# Conference submissions

#### Notes on the approach, methods and results of qualitative research for some classes of dynamic systems

Irina Andreeva 1

1Peter the Great St.Petersburg Polytechnic University , Higher Mathematics , Russia

###### Abstract

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.

#### Shared quantum generation of post-selected entangled states using double teleportation

1INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico

###### Abstract

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 post-selection 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.

###### Acknowledgements:

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.

#### Influence of Geogebra on academic performance in differential equations of separable variables in engineering students from Antofagasta-Chile.

Jorge Olivares1 , Elvis Valero2

2Universidad Mayor de San Andrés, matemáticas, Bolivia

###### Abstract

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 Antofagasta-Chile, during the year 2021. This work is a continuation and expansion of "Animations and interactive creations in first-order linear differential equations: the case of Geogebra".

#### Effects of the Geogebra CAS calculator on academic performance in second-order non-homogeneous linear differential equations in engineering students from Antofagasta-Chile.

Jorge Olivares1 , Elvis Valero2

2Universidad Mayor de San Andrés, matemáticas, Bolivia

###### Abstract

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 non-homogeneous 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".

#### A Unified Algebraic Framework for Information Processing

Fotios Kasolis1

1University of Wuppertal, Chair of Electromagnetic Theory, Germany

###### Abstract

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.

###### Acknowledgements:

This work was supported in parts by the Deutsche Forschungsgemeinschaft (DFG) under grant no. CL143/18-1

#### Non-Archimedean -analytical approach to interected scalar quantum fields.

Jaykov2 Foukzon1

1Israel Institute of Technology, math, Israel

###### Abstract

A new non-Archimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwise-defined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard operator-valued tempered distribution, but a nonclassical operator-valued 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 Non-Archimedean 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

#### Implementation of Optimization-based Algorithms for Maximum Power System Observability using Synchronized Measurements

Nikolaos Theodorakatos1 , Rohit Babu2 , Miltiadis Lytras3 , Angelos Moschoudis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
3The American College of Greece, School of Business and Economics, Deree, Greece
4National Technical University of Athens , School of Electrical and Computer Engineering, Greece

###### Abstract

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 Βranch-and-Βound 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 binary-tree 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 Semi-Define-Programming 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.

#### Research on Optimization Procedure of PMU Positioning Problem Achieving Maximum Observability Based on Heuristic Algorithms

Nikolaos Theodorakatos1 , Rohit Babu2 , Miltiadis Lytras3 , Angelos Moschoudis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
3The American College of Greece, School of Business and Economics, Deree, Greece
4National Technical University of Athens , School of Electrical and Computer Engineering, Greece

###### Abstract

The Phasor Measurement Unit (PMU) is a monitoring device capable with high-precision 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 multi-objective optimization function minimized under a set of 0-1 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 multi-objective constraint linear integer program (m-CILP) towards optimality. This GA-PSO 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 Branch-and-Bound (B&B) algorithm which solves the 0-1 m-CILP towards optimality. The minimization models are tested on standard IEEE power networks to show their applicability regarding this multi-objective optimization making problem. The numerical results derived by the GA-PSO 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.

#### Optimization Algorithm‐based Optimal PMU Placement for Power State Estimation and Fault Observability

Nikolaos Theodorakatos1 , Rohit Babu2 , Miltiadis Lytras3 , Angelos Moschoudis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
3The American College of Greece, School of Business and Economics, Deree, Greece
4National Technical University of Athens , School of Electrical and Computer Engineering, Greece

###### Abstract

Fault observability is an essential application among intelligent monitoring and outage management system tasks used to understand the self-healing 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 self-healing network and to maintain the continuity of power supply. Self-healing is an operational aspect of electrical power networks for real-time 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 state-estimation 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 zero-one integer linear program is used that satisfies global optimality. Metaheuristic algorithms such as a binary-particle swarm optimization and genetic algorithm have been employed to determine a fault observable power system. The algorithm models are illustrated with an IEEE-14 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 zero-one integer linear programming model.

