Search results for: ordinary differential equation

Authors: Jyoti Wadhwa, Arvinder Singh

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This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

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A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: annular fin, dehumidification, fin efficiency, heat and mass transfer, wet fin

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Authors: Toufic Abd El-Latif Sadek

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The Asphalt object represents the asphalted areas, like roads. The best original data of thermal images occurred at a specific time during the days of the year, by preventing the gaps in times which give the close and same brightness from different objects, using seven sample objects, asphalt, concrete, metal, rock, dry soil, vegetation, and water. It has been found in this study a general timing equation for capturing satellite thermal images at different locations, depends on a fixed time the sunrise and sunset; Capture Time= Tcap =(TM*TSR) ±TS.

Keywords: asphalt, satellite, thermal images, timing equation

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

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Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations

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Authors: Vandana N. Purav

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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials.

Keywords:

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Yousef Al-Qaryouti, Besan Alagawani

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The main concern of this study is to evaluate the effect of adding horizontal steel bracing system to ordinary moment resisting steel frames subjected to wind load. Similar frames without bracing systems are also to be compared. A general analytical study was carried out to obtain the influence of such system in resisting wind load. Linear static analysis has been carried out using ETABS software by applying fixed wind load defined according to ASCE7-10 for three-, six-, nine-, and twelve-story ordinary moment steel frame buildings including and not including horizontal steel bracing system. The results showed that the lateral drift due to wind load decreased by adding horizontal bracing system. Also, the results show that effect of such system is more efficient to low-rise buildings.

Keywords: horizontal bracing system, steel moment frames, wind load resisting system, linear static analysis

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Authors: Rana Daneshvar Salehi

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In many Iranian cities including ‎‎Mashhad‎, the capital of ‎‎‎‎Razavi Khorasan Province‏‎, ‎ordinary samples of domestic architecture ‎on a ‎‏small scale is not ‎‎‎considered as ‎heritage. ‎While the ‎principals of house formation are ‎‎respected in all ‎‎traditional Iranian ‎‎‎‎houses‎; ‎from moderate to great ones. During the past decade, Mashhad has lost its identity, and has become a modern city. Identifying it as the capital of the Islamic Culture in 2017 by ISESCO and consequently looking for new developments and transfiguration caused to demolish a large ‎number ‎of ‎traditional modest habitation. ‎For this ‎reason, the present paper aims to introduce ‎the three ‎undiscovered houses with the ‎historical and monumental values located in the ‎oldest ‎neighborhoods of Mashhad which have been neglected in the cultural ‎heritage field. The preliminary phase of this approach will be a measured survey to identify the significant characteristics ‎of ‎selected dwellings and understand the challenges through focusing on building ‎form, orientation, ‎‎room function, space proportion and ornamental elements’ details. A comparison between the ‎‎case studies and the wealthy domestically buildings ‎presents that a house belongs to inhabitants ‎with an average income could introduce the same accurate, regular, harmonic and proportionate ‎design which can be found in the great mansions. It reveals that an ordinary traditional house can ‎be regarded as valuable construction not only for its historical characteristics but also ‎for its ‎aesthetical and architectural features that could avoid further destructions in the future.

Keywords: traditional ordinary house, architectural characteristic, proportion, heritage

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Authors: Yanpei Zhen

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The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Jatindra Lahkar

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The effect of chemical reaction on laminar mixed convection flow and heat and mass transfer along a vertical unsteady stretching sheet is investigated, in the presence of heat generation/absorption with variable viscosity and viscous dissipation. The governing non-linear partial differential equations are reduced to ordinary differential equations using similarity transformation and solved numerically using the fourth order Runge-Kutta method along with shooting technique. The effects of various flow parameters on the velocity, temperature and concentration distributions are analyzed and presented graphically. Skin-friction coefficient, Nusselt number and Sherwood number are derived at the sheet. It is observed that the influence of chemical reaction, the fluid flow along the sheet accelerate with the increase of chemical reaction parameter, on the other hand, temperature of the fluid increases with increase of chemical reaction parameter but concentration of the fluid reduces with it. The boundary layer decreases on the surface of the sheet for all values of unsteadiness parameter, increasing values of the chemical reaction parameter. The increases in the values of Sc cause the species concentration and its boundary layer thickness to decrease resulting in less induced flow and higher fluid temperatures. This is depicted in the decreases in the velocity and species concentration and increases in the fluid temperature as Sc increases.

