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In physics and mathematics educational environments, meaningful learning paths should be balanced interactive explorations of the different epistemological and cognitive phases of the modelling cycle. Our approach in this context involves sequences of interactive engagement learning activities with computational modelling that explore the different kinds of modelling, progressively introduce scientific computation, generate, and resolve cognitive conflicts in the understanding of physics and mathematics, and comparatively analyze complementary mathematical model representations. In this work we present a learning sequence about light polarization for intermediate science, technology, engineering, and mathematics (STEM) university courses during which students can create and explore in the computer relevant mathematical physics models and animations that help and complement the learning processes in theoretical lectures and problem-solving paper and pen activities. [ABSTRACT FROM AUTHOR]

By using the direct method, we create precise travelling wave solutions to the loaded nonlinear Degasperis-Procesi equation in this article. It has been proven that this method works well for locating these precise solutions. We construct exact travelling wave solution for loaded nonlinear Degasperis-Procesi equation. For specific values of the parameters, the traveling wave solutions of this equation lead directly to the solitary wave solutions. The Matlab program has been used to perform all calculations. The method offers a very efficient and straightforward way to formulate the precise travelling wave solutions to nonlinear wave equations appearing in mathematical physics and engineering, according to our results. [ABSTRACT FROM AUTHOR]

This research has been carried out to obtain the overviews of critical thinking questions found due to theoretical and mathematical physics topics found in senior high school physics textbooks. This research is a descriptive research, in which the data was collected through observation by doing document analysis and interviews. Observation was done to physics textbooks currently used in Indonesia, i.e. physics textbooks which have passed the assessment of the national education standard body (BSNP), that are regulated by the Decree of Education and Culture Minister 148/P/2016 on Determination of the Titles of Textbooks for Specialization Courses at Senior High Schools Level. The interviews were done with teachers and students enrolled at tenth, eleventh, and twelfth grades of a senior high school in Bandung District in academic year of 2020/2021. The interviews were oriented to reveal the physics topics that are considered to be theoretical and mathematical by teachers and students. Critical thinking analysis to questions found in physics textbooks was based on the critical thinking indicators developed by Tiruneh et al (2016). Based on the data analysis, it was found that: 1) tenth grade physics topics which are considered to be theoretical and mathematical are vectors, two dimensional motion, and harmonic oscillation, 2) eleventh grade physics topics which are considered to be theoretical and mathematical are kinetic theory of gases, thermodynamics, and light, 3) twelfth grade physics topics which are considered to be theoretical and mathematical are theory of relativity, quantum phenomena, as well as atom and radioactivity, 4) the availability of critical thinking questions (CTQs) in such theoretical and mathematical physics topics found in the physics textbooks in Indonesia is relatively minimum, 5) CTQs mostly found in every physics textbook are CT questions dealing with the aspect of likelihood and uncertainty analysis, especially for indicator of predicting the probability of event, and 6) CTQs dealing with the aspect of problem-solving and decision-making were not found in all physics textbooks. [ABSTRACT FROM AUTHOR]

This paper attempts to obtain generating functions for the polynomials defined by Chebyshev denoted as Tn (x) (Special Ultra Spherical Polynomials of the first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn (x) are used as matching points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly, including filters in signal processing distributed networks. [ABSTRACT FROM AUTHOR]

Viscoelastic sloping multilayer structures with filler have found their application in aircraft construction, construction, design of space structures and other areas. The free vibrations of two flat spherical viscoelastic shells, between which it is filled with a deformable filler, are investigated in the work. The main purpose of the article is to develop a scientific basis for constructing a method for solving the problem, and an algorithm for natural oscillations of spherical shells with a filler. Parametric analysis of the natural frequency of the physical and mechanical parameters of the mechanical system is also carried out. As an example, linear natural oscillations of three-layer structures for shells of free support are considered. The shell materials are isotropic and have identical rheological properties, as well as asymmetric in shell thickness. The viscoelastic properties of the shell and filler materials are subject to the integral Boltzmann-Voltaire relations. The oscillation equations of the filler satisfy the Lame equations of visco-elasticity. And the shell equation is derived on the basis of the Kirchhoff-Love theory. The developed methodology is based on the method of separation of variables, special functions of mathematical physics, the methods of Muller, Gauss and Laplace. It is found that the real and imaginary parts of the natural frequencies increase with increasing stiffness of the shell. Taking into account the viscoelastic properties of the shells and the filler allows to increase the free frequency fluctuations up to 15-20%. [ABSTRACT FROM AUTHOR]