#### Study of the stability for three-dimensional states of dynamic equilibrium of the electron Vlasov-Poisson gas

Yuriy Gubarev1 , Yang Liu2

1Lavrentyev Institute for Hydrodynamics, Laboratory for Fluid and Gas Vortex Motions, Russian Federation
2Novosibirsk State University, Department for Differential Equations, Russian Federation

###### Abstract

The Vlasov-Poisson model of boundless collisionless electron gas in self-consistent 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 Vlasov-Poisson 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 semi-infinite 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 Vlasov-Poisson gas in three-dimensional 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 self-consistent 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 Vlasov-Poisson gas with respect to small three-dimensional 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 well-known sufficient Newcomb-Gardner-Rosenbluth 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 second-order inequality with constant coefficients was obtained for the Lyapunov functional. An a priori exponential lower estimate for growth of small three-dimensional 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 Vlasov-Poisson gas with respect to small three-dimensional 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 Vlasov-Poisson 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.

###### Acknowledgements:

This work was supported partially by China Scholarship Council.

#### The Mathematical, Reading, and Scientific Literacies for Sustainable Development in the Fourth Industrial Revolution

Michel Plaisent1

1universite du quebec a montreal , management, Canada

###### Abstract

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 seventy-seven (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 non-global 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.

#### Unifying Approach to a Solution of Linear Systems of Equations $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$: Outer Product Application and Angular Conditionality

Vaclav Skala1

1University of West Bohemia, DEpt. of Computer Science and Engineering, Czech Republic

###### Abstract

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 cross-product). 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 non-squared 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 right-hand side influence, if given.

#### A Quintuple Integral containing the Hermite Polynomial $H_n(x)$ and a Generalized Logarithmic Function: derivation and evaluation

Robert Reynolds1

1York University, Mathematics and Statistics, Canada

###### Abstract

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 Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.

###### Acknowledgements:

We wish to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).

#### Fluorescence characteristics analysis of rodamine B

Yongzhong Ma1

1Engineering University of PAP, School of Equipment Management & Support, China

###### Abstract

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 1×10-4g/L, the fluorescence intensity was positively correlated with the concentration. When the concentration of basic rose essence was greater than 4×10-3g/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.

#### Simulation analysis of explosive power of a detonation bomb

Yongzhong Ma1

1Engineering University of PAP, School of Equipment Management & Support, China

###### Abstract

In order to analyze the safety of detonation bomb, an explosion simulation model of the bomb was established based on LS-DYNA 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 large-mass low-speed 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 high-light detonation bomb, and also provides a useful reference for the research and design of similar ammunition.

#### Nonlinear Dynamics Transmission Error Analysis of a two-stage gear system with gear flexibility and high load

Chao Li1

1Jiangsu Automation Research Institute, Department of Computer, China

###### Abstract

A non-linear dynamic model of a 14-DOF (degree of freedom) two-stage spur gear with time-varying stiffness and flexible gears is developed for the practical problem of non-linear disturbances in a two-stage 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 two-stage 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 non-linear dynamics model of a two-stage spur gear and the transmission error of high load loads is enriched, providing an important reference for the practical design of gear systems.

#### Fast Neutron Detector Simulation

Olga Sidorova1

1Joint Institute for Nuclear Research, Laboratory of Neutron Physics, Russia

###### Abstract

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 U-235. 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 cross-talks were taken into account in order to evaluate contribution of those effects in the final results.

#### PFN multiplicity variations measurement at IREN

Shakir Zeynalov1

1JINR, FLNP, Russia

###### Abstract

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) [2-10] 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.

#### Temperature extremes and slow trends: effect on resource competition ecosystems

Ivan Sudakow1 , Dubrava Kirievskaya2 , Ekaterina Cherniavskaia3

1University of Dayton, Physics, United States
2University of Dayton, Geology, United States
3AARI, Oceanography, Russian Federation

###### Abstract

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.