Keywords: chemical reaction, heat generation/absorption, magnetic number, unsteadiness, variable viscosity

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Abdulsamad Qadir Hussien

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The development of new technology in recent years has offered ordinary people various online digital platform tools and internet access to provide news stories, information, and subjects of public interest in the Kurdistan Region Government-Iraq (KRI). This shifting aspect has offered more chances for ordinary people to engage with other individuals on many issues in order to discuss and argue matters relating to their everyday lives. The key purpose of this research project will examine the role of citizen journalism in the increase of public awareness in the Kurdish community in the KRi; particularly, citizen journalism provides a new opportunity for ordinary people to raise their voices about problems and public matters in the KRI. The sample of this research project encompasses ordinary people who use social media platforms as sources of information and news concerning the KRI government policy. In the research project, the focus is on the ordinary people who are interacting with the blogs, posts, and footage that are produced by citizen journalism. The questionnaire was sent to more than 1,000 participants in the Kurdish community; this aspect produces statistically acceptable numbers to obtain a significant result for this research project. The sampling process is mainly based on the survey method in this study. The online questionnaire form includes many sections, which are divided into four key sections. The first section contains socio-demographic questions, including gender, age, and level of education. The research project applied the survey method in order to gather data and information surrounding the role of citizen journalism in increasing awareness of individuals in the Kurdish community. For this purpose, the researcher designed a questionnaire as the primary tool for the data collection process from ordinary people who use social media as a source of news and information. During the research project, online questionnaires were mailed in two ways – via Facebook and email – to participants in the Kurdish community, and this questionnaire looked for answers to questions from ordinary people, such as to what extent citizen journalism helps users to obtain information and news about public affairs and government policy. The research project found that citizen journalism has an essential role in increasing awareness of the Kurdish community, especially mainstream journalism has helped ordinary people to raise their voices in the KRI. Furthermore, citizen journalism carries more advantages as digital sources of news, footage, and information related to public affairs. This study provides useful tools to fore the news stories that are unreachable to professional journalists in the KRI.

Keywords: citizen journalism, public awareness, demonstration and democracy, social media news

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Dorit Lemberger

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Wittgenstein directly used the term "metaphor" only infrequently and with reservations, but his writings include a number of metaphors that have become imprinted in the philosophical memory of Western thought. For example, the ladder in his book Tractatus, or in Philosophical investigations - the ancient city, the beetle in a box, the fly in the fly-bottle, and the duck-rabbit. In light of Wittgenstein's stressing, throughout his investigations, that the only language that exists is ordinary language, and that there is no "second-order" language, the question should be asked: How do these metaphors function, specifically, and in general, how are we to relate to language use that exceeds the normal? Wittgenstein did not disregard such phenomena, but he proposed viewing them in a different way, that would enable understanding them as uses in ordinary language, without necessarily exceeding such language. Two important terms that he coined in this context are "secondary sense" and "experience of meaning". Each denotes language use as reflective of a subjective element characteristic of the speaker, such as intent, experience, or emphasis of a certain aspect. More recent Wittgenstein scholars added the term "quasi-metaphor", that refers to his discussion of the possibility of aesthetic judgment. This paper will examine how, according to Wittgenstein, these terms function without exceeding ordinary language, and will illustrate how they can be applied, in an analysis of the poem "Butterfly" by Nelly Sachs.