In the present note we consider the Laplacian of the "Analytical" vector functions (AVF). The notion of Analytical vector function was introduced by the author in previous publications. In these publications appeared a new idea of what should be the Laplacian of AVF. Here is considered the classical Laplacian of AVF. Then we consider some applications in mathematical physics. [ABSTRACT FROM AUTHOR]

Distribution function seems be the most full analytical description of any stochastic process. Distribution function for multiple Coulomb scattering for infinite and uniform medium had been obtained at the first half of the last century. We have used it successfully for the dynamics exploration of the beam crossing thin foil normally to its surface. The function mentioned cannot be used directly for the case of the foil installed at some angle to the beam direction of propagation. In mathematical sense, this case is already new problem and new analytical solution is required. To find out the analytical solution for this case, partial differential equation with appropriate boundary conditions must be solved. As it takes place for the majorities of the mathematical physics problems, the exact analytical solution in this specific case is unavailable. We tried to find a different approach searching for approximate solution of boundary problem based on exact solution for infinite scattering. The paper describes the flow lines model for multiple Coulomb scattering that results in analytical explanations of different phenomena taking place in the case of beam incline incidence on the border separating vacuum and scattering medium [ABSTRACT FROM AUTHOR]

In this work we have analyzed the physics Concept Inventory (CI) scores and knowledge shortcomings in high school students, considering detrimental effects of the full-scale online learning due to the pandemic closure. This examination is performed through descriptive analysis based on the Force Concept Inventory approach and empirical modeling, by using the outcomes of dedicated tests which we conducted in various conditions and students' groups. Initially, we have assessed the CI scores and student's ability to answer the test by employing the Rasch technique, and next we have examined influential factors and their features, from a general methodical approach. In this regard, we have evidenced the non-decisiveness of mathematical (calculus) knowledge incapacities on physics knowledge failures and have employed this fact to confirm the conceptual knowledge failures as key concern linked with physics exam's unsatisfactory outcomes. It is used also to qualify the shortage on mathematics classes attendances as an independent factor in the modeling stage. Next, by considering the nature of the most frequent errors observed and dynamical properties of CI scores, the insufficiency on laboratory work, practices and demonstrations support for physics learning is identified as another important factor for conceptual knowledge failures observed. The teaching effectiveness issues, which herein is associated with communication technology performance and adaptiveness of teachers and students with online activities, has been investigated specifically, as another key factor. So, the procedural tests' faults are decomposed in conceptualization errors and calculus errors and all tests' shortcomings are classified corresponding to the resulting four error states. The estimation hereto is based on the Likert technique analysis. The findings of this step are interpreted in terms of the Force Concept Inventory analysis and six common misconceptions in Newtonian mechanics. Following those observations, this factor is recognized as an independent variable too, and for modeling purpose it has been embodied in a "location" variable based on the school's city ranking. Other expected influential factors, the attendance in physics and mathematics classes during online learning, the school type and category, and students' preference for physics, are analyzed simply in the stage of the modeling regression. Those factor variables used in linear and logistic model discussed hereto are taken categorical and their values have been assigned by simple conventions explained on the text, whereas their weightiness on the knowledge indicator variable is estimated directly from the regression. Next, using the predicted value for students' ability to solve a CI test, we proposed some variable configuration scenarios to allocate optimal strategies, which is defined herein as education activities that increase student's ability to solve a standard test, and keep difficulties unaffected or even improve them. We argued that within some extension, several findings of this work can be used more generally for similar system. [ABSTRACT FROM AUTHOR]

In this paper the correspondences between electromagnetic and fluid dynamic elements of many authors have been studied in detail, using the mathematical tool-geometric algebra. The physical as well as topological properties of the components are then analysed. Studying the different analogies indeed help to have a clear and compact visualisation of both fields and thus to understand the nature of their field mechanisms. The use of geometric algebra within mathematical physics, further envisages geometrical meaning as well as the physical interpretation of mathematical elements. [ABSTRACT FROM AUTHOR]