#### MATHEMATICAL MODELLING OF THE DISTRIBUTION NETWORK FOR THREE-PHASE POWER FLOW ANALYSIS

Samson Ayanlade1 , Abdulrasaq Jimoh2 , Emmanuel Ogunwole3 , Abdulsamad Jimoh4 , Sunday Ezekiel5

1Lead City University, Electrical and Electronic Engineering, Nigeria
2Obafemi Awolowo University, Electronic and Electrical Engineering, Nigeria
3Cape Peninsula University of Technology , Electrical, Electronic and Computer Engineering, South Africa
4University of Ilorin, Electrical and Electronic Engineering, Nigeria
5Olabisi Onabanjo University, Electrical and Electronic Engineering, Nigeria

###### Abstract

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, single-phase 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, three-phase mathematical modeling was used to analyze the power flow of a practical Nigerian distribution network, and the results were compared to those of a single-phase 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 three-phase bus admittance matrix of the network under study was developed. The three-phase power flow equations of the distribution network were formulated in the phase frame. The Newton-Raphson power flow technique was adopted to solve the network three-phase 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 single-phase mathematical modeling. Therefore, three-phase power flow analysis better matched the actual distribution network operating circumstances than single-phase power flow analysis.

#### Stability investigation for three-dimensional states of dynamic equilibrium of two-component Vlasov-Poisson plasma

Yuriy Gubarev1 , Jingyue Luo2

1Lavrentyev Institute for Hydrodynamics, Laboratory for Fluid and Gas Vortex Motions, Russian Federation
2Novosibirsk State University, Department for Differential Equations, Russian Federation

###### Abstract

In the electrostatic approximation, when the electric field of electrons and ions is self-consistent, the plasma dynamics is described by the kinetic Vlasov-Poisson 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 three-dimensional statement, the mathematical model for the two-component Vlasov-Poisson 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 self-consistent 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 two-component Vlasov-Poisson 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 two-component Vlasov-Poisson 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 three-dimensional 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 Vlasov-Poisson equations (2) are transformed to the previously known infinite system of three-dimensional 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 three-dimensional 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 three-dimensional perturbations. Thus, the Newcomb-Gardner-Rosenbluth 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 well-known 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 three-dimensional perturbations. This can be achieved by creation of numerical and physical models, which correspond to the linearized initial-boundary 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 three-dimensional 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.

###### Acknowledgements:

This work was supported partially by China Scholarship Council.

#### A simple derivation for teaching the tunneling effect through n-sequential barriers

Cristia Vacacela Gomez1

1Istituto Nazionale di Fisica Nucleare , Laboratori Nazionali di Frascati, Italy

###### Abstract

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, non-predicted 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, quantum-dot cellular automata, tunnel diode, tunnel field-effect 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 one-dimensional quantum tunneling through 𝑛-successive potential barriers, separated by intermediate free and non-free 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.

###### Acknowledgements:

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 18-Tecnologias Inmersivas” fund.

#### Finite Element Method for Modelling Real Leaves Surface

Osama Ogilat1

1Al-Ahliyya Amman University, Basic sciences, Jordan

###### Abstract

In this article, a novel technique depends on Fitting the Clough-Tocher approach (CT) and the multiquadric radial basis function (RBF) associated through a linear polynomial (RBFL) is applied to recreate three-dimensional 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 Clough-Tocher 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.

#### Uncovering the geometry of protein interaction network: the case of SARS-CoV-2 protein interactome

Paola Lecca1

1Free University of Bozen-Bolzano, Faculty of Computer Science, Italy

###### Abstract

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 SARS-Cov-2 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/s42254-020-00264-4 [2] Mulder D., Bianconi, G. Network Geometry and Complexity. J Stat Phys 173, 783–805 (2018). https://doi.org/10.1007/s10955-018-2115-9 [3] Fernanda S. Tonin, Helena H. Borba, Antonio M. Mendes, Astrid Wiens, Fernando Fernandez-Llimos, Roberto Pontarolo, Description of network meta-analysis 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 SARS-CoV-2 protein interactome map, IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2021) - Workshop on Integrative Data Analysis in Systems Biology (IDASB 2021), 9-12 December 2021 - Virtual online conference, pp. 2429-2436, doi: https://doi.org/10.1109/BIBM52615.2021.9669641 [5] Gordon D.E., Jang G.M., Bouhaddou M. et al. A SARS-CoV-2 protein interaction map reveals targets for drug repurposing. Nature 583, 459–468 (2020). https://doi.org/10.1038/s41586-020-2286-9

###### Acknowledgements:

This study is supported by the project SABLE (Computational methods to simulate the SARS-CoV-2 attack to red blood cells), RTD 2021 nr. 5744, funded by the Free University of Bozen-Bolzano, Italy.

