present analysis. In addition, the Reynolds number was changed to verify the current analysis. This analysis showed little difference among the models, regardless of Reynolds number, period, or amplitude. This result suggests that there is little need to correct the model constant values for the Smagorinsky model in unsteady homogeneous turbulent flow fields in the low Reynolds number region.
Riku Hirabayashi^{1} , Hiroki Suzuki^{2} , Shinsuke Mochizuki^{3}
^{1}Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
^{2}Okayama University, Graduate School of Natural Science and Technology, Japan
^{3}Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
This study presents the effects of reduced spatial resolution in an anisotropic turbulence field. Here, this turbulence field is set to be stationary. We use the implicit largeeddy simulation (ILES) without subgrid scale (SGS) stresses and LES with the Smagorinsky model to analyse this turbulent field. The convective terms were discretized with second or fourthorder central difference schemes, and the viscous terms were discretized with second, fourth, sixth, and eighthorder central difference schemes to examine the accuracy of the spatial resolution. The effects of the reduced spatial resolution were examined using the Reynolds number dependence of the turbulence statistics. We have seen that the effects of decreasing spatial resolution depend more on the viscous terms than on the convective terms. When the viscous terms have secondorder accuracy, the effects on spatial resolution are more apparent. Smallscale turbulent fields appeared to be significantly affected by the spatial resolution at low Reynolds number conditions.
Mahendra Samarawickrama^{1}
^{1}University of Technology Sydney, Computer Science, Australia
We modelled consciousness to explain how it interfaces with the brain and interacts with matter and energy. As per the mode, consciousness is a fundamental law of nature and life or reality. Regardless of the brain’s massive parallelprocessing capability, consciousness has been defined as a highspeed sequential process that leads to awareness. Like time, consciousness is also subjected to relativity. When the observer is moving, both time and consciousness dilate, which does not give an advantage to the moving observer to enhance the awareness over the resting observer. Further, electromagnetic energy of consciousness follows quantum principles and waveparticle duality, which interplays with matter and energy. The rest mass of the consciousness particle increases when increasing the consciousness frequency or decreasing the speed of the consciousness particle. This interplay of consciousness with matter and energy makes consciousness and reality interrelate and follows determinism, realism, and physicalism, the fundamental essences of modern physics. Further, that explains the limitations of the five senses of an observer (i.e., sight, hearing, taste, touch and smell) and the role of consciousness in understanding reality. In future, we would like to extend this model to explain dark matter and dark energy.
Francisco Delgado^{1} , Agustín VázquezSánchez^{2}
^{1}INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico
^{2}Tecnologico de Monterrey, Mechtronics Engineering, Mexico
COVID19 confinement has shaken the educative system with deep changes in teaching, discipline, persistence, and new learning horizons. Student evaluation for instructors in Higher Education is applied as a feedback assessment to improve Education. Such instruments have been applied consistently for decades. Those instruments are commonly paired with other insights to evaluate the learning and teaching impact of teaching innovation or other innovation interventions. Extracting Patterns from Students’ Evaluations of Instructors is a very recurrent practice in university assessments. Commonly based on Likert scales, their analysis to get conclusive findings have been criticized because such gathering techniques fail to exhibit a real ordered and metric scale. Recently, analysis based on statistical data mining and machine learning has led to the construction of new approaches to better understand those scales for such a concrete application. In this work, we explore such techniques based on several joint statistics to analyze the crossing of COVID19 confinement (from preCOVID to New Normal) extracting certain student patterns through such period. We propose a joint statistical dashboard to interpret the outcomes for several cohorts crossing the pandemic confinement and transitions from facetoface to virtual education, and again to facetoface education.
Teimuraz Tsabadze^{1}
^{1} Georgian Technical University, Computational Mathematics, Georgia
The objective of this paper is to introduce a new method for constructing a hierarchical structuring in systems with fuzzy relationships between elements. The expediency of creating the proposed method is substantiated. The appropriate theoretical basement of the offered method is laid out in the lattice of binary fuzzy relations. The requirements are formulated for the implementation of the process of hierarchical structuring. A key theorem is proved that defines the structural units and types of fuzzy connections between them at each hierarchical level. A detailed practical example, accompanied by graphic illustrations, is given to demonstrate the work of the proposed method. Possible prospects for the development of this direction are outlined.