The present article presents a detail theoretical study of the hydrodynamics boundary layer generated over a flat plate considering laminar, transition and turbulent regions. The importance of Reynolds number within the boundary layer and how it plays a major role for the heat and fluid flow has been discussed thoroughly this article. The corner stone equations of heat and fluid flow has been presented which they are the three physics laws; mass, energy and momentum of fluid. In the subsequent sections the basic concept of the boundary layer characteristics likes displacement, momentum and energy thickness are discussed. A separate section for deriving momentum integral equation and various relations of drag, rate of growth of each layer have been presented from this equation. In this work authors have focused in the transition region which plays a crucial role in both heat transfer and fluid flow phenomenon and there are limitations in explaining this region and most of the previous published work describes only on the laminar and turbulent region without considering the transition zone. Hence the present work provides a comprehensive analysis for this region. The boundary layer thickness, drag and drag coefficient for the transition zone derived mathematically. [ABSTRACT FROM AUTHOR]

Advancements in the field of physics gave birth to remote sensing for analyzing climate problems effectively and smoothly in form of providing vulnerable and significant data. Mathematics and statistics play a pivot role in the succeeding domains to cater to data analysis in a structured and lucid manner. This paper incubates a climate-related study with the help of enrichments in mathematics and physics. The paper states clearly all about the temperature profile of an Indian city, Ajmer. The incorporation of data from 2011 to 2020 depicts a good picture of land skin temperature as a result. Duo-Satellite imageries of ten years had been examined carefully and software-derived data was acted upon by mathematical analysis to find a pattern meticulously. Significant findings were that the summer season was found out the hottest among all the seasons during both day and night time. The winter season had the least anomalies and the monsoon had the most. The paper and its findings were showed alarming information about the gradual rise in temperature which will create a difficult situation in near future for human beings. [ABSTRACT FROM AUTHOR]

Currently the problem of researching the thermal effect of an electron beam on through-target material, and also researching the physical limitations for maximum power value of microfocus X-ray tubes is relevant. Experimental research of anode thermal operation modes in transmission-type targets of microfocus X-ray tubes is a complex task. The use of modern software systems capable of numerically simulating problems of mathematical physics makes it possible to obtain results that are acceptable in terms of their accuracy. In this paper used a mathematical model developed in the COMSOL Multiphysics 5.4, which makes it possible to simulate heat transfer processes in solids under the conditions of conjugate heat transfer. [ABSTRACT FROM AUTHOR]

Technology integration has been applied in the industrial world for the production process, distribution, employment to worker training. The training in Vocational Education is expected to facilitate every learning with various technological transformations that develop. Engineering Mathematics and Engineering Physics are lessons that must be given to vocational students as a vocational basis. This study aims to explore the impact of using technology in vocational learning. This study uses qualitative research methods, with an emic approach. The theories used are: (1) Critical Theory from Max Horkheimer and Theodor W. Adorno regarding assumptions; (2) Technology Acceptance Model (TAM) theory regarding perceived usefulness and perceived ease of use; and (3) the concept of Ki Hadjar Dewantara's teachings about "ngerti", "ngroso" and "nglakoni". The results of this study are: (1) the integration of technology provides benefits to student learning activities seen from the critical theory that learning theory is not boring so that students become more active to take part in learning engineering mathematics and engineering physics; (2) the integration of technology in learning provides positive emotions for students in terms of the perceived benefits and perceived ease of use both from the software and hardware devices they have to solve problems in engineering mathematics and engineering physics; (3) technology integration benefits students' curiosity about "ngerti", "ngroso" and "nglakoni" according to the concept of Ki Hadjar Dewantara's teachings seen from seeing the lecturer in explaining the material, demonstrating software and hardware devices, viewing, remember and mark, and imitate implementation in everyday life. [ABSTRACT FROM AUTHOR]

In this paper, certain properties of newly defined generalized hypergeometric polynomials in two variables{Rn (β ;γ ; x, y)} have been derived, namely, recurrence relations of ascending and descending type, ordinarydifferential equation and linear generating function, which are essential to derive generating relations of various types from the group-theoretic method point of view. Furthermore, Laguerre polynomials of single and two variables, Meixner, Gottlieb and Krawtchouk polynomials are deduced as special cases, which arises in mathematical physics and communication engineering. [ABSTRACT FROM AUTHOR]