#### Modeling and Simulation of Heat Propagation Processes in the Five-Layer Detection Pixel of Thermoelectric Single-Photon Detector

Armen Kuzanyan1 , Astghik Kuzanyan2 , Vahan Nikoghosyan3

1Institute for Physical Research, National Academy of Sciences of Armenia, Material Science Lab., Armenia
2Institute for Physical Research, National Academy of Science of Armenia, Material science , Armenia
3Institute for Physical Research, National Academy of Sciences of Armenia, , Armenia

###### Abstract

We present the results of modeling of heat propagation processes in the $SiO_2/W/FeSb_2/W/Al_2O_3$ five-layer detection pixel of thermoelectric single-photon 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 three-dimensional 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 five-layer detection pixel of the thermoelectric single-photon 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.

###### Acknowledgements:

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 №21T-1C088 “Sensor development of the thermoelectric single-photon detector for UV radiation taking into account thermal noise”.

#### Comparative validation of sub-grid scale models with converging zero/non-zero value in the laminar flow using Reynolds number dependence of an unsteady turbulence field

Naoyuki Iwata1 , Hiroki Suzuki2 , Shinsuke Mochizuki3

1Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
2Okayama University, Graduate School of Natural Science and Technology, Japan
3Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan

###### Abstract

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 large-eddy 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.

#### LES analysis on the impact of isotropically reduced spatial resolution of viscous terms on an anisotropic homogeneous turbulence field

Riku Hirabayashi1 , Hiroki Suzuki2 , Shinsuke Mochizuki3

1Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
2Okayama University, Graduate School of Natural Science and Technology, Japan
3Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan

###### Abstract

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 large-eddy simulation (ILES) without sub-grid scale (SGS) stresses and LES with the Smagorinsky model to analyse this turbulent field. The convective terms were discretized with second- or fourth-order central difference schemes, and the viscous terms were discretized with second-, fourth-, sixth-, and eighth-order 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 second-order accuracy, the effects on spatial resolution are more apparent. Small-scale turbulent fields appeared to be significantly affected by the spatial resolution at low Reynolds number conditions.

#### Unifying Matter, Energy and Consciousness

Mahendra Samarawickrama1

1University of Technology Sydney, Computer Science, Australia

###### Abstract

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 parallel-processing capability, consciousness has been defined as a high-speed 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 wave-particle 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.

#### Statistical insight about students’ perception of teaching performance patterns across the COVID-19 confinement in Engineering programs of Higher Education

1INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico
2Tecnologico de Monterrey, Mechtronics Engineering, Mexico

###### Abstract

COVID-19 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 COVID-19 confinement (from pre-COVID 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 face-to-face to virtual education, and again to face-to-face education.

#### A method for constructing a hierarchy in systems with fuzzy relationships

1 Georgian Technical University, Computational Mathematics, Georgia

###### Abstract

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.

#### The gravitational mass of the rarefied cloud of the relativistic massive particles

1Joint Stock Company "D.V. Efremov Institute of Electrophysical Apparatus", Scientific Technical Center "Sintez", Russia

###### Abstract

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.

#### Selected Mathematical Tools for Modeling in Tomography and Image Processing with Some Applications

Fawaz Hjouj1

1Khalifa University, Math, United Arab Emirates

###### Abstract

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.

#### Crack Behaviour in Materials: A Comparative Study

1Universiti Malaya, Mathematics, Malaysia

###### Abstract

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 magneto-electro-thermo-elastic 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 skin-depth 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.

#### Texture segmentation of 3D X-Ray micro-computed tomography images using U-NET

Mohamed Jouini1 , Rashad Heggi 2 , Naser Al-Khalayaleh 3 , Fawaz Hjouj4

1Khalifa University , Mathematics, United Arab Emirates
2Khalifa University , Mathematics, United Arab Emirates
3Khalifa University , Mathematics, United Arab Emirates
4Khalifa University, Math, United Arab Emirates

###### Abstract

Recent advances in numerical methods combined with the use of 3D X-ray 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 X-ray 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 U-NET architecture to segment 3D X-Ray 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.