Vladimir Belayev^{1}
^{1}Joint Stock Company "D.V. Efremov Institute of Electrophysical Apparatus", Scientific Technical Center "Sintez", Russia
A cloud of relativistic material particles is considered, the gravitational interaction between which can be neglected. The gravitational mass of the cloud is determined for the region where it can be considered as a point body. The dependence of this mass on complete elliptic integral of the 2nd kind on the ratio of the particle velocity to the speed of light is established.
Fawaz Hjouj^{1}
^{1}Khalifa University, Math, United Arab Emirates
This is a theoretical presentation on some useful Mathematical Models and tools for conducting research in the fields of Tomography and Image processing. Several exact models are introduced including: Analytical formulation of the Radon Transform for three elementary functions: The Box function, the Unit Cylinder, and the Unit Gaussian. A family of block binary images for testing ideas. Representation of an image using the box function. This representation allows exact computations for the Radon Transform, Fourier Transform, Moments, and many others. This representation can also be involved in the mathematical arrangements of the iterative reconstruction algorithms of Tomography so that the coefficient matrix of the linear system is exact. Overall, we believe that these tools are helpful for young researchers in these fields. We show accurate results in several calculations on synthetic images as well as an accurate iterative reconstruction of images from limited data.
AHMAD ZAKI MOHOMAD AMIN^{1}
^{1}Universiti Malaya, Mathematics, Malaysia
Crack difficulties are important research topics for multiferroic composite media, which offer a lot of potential for producing multifunctional devices. It is put into consideration the magnetoelectrothermoelastic coupling effect. The two crack surfaces are symmetrically loaded by a combination of homogeneous thermal, magnetic, electric, and mechanical loadings. Only the shallower region of a deep flaw in the wall structure inside the skindepth layer impacts the initial temperature Induction Thermography (IT) response while assessing ferromagnetic constructions, but the deeper part has zero influence. This paper provides an exhaustive overview of these crack behavior studies as well as proposes a course of action for future exploration. Based on the literature, three types of crack behavior, which are magnetoelastic, ferromagnetic, and piezoelectric (PE), were explored significantly. Literature reviews have indicated that the magnetoelastic crack studied is popular among researchers around the world. Besides, the procedure and conditions are easier and faster compared to ferromagnetic and PE. Future research should therefore concentrate on the investigation effects of the magnetoelastic crack.
Mohamed Jouini^{1} , Rashad Heggi ^{2} , Naser AlKhalayaleh ^{3} , Fawaz Hjouj^{4}
^{1}Khalifa University , Mathematics, United Arab Emirates
^{2}Khalifa University , Mathematics, United Arab Emirates
^{3}Khalifa University , Mathematics, United Arab Emirates
^{4}Khalifa University, Math, United Arab Emirates
Recent advances in numerical methods combined with the use of 3D Xray micro computed tomography acquisition systems improved the characterization of reservoir rocks at pore scale. This approach, known as digital rock physics (DRP), consists on simulating rock properties using 3D Xray micro computed tomography images at pore scale. DRP has been extensively used to estimate numerically rock properties like porosity and permeability. This methodology was successful in sandstone reservoir rocks due to their relative homogeneity. Nevertheless, this approach failed in many cases when applied for carbonate reservoirs due to their heterogeneity at several length scales. In order to overcome this limitation, we propose to use the texture information in the images to identify and segment the most representative textural regions. Indeed, several studies showed that texture information is correlated to variations of physical rock properties. In recent years, the advancements made in deep learning algorithms improved largely the performance of segmentation methods. In particular, we focus on a machine learning method based on convolutional neural network called the UNET architecture to segment 3D XRay micro computed tomography images in terms of textures. The challenge is to identify precisely representative textures in highly heterogeneous rocks such as carbonate rocks. We investigate the performance of the proposed segmentation method on both synthetic and real data.