The paper considers a relatively simple method for creating interactive electronic models of physical systems that does not require programming and automatic generation of numerical models of complex physical systems. The created training models are available for use via the Internet and allow almost unlimited on-line editing by users. The options of using the created electronic models to support mass individualized learning and the organization of independent educational and scientific research of students are discussed. The development is based on the original method of physical object-oriented modeling (POOM), which is an application of traditional ideas of object-oriented programming to the problems of constructing and configuring numerical models of relatively complex physical systems. Within its framework, a computer model of a physical system is constructed as a set of software objects that model the behavior of its components relative to separate physical elements: particles and fields. The interaction between the elements of the model is described using self-adapting algorithms, the choice of which is set during the construction of the model, depending on the physical approximation used: classical or relativistic. An electronic designer of interactive models of physical systems, represented in the form of arbitrary aggregates of classical and relativistic particles interacting with each other and external fields, has been created on the basis of the POOM ideology and Java-Script technology. The possibility of using an electronic designer as a basis for students to conduct independent research work on the study of the physical properties of complex mechanical systems, the analysis of which goes beyond the standard programs in physics and mathematics, is tested. The heuristic capabilities of the models created with the help of an electronic designer are demonstrated. The electonic designer is focused on the development of a series of virtual physical models to support classroom and online courses in physics and the organization of independent creative work of students in the MOOC–education system. [ABSTRACT FROM AUTHOR]

A new closed solution of the coupled non-stationary problem of thermoelectroelasticity for a long piezoceramic radially polarized cylinder is constructed when the boundary conditions of the 1st kind of thermal conductivity are satisfied on its front surfaces. The case is considered when the rate of change of the temperature field does not affect the inertial characteristics of the elastic system, which makes it possible to include in the initial calculated relations of the problem under consideration the linear equations of equilibrium, electrostatics and thermal conductivity with respect to the radial component of the displacement vector, electric potential, as well as the function of changing the temperature field. The calculations use the classical Fourier law of thermal conductivity. To solve the problem, the mathematical apparatus of incomplete separation of variables is used in the form of a generalized biorthogonal finite integral transformation (CIF), based on a multicomponent relation of eigenvector-functions of two homogeneous boundary value problems. An important point in the procedure of the structural algorithm of this method is the selection of the adjoint operator, without which it is impossible to solve non-self-adjoint linear problems of mathematical physics. [ABSTRACT FROM AUTHOR]

The purpose of this research is to develop the method of shape coefficient interpolation for calculating the maximum deflection of thin plates on an elastic Winkler base, which are widely used in modeling the operation of elements of complex technical systems. The above calculation method allows to obtain solutions based on direct analytical dependences, the argument of which is an integral characteristic of a flat convex one-connected area - the shape coefficient. This characteristic has applications in a number of problems of mathematical physics and is known from the works of scientists G. Polia and G. Szegö. The shape coefficient was first applied to the calculation of plates by Professor V.I. Korobko. The method of interpolation by shape factor was developed by Professor A.V. Korobko. When determining the maximum deflection of thin plates on an elastic base, some parameters of the problem are considered as functions of the shape coefficient of the plate in consideration and are determined by the type of boundary conditions on its contour. The present study is devoted to the construction of approximating functions for continuous sets of plates of characteristic outlines and boundary conditions. The paper presents functions for calculating the maximum deflection of elastic plates in the form of isosceles triangles, rhombuses and rectangles. The plates with various combinations of hinged support and rigid pinch along their individual sides, loaded with a continuous uniformly distributed load, are considered. The established functional dependences are intended for direct use in the calculation of plates of the specified outlines, as well as for obtaining reference solutions during interpolation of the values of maximum deflections of plates of more complex outlines. [ABSTRACT FROM AUTHOR]