###### Acknowledgements:

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 EX2018-024. Acknowledgments:

#### Prediction of Plant Allergenic Proteins: machine learning classification approach

Miroslava Nedyalkova1

1unify, chemistry , Switzerland

###### Abstract

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 K-means. The K-nearest neighbor (KNN) classifier was used. The 5-fold cross-validation 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.

###### Acknowledgements:

This work was supported in part by the Bulgarian Science Found - (grant number: K-06- KO /17 - 16.12.2020.)

#### Temporal spectrum of scattered electromagnetic waves in the equatorial ionosphere

Giorgi Jandieri1

1Georgian Technical Uiversity, Internationa Space Agency Georgian Society, Georgia

###### Abstract

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 space-time fluctuations of electromagnetic waves radiation are of essential interest for radio astronomy and atmospheric physics. These fluctuations are a disturbing factor at ground-based astronomic observations.

###### Acknowledgements:

This work is supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant NRF-21-316 "Investigation of the statistical characteristics of scattered electromagnetic waves in the terrestrial atmosphere and application"

#### Model $P(ɸ)_4$ Quantum Field Theory. A Nonstandard Approach Based on Pointwise-Defined Free Quantum fields

Jaykov Foukzon1

1 Israel Institution of Technology, Haifa, Israel., Center for Mathematical Sciences,, Israel

###### Abstract

A new non-Archimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwise-defined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard tempered operator- valued distribution, but a nonclassical operator-valued 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 Non-Archimedean 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

#### FTIR and LRS of 2NH3-thiosemicarbazon and quantum-chemical analysis

Sergo Gotoshia1

1Ivane Javachishvili Tbilisi State University, R. Aglaze Institute of Inorganic Chemistry and Electroqemistry , Laser Center, Georgia

###### Abstract

Thiosemicarbazon (TSC) is known as one the of active complex-productive ligands with different metals. TSC and its derivatives are known as antibacterial, antiviral, antifunginal, antinevrological, biologically active compounds. The complex-productivity ability of TSC with transition metals enhances their pharmacological activity . We have recorded the IR spectrum of 2NH3-thiosemicarbazon on the Fourier IR spectrometer Varian 660 and The Raman spectrum – on the homemade Raman-system, with the excitation wavelength 632.8 nm. For quantum-chemical computations the semi-empirical 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.

#### Tensor Representation of Quadrupole Expansion for Softened Potentials in N-body Simulations

Eraldo Marinho1

1Universidade Estadual Paulista Julio de Mesquita Filho / UNESP, Statistics, Applied Mathematics and Computing, Brazil

###### Abstract

A tensor representation for quadrupole expansion is proposed as a recipe for n-body 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 non-softened 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 n-body codes like TREECODE and particle-mesh methods.

#### Structural health monitoring of tall buildings: the case of Enel Skyscrape

Giorgio Frunzio1

1Università degli Studi della Campania Luigi Vanvitelli, Architecture and Industrial Design, Italy

###### Abstract

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.

###### Acknowledgements:

The authors gratefully acknowledge the University of Campania financial contribute and professors Michela Monaco and Antonio Gesualdo for their helpful conversations and support.

#### The influence of the local dynamics in the phase synchronization of a network of a Hindmarsh-Rose neurons.

Emanuel Cambraia1

1Universidade Federal do Paraná, Physics, Brazil

###### Abstract

In this work we study the phenomenon of phase synchronization of a network composed of Hindmarsh-Rose 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 bi-dimensional 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 non-monotonic 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.

#### Holomorphic representation of Olshanetsky-Perelomov operators associated with the Weyl group of type Bn

Ibrahim Nonkané1 , Duni Y. F. ZONGO2 , Latévi Lawson3 , ALIDA ZINSOU4

1Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
3African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
4Université THOMAS SANKARA, IUFIC, Burkina Faso

###### Abstract

In this paper, we study the holomorphic representation of Olshanetsky-Perelomov 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.

#### Mathematical Modelling of Dendritic Complexity Mechanism in Alzheimer's Disease

RASHMI KUMARI1

1BENNETT UNIVERSITY TIMES OF INDIA GROUP GREATER NOIDA , INDIA, SCHOOL OF COMPUTER SCIENCE ENGINEERING & TECHNOLOGY (SCSET), India

###### Abstract

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. Real-time simulations have been performed to validate the different types of medications that have failed or are presently undergoing clinical trials.