The authors would like to thank Abu Dhabi Department of Education and Knowledge (ADEK) in United Arab Emirates for funding the project under grant number EX2018024. Acknowledgments:
Miroslava Nedyalkova^{1}
^{1}unify, chemistry , Switzerland
The presented perspective comes to the line for building and exploring the allergenic nature of food proteins. The general application of the contribution was to propose a new way of arising the way of understanding in the light of machine learning (supervised and unsupervised) method predicting the allergenic plant proteins. To strategy was based on scoring the descriptors regarding testing the descriptors for calssification and the partitioning procedure based on Kmeans. The Knearest neighbor (KNN) classifier was used. The 5fold crossvalidation approach was used to validate KNN classifier in the variable selection step and final classifier. The necessity of developing a robust and valuable method can be set out as efficient to overcome the problem with allergenisity.
This work was supported in part by the Bulgarian Science Found  (grant number: K06 KO /17  16.12.2020.)
Giorgi Jandieri^{1}
^{1}Georgian Technical Uiversity, Internationa Space Agency Georgian Society, Georgia
Statistical characteristics of the temporal spectrum of scattered ordinary and extraordinary electromagnetic waves in the equatorial region of the terrestrial ionosphere are investigated using the stochastic transport equation for frequency fluctuations applying the ray(optics) method. Currently equatorial ionosphere is of great interest. Statistical characteristics of scattered electromagnetic waves in this region were not considered till now. Ionospheric conductivity is one of the main properties of the ionosphere which plays an important role in the ionospheric transport mechanism and in the propagation of wave sent from the Earth to ionosphere. The conductivity plays a key role in the dynamics of plasma in the ionosphere and irregularities have different spatial scales usually elongating in the direction of an external magnetic field. Refractive index for the equatorial region has been obtained for the first time. Statistical moments (broadening of the spectrum and shift of its maximum) are analyzed analytically and numerically using the experimental data. The obtained results contain anisotropic factors of elongated electron density irregularities, velocity of a plasma stream, temporal pulsations of the plasmonic structures and inclination angle of electron density irregularities with respect to the geomagnetic lines of force. Investigations of spacetime fluctuations of electromagnetic waves radiation are of essential interest for radio astronomy and atmospheric physics. These fluctuations are a disturbing factor at groundbased astronomic observations.
This work is supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant NRF21316 "Investigation of the statistical characteristics of scattered electromagnetic waves in the terrestrial atmosphere and application"
Jaykov Foukzon^{1}
^{1} Israel Institution of Technology, Haifa, Israel., Center for Mathematical Sciences,, Israel
A new nonArchimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwisedefined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard tempered operator valued distribution, but a nonclassical operatorvalued function [1][2]. Then formal expressions containing, e.g., ϕⁿ(x),<ϕⁿ(x)>,etc. can be understood literally, and shown to be well defined as {∗}^ℝ_{с}^{#}valued functions. In the free field cases, we show that the Wightman functions are explicitly calculated with the pointwise field, without any regularization, e.g., Wick product. We show that some of physicists' naive expressions of Lagrangian λϕⁿ(x) can be rigorously justified. REFERENCES [1] Jaykov Foukzon, Basic Real Analysis on External NonArchimedean Field ℝ_{c}^{#}. Basic Complecs Analysis on External Field ℂ_{c}^{#}=ℝ_{c}^{#}+iℝ_{c}^{#}. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3989960 [2] Jaykov Foukzon,The Solution of the Invariant Subspace Problem. Part I. Complex Hilbert space. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4039068
Sergo Gotoshia^{1}
^{1}Ivane Javachishvili Tbilisi State University, R. Aglaze Institute of Inorganic Chemistry and Electroqemistry , Laser Center, Georgia
Thiosemicarbazon (TSC) is known as one the of active complexproductive ligands with different metals. TSC and its derivatives are known as antibacterial, antiviral, antifunginal, antinevrological, biologically active compounds. The complexproductivity ability of TSC with transition metals enhances their pharmacological activity . We have recorded the IR spectrum of 2NH3thiosemicarbazon on the Fourier IR spectrometer Varian 660 and The Raman spectrum – on the homemade Ramansystem, with the excitation wavelength 632.8 nm. For quantumchemical computations the semiempirical program MOPAC 8 Ultra has been used. On the basis of theory AM1 the geometrical parameters of optimized molecular structures bound lengths and angles have been computed. Also the theoretical spectrum and normal frequencies have been computed. The experimental and theoretical data are in satisfactory fit.