The article demonstrates the main aspects of the method of lines on the example of solving a one-dimensional parabolic equation. The transition to the grid functions is performed along the x coordinate when a boundary condition of the first type is imposed at the beginning of the segment, and a condition of the third type is imposed at the end of it at x = l, according to the statements of the method of lines. The ways of searching for eigenvalues and vectors of a tridiagonal matrix at various values of the complex αl are shown. With them, the transition to autonomous ordinary differential equations relative to new grid functions is performed. The ordinary differential equations derived are solved numerically. Formulas for the forward transition from the original grid function to the new sought-for function and the inverse transition are given. Comparison with the discontinuous solution of the test problem showed good agreement. The results can be used to solve multidimensional parabolic equations and one-and multidimensional equations of elliptic and hyperbolic types if mixed boundary conditions hold at least one of the coordinates. [ABSTRACT FROM AUTHOR]

Analysis of deformation processes in retaining walls of hydraulic structures requires the creation of fundamentally new methodologies and specialized equipment that will allow accurate measurement of various types of deformations: settlements, inclination of structures, angular displacements. During operation, the retaining walls are subjected to serious wave loads, the calculation and prediction of which is necessary for the design of the structures of berthing facilities, the conditions for mooring ships. To determine the characteristics of waves and wave processes, it is proposed to use the method of numerical modeling, which involves the formulation of a boundary value problem of mathematical physics and the development of a numerical solution to this problem. This method has been actively developing recently and is used to solve problems of determining wave loads and impacts on port hydraulic structures. On the basis of a mathematical model, a program is implemented that calculates the hydrodynamic processes occurring in channels of arbitrary shape, taking into account the Coriolis forces and friction. For the solution, the finite difference method (grid method) was used. As a result of applying this method, data are obtained that are convenient for plotting graphs. Also, the finite difference method is easy to program. Parallel programming methods can be easily applied to this code, which makes it possible to speed up the receipt of the result. Based on the model, the obtained data are compared with real hydrodynamic processes and conclusions are drawn. [ABSTRACT FROM AUTHOR]

This research is an initial study on student learning outcomes in the Mathematics Physics course. Mathematics Physics is a compulsory subject for the Physics Education Study Program, University of Muhammadiyah Makassar. Mathematical Physics examines the application of mathematics in solving physical phenomena. However, mathematical Physics is often considered difficult by students. Still, Mathematical Physics is essential because of its role as a provision for students to study advanced Physics courses, such as Mechanics, Optics, Waves, Electricity, and so on. Therefore, the search on the perception and acquisition of student learning outcomes in Mathematics Physics lectures is the basis for providing intervention for researchers through research and lessons in the selection of strategies, learning methods, and even the development of learning tools. This research is survey research. The way of data collection is through interviews with 14 fourth semester students of the Physics Education Study Program at the University of Muhammadiyah Makassar. The results of the study found that as many as 57,14% of students scored less than 70 (categories C, D, and E). this percentage gain is still far from the expected results in Mathematics Physics learning. In addition, the absence of learning tools that are following the characteristics of the Mathematics Physics course for Physics Education students also has an impact on the common understanding of students' Physics concepts. [ABSTRACT FROM AUTHOR]

In many problems of mathematical physics, theory of elasticity, visco-dynamics fluid and mixed problems of mechanics of continuous media reduces to the integral and intro-differential equation (Volterra or Fredholm type) first or second kind. In the early XXth (around 1910) century, to solve some problems in the field of mechanics Volterra had to solve integro-differential equations (IDEs) with variable boundaries. One of the popular methods for solving Volterra IDEs is the method of quadratures when problem of consideration is a linear problem. When IDEs are nonlinear or integral kernel are complicated (singular or nonlinear) then quadrature rule is not most suitable therefore other type of methods are needed to develop. In this note, we have used the standard and new-development of homotopy analysis method (ND-HAM) for the general second order linear integral-differential equations (IDEs) of the second kind. Both methods reduce IDEs into iterative sequence of algebraic integral equations with known integrant function. Gauss-Legendre quadrature formulas are applied for kernel integrations. Obtained system of algebraic equations are solved numerically. Moreover, numerical examples demonstrate the high accuracy of the proposed method. Comparisons with other methods are also provided. The results show that the proposed method is simple, effective and reliable. [ABSTRACT FROM AUTHOR]