Keywords: metaphor, quasi-metaphor, secondary sense, experience of meaning

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Qinghua Zhang, Yanhe Zhu, Xiang Zhao, Yeqin Yang, Hongwei Jing, Guoan Zhang, Jie Zhao

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This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Keywords: cable-driven, differential actuated joints, reconfigurable, supernumerary robotic limb

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Authors: Olukunle C. Olawole, Dilip Kumar De

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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Dede Basturk, Metin Kaya, Halil Taskin, Nurtekin Erkmen

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In total, 29 students studying in Selçuk University Physical Training and Sports School who are recreationally active participated voluntarilyin this study which was carried out in order to examine effects of Vertimax trainings on agility, quickness and acceleration. 3 groups took their parts in this study as Vertimax training group (N=10), Ordinary training group (N=10) and Control group (N=9). Measurements were carried out in performance laboratory of Selçuk University Physical Training and Sports School. A training program for quickness and agility was followed up for subjects 3 days a week (Monday, Wednesday, Friday) for 8 weeks. Subjects taking their parts in vertimax training group and ordinary training group participated in the training program for quickness and agility. Measurements were applied as pre-test and post-test. Subjects of vertimax training group followed the training program with vertimax device and subjects of ordinary training group followed the training program without vertimax device. As to control group who are recreationally active, they did not participate in any program. 4 gate photocells were used for measuring and measurement of distances was carried out in m. Furthermore, single gate photocell and honi were used for agility test. Measurements started with 15 minutes of warm-up. Acceleration, quickness and agility tests were applied on subjects. 3 measurements were made for each subject at 3 minutes resting intervals. The best rating of three measurements was recorded. 5 m quickness pre-test value of vertimax training groups has been determined as 1,11±0,06 s and post-test value has been determined as 1,06 ± 0,08 s (P<0,05). 5 m quickness pre-test value of ordinary training group has been determined as 1,11±0,06 s and post-test value has been determined as 1,07±0,07 s (P<0,05).5 m quickness pre-test value of control group has been determined as 1,13±0,08 s and post-test value has been determined as 1,10 ± 0,07 s (P>0,05). Upon examination of 10 m acceleration value before and after the training, 10 m acceleration pre-test value of vertimax training group has been determined as 1,82 ± 0,07 s and post-test value has been determined as 1,76±0,83 s (P>0,05). 10 m acceleration pre-test value of ordinary training group has been determined as 1,83±0,05 s and post-test value has been determined as 1,78 ± 0,08 s (P>0,05).10 m acceleration pre-test value of control group has been determined as 1,87±0,11 s and post-test value has been determined as 1,83 ± 0,09 s (P>0,05). Upon examination of 15 m acceleration value before and after the training, 15 m acceleration pre-test value of vertimax training group has been determined as 2,52±0,10 s and post-test value has been determined as 2,46 ± 0,11 s (P>0,05).15 m acceleration pre-test value of ordinary training group has been determined as 2,52±0,05 s and post-test value has been determined as 2,48 ± 0,06 s (P>0,05). 15 m acceleration pre-test value of control group has been determined as 2,55 ± 0,11 s and post-test value has been determined as 2,54 ± 0,08 s (P>0,05).Upon examination of agility performance before and after the training, agility pre-test value of vertimax training group has been determined as 9,50±0,47 s and post-test value has been determined as 9,66 ± 0,47 s (P>0,05). Agility pre-test value of ordinary training group has been determined as 9,99 ± 0,05 s and post-test value has been determined as 9,86 ± 0,40 s (P>0,05). Agility pre-test value of control group has been determined as 9,74 ± 0,45 s and post-test value has been determined as 9,92 ± 0,49 s (P>0,05). Consequently, it has been observed that quickness and acceleration features were developed significantly following 8 weeks of vertimax training program and agility features were not developed significantly. It is suggested that training practices used for the study may be used for situations which may require sudden moves and in order to attain the maximum speed in a short time. Nevertheless, it is also suggested that this training practice does not make contribution in development of moves which may require sudden direction changes. It is suggested that productiveness and innovation may come off in terms of training by using various practices of vertimax trainings.

Keywords: vertimax, training, quickness, agility, acceleration

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: Lukas Vierus, Thomas Schuster

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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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