Eraldo Marinho^{1}
^{1}Universidade Estadual Paulista Julio de Mesquita Filho / UNESP, Statistics, Applied Mathematics and Computing, Brazil
A tensor representation for quadrupole expansion is proposed as a recipe for nbody simulations of collisionless stellar systems that do not perform the direct summation method, as is the case of TREECODE. The quadrupole expansion is almost straightforward in the nonsoftened case, but it is pretty complicated when some softening artifice modifies the potential. A shorthand formula of quadrupole correction for potential and gravity force is derived that can be easily adapted to computer codes like C and FORTRAN. A test is performed to show how relevant it is to incorporate quadrupole correction in nbody codes like TREECODE and particlemesh methods.
Giorgio Frunzio^{1}
^{1}Università degli Studi della Campania Luigi Vanvitelli, Architecture and Industrial Design, Italy
The analysis of flaws in structures is an important engineering problem. The identification technique can be a useful tool to develop predictive models that easily allow detecting defects and unexpected problems. Many studies have been carried out to obtain the parameters to represent the behaviour of structures in terms of time histories, frequency, response curves, and mode shapes. The use of simple models based on experimental data is a need to prevent the occurrence of undesired phenomena. In this paper, a method for the structural identification of tall buildings is presented. The method has been applied to the Enel skyscraper situated in Naples, Italy. The 120 meters building is made by the composition of two towers linked on the top by a steel girder with reinforced concrete piled foundations. The identification of this particular reinforced concrete structure has been based on the experimental data obtained by a scaled model. The simplified method proposed consists of a procedure of steps of system identification using a finite element model. An iterative process has been performed updating step by step the model, starting from the first three experimental natural frequencies and modes. The comparison between analytical and experimental results is finally shown.
The authors gratefully acknowledge the University of Campania financial contribute and professors Michela Monaco and Antonio Gesualdo for their helpful conversations and support.
Emanuel Cambraia^{1}
^{1}Universidade Federal do Paraná, Physics, Brazil
In this work we study the phenomenon of phase synchronization of a network composed of HindmarshRose neuron. We show how the individual dynamics of the neurons (periodic or chaotic) affects the phase synchronization process of the network, when the coupling parameter is varied. We show that the synchronization process is a function of the individual neuron dynamics, regardless the network topology. To do so, we construct a bidimensional parameter space where the individual dynamics of the neurons may be periodic or chaotic. We notice three regions of interest: the first one, where the individual action potential of the neurons is chaotic and depicts burst regime; the second one, where the dynamics is periodic and depicts burst regime; and a third one, where the neuron dynamics is periodic but depicting spiky regime. For chaotic neurons, the synchronization rote as the coupling parameter grows, shows a monotonic transition, characterized as the large the coupling, the large the synchronization level. When the action potentials of neurons are periodic, the dynamics depicts phase locking for small coupling, leading to a phase synchronized network. As the coupling increases a desyncronization process first occurs, followed by the traditional synchronization rote as the coupling increases. That characterizes a nonmonotonic transition to phase synchronization of the network, where two very distinct thresholds of synchronization occur. Finally, a case in which the action potential of neurons is periodic in a spike regime. For this case, a small coupling promotes chaotic dynamics before any phase locking process take place. In this case, again, an almost monotonic transition to synchronization takes place as the coupling parameter is increased.
Ibrahim Nonkané^{1} , Duni Y. F. ZONGO^{2} , Latévi Lawson^{3} , ALIDA ZINSOU^{4}
^{1}Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
^{2}Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
^{3}African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
^{4}Université THOMAS SANKARA, IUFIC, Burkina Faso
In this paper, we study the holomorphic representation of OlshanetskyPerelomov operators associated with the weyl group W of type $B_n$. Thus, we view the algebra $\mathcal{H}(\mathbb{C}^n)$ of holomorphic functions as a module over the ring D of invariant differential operators under the group W. Then, we study the holomorphic representation of $\mathcal{D}$. Using the representation theory of the Weyl group W, we construct the irreducible components of $\mathcal{H}(\mathbb{C}^n)$, by explicity providing their generators.