Integration and integral transforms are playing an important role in various branches of applied mathematics and physical sciences. In the present article, first we define modified I-function of two variables and after that we will set up and prove two double integral formulas involving a product of I-function with two other special functions. In the last, we have given some integral transforms of these two double integral formulas and it is our belief that the results derived in this paper are new in literature. [ABSTRACT FROM AUTHOR]

Energy efficiency of the modern motor cars is its most significant property and is turned into main efforts of all automakers. These trends lead to producing the alternative solution as the perspective hybrid electric vehicles (HEV). The HEV use energy from more than one sources, mainly from internal combustion engine (ICE) and electric motor (EM) through the battery set which led to improving the energy efficiency The HEV energy efficiency (HEVEE) consists of the HEV fuel consumption and electricity consumption, as well as the electricity regenerated and re-used again to propel the HEV. The analytical researching of the HEVEE represents the fuel and electricity consumption by the analytical equations and graphs which is obtained by the HEVEE modelling. The input parameters of the analytical researching are according to specific HEV model and certain HEV modes of driving and road conditions. The HEVEE model process these input data according to physics laws and mathematical dependencies. After the calculation is obtained the output results in form of numerical values and graph characteristics. These output data represent the analytical researching evaluation of the HEVEE. [ABSTRACT FROM AUTHOR]

Mathematics contributes an important role in science that provides the basis for the logic of human thinking. This study was a survey to know the influence of learning discipline and mastery of mathematical concepts on physics learning outcomes of high school students, either directly or indirectly, with 180 public high school students in South Jakarta as the research sample. The research data used test questions to understand mathematical concepts and physics learning outcomes, while the learning discipline data used a questionnaire with a Likert scale. The data obtained were tested for validity and reliability and analyzed using software tools for partial least squares, structural equation modeling (PLS-SEM). The analysis results prove that there was a direct effect of learning discipline and mastery of mathematical concepts towards learning outcomes of physics, student learning discipline on mastery of mathematical concepts, and an indirect effect of learning discipline on learning outcomes of physics through mastery of mathematical concepts. Based on research, understanding and mastering mathematical concepts is a prerequisite for achieving maximum physics learning outcomes. [ABSTRACT FROM AUTHOR]

It is a spherical body located in the natural vibrations of the same-sex systems, that is, in a deformed viscoelastic environment. The main emphasis is on the study of low-contrast inhomogeneitlarni in the viscoelastic environment. Deformation the issue of radial, torsional and spherical vibrations of spherical bonds is considered in an infinite viscoelastic environment. In the viscoelastic environment, the theory and methods of calculating complex natural frequencies and oscillatory patterns of viscoelastic spherical inhomogeneity are created. Such vibrations carry out radial, torsional and spheroidal classification. In the viscoelastic environment, frequency-transcendental equations of spherical inhomogeneity are formed. The general solution of the vector equation of motion of the three-dimensional theory of viscoelasticity in the displacement potentials of a spherical coordinate system is used. With the help of special functions of mathematical physics of Bessel, Hankel and Legendre, the Muller method and the Gauss method, an algorithm for solving computer problems is developed. Based on the constructed complex frequency equations with complex input parameters, numerical results are obtained. The considered problems were reduced to finding those complex eigenfrequencies at which the system of equations of motion of a spherical inclusion with shortened radiation conditions has a non-zero solution in the class of infinitely differentiable functions. Detailed numerical calculations of the complex eigenfrequencies of three modes of radial, torsional, and spheroidal oscillations of spherical inhomogeneities in an infinite viscoelastic medium are performed. It is shown that the problem has a discrete complex spectrum. It is found that the eigenfrequencies of spheroidal oscillations of low-contrast inhomogeneities are divided into two groups: radially similar and torsion-like. Due to the fact that the imaginary part of the natural frequency is large, it is established that low-frequency natural oscillations occur at certain values of the viscosity density parameters. The results obtained allow to predict the dispersion of viscoelastic (or seismic) waves in deformed environments with the participation of inclusions. [ABSTRACT FROM AUTHOR]