#### On dark matter, dark energy and Bose-Einstein condensate

Igor Nikitin1

1Fraunhofer Institute for Algorithms and Scientific Computing, SCAI, Germany

###### Abstract

Equation of state for Bose-Einstein condensate is evaluated in two cases: non-interacting particles and particles interacting via potential possessing a non-trivial 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 quasi-black holes to galactic halo, followed by Bose-Einstein condensation in the intergalactic medium is considered.

#### Quantum superradiant entanglement of a bipartite system in Schwarzschild space-time

mohamed abdelouahab1

1University of M'sila - Mohamed Boudiaf - Algeria, physics department/ Physics and Chemistry of Materials Laboratory,, Algeria

###### Abstract

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.

#### Modeling the stratospheric aerosol sources optimal space distribution for climate stabilization

Valeriy Parkhomenko1

1The Federal Research Center "Computer Science And Control" of The Russian Academy Of Sciences, Bauman Moscow State Technical University, Dorodnicyn Computing Centre, Russian Federation

###### Abstract

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 three-dimensional 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.

#### On local solvability of the nonlinear integro-differential equation of peridynamics

Asal Yuldasheva1

1Tashkent branch of Moscow State University, applied mathematics and informatics, Uzbekistan

###### Abstract

The peridynamic theory is a nonlocal theory of continuum mechanics based on an integro-diﬀerential 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 well-posedness and smoothness of the solutions are discussed.

#### Holomorphic representation of the Calogero-Moser system

Ibrahim Nonkané1 , Duni Y. F. ZONGO2 , Latévi Lawson3 , ALIDA ZINSOU4

1Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
3African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
4Université THOMAS SANKARA, IUFIC, Burkina Faso

###### Abstract

In this note, we study the action of the Calogero-Moser 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.

#### Faceted-Rough Surface between Thermodynamically Rough and Atomically rough Surfaces

Noriko Akutsu1

1Osaka Electro-Communication University, Faculty of Engineering, Japan

###### Abstract

The faceted shape in a growing crystal is often observed in the materials which are necessary to sustain our daily life. The phase-field 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 sub-millimeter scale caused by the Mullins-Sekerka 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 phase-field modeling and the Mullins-Sekerka 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 nano-scale rough surface, though some of the atomically rough surfaces are thermodynamically smooth in equilibrium. Here, another scenario using the faceted-rough 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, 1--7.
[2] Tokairin, M.; Fujiwara, K.; Kutsukake, K.; Usami, N.; Nakajima, K. Phys. Rev. B, (2009), 80, 174108, 1--4.
[3] Mitani, T.; Komatsu, N.; Takahashi, T.; Kato, T.; Harada, S.; Ujihara, T.; Matsumoto, Y.; Kurashige, K.; Okumura, H. J. Cryst. Growth, (2015), 423, 45--49.
[4] Akutsu, N.; Akutsu, Y. J. Phys. Soc. Jpn., (1987), 56, 1443--1453.
[5] Akutsu, Y.; Akutsu, N.; Yamamoto, T. Phys. Rev. Lett., (1988), 61, 424--427.
[6] Akutsu, N. Sci. Rep., (2021), 11, 3711, 1-11.

###### Acknowledgements:

This work was supported by KAKENHI Grants-in-Aid (no. JP17K05503) from the Japan Society for the Promotion of Science (JSPS). This work was supported in part by the Collaborative Research Program (2020 S2-1, 2021 S3-5) of the Research Institute for Applied Mechanics, Kyushu University.

#### Variational synthesis of dynamical systems with elastic properties into element base

1ITMO University, Faculty of Control Systems and Robotics, Russian Federation
2ITMO University , , Russia

###### Abstract

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 sti ness. In solving a general conditional variation problem, the obtained di erential 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.

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#### Quadratic programming for estimating the intensity of intermittent emissions from a point source of air pollution

David Parra-Guevara1 , Yuri Skiba2

1National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico
2National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico

###### Abstract

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 well-posed 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. One-dimensional synthetic numerical examples demonstrate the capability of the method for estimating the intensity of intermittent emissions.

###### Acknowledgements:

This research was supported by the grants 25170 and 14539 of the National System of Investigators (SNI-CONACyT, México).

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