RASHMI KUMARI^{1}
^{1}BENNETT UNIVERSITY TIMES OF INDIA GROUP GREATER NOIDA , INDIA, SCHOOL OF COMPUTER SCIENCE ENGINEERING & TECHNOLOGY (SCSET), India
Alzheimer's disease (AD) is a neurological disease that wreaks havoc on memory and cognition. Extracellular plaques composed of amyloid peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins are two neuropathological markers of Alzheimer's disease. Currently, there is no medicine that can cure, stop, or even delay the disease's progression. In this paper, a mathematical model of AD is developed that incorporates pyramidal neurons, hyperphosphorylated tau proteins, microglia, and peripheral macrophages to calculate dendrites' complexity. A set of partial differential equations represents the model by incorporating Aβ cascade, tau, and oxidative stress hypothesis. Realtime simulations have been performed to validate the different types of medications that have failed or are presently undergoing clinical trials.
Igor Nikitin^{1}
^{1}Fraunhofer Institute for Algorithms and Scientific Computing, SCAI, Germany
Equation of state for BoseEinstein condensate is evaluated in two cases: noninteracting particles and particles interacting via potential possessing a nontrivial minimum. In astrophysical context, the first case becomes equivalent to cold dark matter, while the second case  to dark energy. A particular cosmological scenario with dark matter injection from quasiblack holes to galactic halo, followed by BoseEinstein condensation in the intergalactic medium is considered.
mohamed abdelouahab^{1}
^{1}University of M'sila  Mohamed Boudiaf  Algeria, physics department/ Physics and Chemistry of Materials Laboratory,, Algeria
In this work, our main goal was to extend quantum entanglement to superradiance. For this, it was necessary to identify the common point between the two physical concepts. This is what has been proposed and achieved, thanks to the common properties carried by the wave function solution of the Klein Gordon equation which defines the bipartite system at spin ½ in a Schwarzschild space time. A detailed study was completed where it was found that superradiance extended to quantum entanglement is more robust so far it is from the black hole.
Valeriy Parkhomenko^{1}
^{1}The Federal Research Center "Computer Science And Control" of The Russian Academy Of Sciences, Bauman Moscow State Technical University, Dorodnicyn Computing Centre, Russian Federation
Global warming climate changes are observed in recent decades. These changes largely associated with anthropogenic increases in greenhouse gases in the atmosphere (CO2 – most important among them). The problem and opportunity of the global climate stabilization at a current level were investigated early. The current study is based on a threedimensional hydrodynamic global climate coupled model, including ocean model with real depths and continents configuration, sea ice evolution model and atmospheric general circulation model. Aerosol concentration from the 2010 up to 2100 year is calculated as a controlling parameter to stabilize mean year surface air temperature. It is investigated opportunity to get prescribed space and time global distribution of the stratosphere aerosol when exist limited number of aerosol sources. Wind transport and deposition of aerosol are taken into account.
Asal Yuldasheva^{1}
^{1}Tashkent branch of Moscow State University, applied mathematics and informatics, Uzbekistan
The peridynamic theory is a nonlocal theory of continuum mechanics based on an integrodiﬀerential equation without spatial derivatives, which can be easily applied in the vicinity of cracks, where discontinuities in the displacement ﬁeld occur. This paper studies the Cauchy problem for nonlinear equation of the peridynamics. The issues of local wellposedness and smoothness of the solutions are discussed.
Ibrahim Nonkané^{1} , Duni Y. F. ZONGO^{2} , Latévi Lawson^{3} , ALIDA ZINSOU^{4}
^{1}Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
^{2}Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
^{3}African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
^{4}Université THOMAS SANKARA, IUFIC, Burkina Faso
In this note, we study the action of the CalogeroMoser system on the algebra $\mathcal{H}(\mathbb C^n)$ of holomorphic functions over the complex field $\mathbb{C}^n$. We consider the algebra $\mathcal{D}$ of invariant differential operators with analytic coefficients under the symmetric group and its representation on $\mathcal{H}(\mathbb C^n)$. We elaborate the irreducible decomposition of $\mathcal{H}(\mathbb{C}^n)$ as a module over $\mathcal{D}$. We explicitly describe the irreducible component by giving it generators.