The problem of radial, torsional, and spheroidal vibrations of a deformable spherical inclusion in an infinite viscoelastic medium is considered. With the help of special functions of mathematical physics of Bessel, Hankel and Legendre, the Muller method and the Gauss method, an algorithm for solving the problem on a computer is developed. Based on the constructed complex frequency equations with complex output parameters, numerical results are obtained. The considered problems were reduced to finding those complex eigenfrequencies at which the system of equations of motion of a spherical inclusion with shortened radiation conditions has a non-zero solution in the class of infinitely differentiable functions. Detailed numerical calculations of the complex eigenfrequencies of three modes of radial, torsional, and spheroidal oscillations of spherical inhomogeneities in an infinite viscoelastic medium are performed. It is shown that the problem has a discrete complex spectrum. It is found that the eigenfrequencies of spheroidal oscillations of low-contrast inhomogeneities are divided into two groups: radially similar and torsion-like. It is revealed that at certain values of the viscoelastic density parameters, low-frequency natural oscillations occur, which are essentially some aperiodic motion, since the imaginary part of the natural frequency is large. The results obtained will allow us to predict the scattering of viscoelastic (or seismic) waves in deformable media in the presence of an inclusion. [ABSTRACT FROM AUTHOR]

In the article "Struggling with physics and mathematics curricula based on the notion of function in the context of the educational reform in Poland" (AIP Conf. Proc. 2152; 2019) we analyzed the phenomenon of the lack of correlation between mathematics and physics teaching in the context of the concept of function. It is now taught the secondary school level of mathematics, but is also needed in the teaching of kinematics at the elementary school level of physics. In this paper, we present the chosen results of a pilot pedagogical remote-teaching experiment to provide a preliminary answer to several research questions on this issue: Does the attempt to integrate mathematics and physics have an impact on the understanding of functional relationships in a physics context? Specifically, does the introduction of a propaedeutic of the concept of function in mathematics lessons have an impact on the understanding and ability of analyzing motion? Similarly, do additional lessons on motion analysis affect the proficiency in representing, reading, and interpreting functional relationships? How do students process information about functional relationships in a physical context presented in a variety of representations? Is an elementary school student's intuitive understanding of the concept of functions enough to understand the analysis of motion in physics? What role do the remote experiments performed during the lesson play in learning new issues related to the concept of function in the context of motion analysis? [ABSTRACT FROM AUTHOR]

Experiment is a key element not only for physics as science, but also for physics education. Even though research attention has been lately focused more on students' hands-on experiments in inquiry-based science education, demonstration experiments still play an important role in today's education. Department of Physics Education (Charles University, Faculty of Mathematics and Physics) has been performing physics demonstrations for secondary education students for more than 30 years. Seven different topics are currently offered by the Department. A survey conducted in years 2017/18 on a population of est. 5,100 students showed that the students' perception varies quite significantly, depending on specific topic, especially considering their intrinsic motivation and subjectively perceived value and usefulness of a given topic. The questions at hand are whether parameters that influence students' perception in negative or positive way do exist and how they are related to the choice of the experiments themselves or the lecturer's work with the audience. The study presented in our contribution focuses on the last of these aspects, i.e. the role of audience-lecturer interaction in students' perception of physics demonstrations. We present a category-based video study conducted on video recordings of all seven aforementioned topics of physics demonstrations, its results and interpretation. Our results show that lecturer's approach to interaction with students and usage of AV technology strongly varies topic by topic; the possible link between this diversity on one hand and the diverse students' perception of particular topics on the other hand will be inspected in a follow-up research. [ABSTRACT FROM AUTHOR]

The Fredholm integral equations (FIEs) II kind describe as the most versatile areas of study in history in which being utilized in various fields such as biology, chemistry, engineering, mathematics and physics. Thus, several numerical methods have been imposed to discretize the mentioned equations in order to get their corresponding approximation equations. In this article, the first-order piecewise polynomial collocation scheme and first-order Quadrature method have been put in order to derive the first-order quadrature-piecewise collocation approximation equation via the discretization process. The approximation equation eventually developed a dense linear system. To get the quadrature-piecewise collocation solution of this linear system, we also ascertain the performance of Extrapolated Successive Over-Relaxation (ESOR) iterative method applied to this dense linear system. Therefore, the formulation and application of iterative methods as described are also presented. Based on the numerical computational derived from the first-order quadrature-piecewise collocation approximation equation, it shows that ESOR iteration has significantly least computational efforts in terms of number of iterations and CPU time when compared with Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) iterative schemes. [ABSTRACT FROM AUTHOR]