Noriko Akutsu^{1}
^{1}Osaka ElectroCommunication University, Faculty of Engineering, Japan
The faceted shape in a growing crystal is often observed in the materials which are necessary to sustain our daily life.
The phasefield modeling of ice in a mesoscopic scale reproduces snow like the faceted dendritic shapes of a crystal [1].
Silicon (Si) crystal grown from its melted state can form faceted dendrites in a submillimeter scale caused by the MullinsSekerka instability [2].
Silicon carbide (SiC) crystal grown from Si melted state forms {\it faceted} macrosteps which degrade the quality of a crystal [3].
Theoretically, both the phasefield modeling and the MullinsSekerka instability assume thermodynamically rough crystal surfaces.
However, in equilibrium, the faceted shape is directly connected to the thermodynamically smooth surface, where surface quantities become singular [4, 5].
Hence, the atomically rough surface has been regarded as the nanoscale rough surface, though some of the atomically rough surfaces are thermodynamically smooth in equilibrium.
Here, another scenario using the facetedrough surface [6] is proposed to explain how the atomically and thermodynamically smooth surface in equilibrium becomes a thermodynamically rough surface in a growing crystal.
[1] Demange, G; Zapolsky, H.; Patte, R.; Brunel, M.
npj Comutaional Materials, (2017), 3, 15, 17.
[2] Tokairin, M.; Fujiwara, K.; Kutsukake, K.; Usami, N.; Nakajima, K.
Phys. Rev. B, (2009), 80, 174108, 14.
[3] Mitani, T.; Komatsu, N.; Takahashi, T.; Kato, T.; Harada, S.; Ujihara, T.; Matsumoto, Y.; Kurashige, K.; Okumura, H.
J. Cryst. Growth, (2015), 423, 4549.
[4] Akutsu, N.; Akutsu, Y. J. Phys. Soc. Jpn., (1987), 56, 14431453.
[5] Akutsu, Y.; Akutsu, N.; Yamamoto, T. Phys. Rev. Lett., (1988), 61, 424427.
[6] Akutsu, N. Sci. Rep., (2021), 11, 3711, 111.
This work was supported by KAKENHI GrantsinAid (no. JP17K05503) from the Japan Society for the Promotion of Science (JSPS). This work was supported in part by the Collaborative Research Program (2020 S21, 2021 S35) of the Research Institute for Applied Mechanics, Kyushu University.
Irina Noskova^{1} , Vladimir TertychnyDauri^{2}
^{1}ITMO University, Faculty of Control Systems and Robotics, Russian Federation
^{2}ITMO University , , Russia
We consider the synthesis problem of dynamical systems relating to a class of conditional variation problems with variable endpoints. Variational method is applied for research of the elastic oscillator with controllable spring stiness. In solving a general conditional variation problem, the obtained dierential system of equations in closed form is studied for design of an optimal system for the initial dynamic object with a given quality functional. Transversality condition in the variational problem is formulated in terms of local programming. An optimal algorithm is constructed in the elastic oscillator, and the value of nite transition period is found.

David ParraGuevara^{1} , Yuri Skiba^{2}
^{1}National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico
^{2}National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico
A method for estimating the intensity of intermittent emissions of an air pollutant from a point source is presented. The intensity parameters are obtained using time series (data) of pollutant concentrations recorded at the monitoring site. A wellposed model of atmospheric dispersion and its adjoint model are formulated for estimating the pollutant transfer from the source. Such dispersion models are used to establish relationships between the intermittent emissions from the source and data. The parameter estimation method is formulated as a quadratic programming problem which depends on the regularization parameter. The existence and uniqueness of a solution to this optimization problem are proved. Particular solutions of the dispersion model are used to establish the constraints of the quadratic programming problem. We stress out the computing advantage of using adjoint functions to compute such solutions. Onedimensional synthetic numerical examples demonstrate the capability of the method for estimating the intensity of intermittent emissions.
This research was supported by the grants 25170 and 14539 of the National System of Investigators (SNICONACyT, México).
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