Search results for: population balance equations

Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: T. Hirata, M. G. Silva, L. M. Rosa

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The balance ability during task kick in soccer is a determining factor in the execution of functional movements that require a high-performance motor coordination. The current experiment explored it during an instep soccer kick and functional task kicking. Their kicking performance was measured in terms of the sway characteristics using lateral and antero-posterior balance of the center of pressure (COP) for the supporting leg and the kinematic data, the supporting leg’s knee angle. The motion was realized with one-legged stance of five male indoor soccer players and using the trigger device ball controller. The results showed large balance in antero-posterior direction than in lateral direction. However, each player adopts a different way to kick the ball, and the media-lateral displacement of the COP showed no correlation with the balance skill.

Keywords: kicking performance, center of pressure, one-legged stance, balance ability

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Astghik R. Sukiasyan

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Under the drought stress condition, the plants would grow slower. Temperature is one of the most important abiotic factors which suppress the germination processes. However, the processes of transpiration are regulated directly by the cell water, which followed to an increase in volume of vacuoles. During stretching under the influence of water pressure, the cell goes into the state of turgor. In our experiments, lines of the semi-dental sweet maize of Armenian population from various zones of growth under mild and severe drought stress were tested. According to results, the value of the water balance of the plant cells may reflect the ability of plants to adapt to drought stress. It can be assumed that the turgor allows evaluating the number of received dissolved substance in cell.

Keywords: turgor, drought stress, plant growth, Armenian Zea Maize Semidentata

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Authors: J. W. Kim, Y. R. Kwon, Y. J. Ho, H. M. Jeon, G. M. Eom

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The aim of this study was to investigate the association of anthropometry with static balance in the elderly and their possible gender difference. Forty six subjects (23 men and 23 women) participated in this study. COP (Center of Pressure) was measured on a force-platform during quiet feet-together standing. As outcome measures, mean distance were derived from the COP. Weight was significantly correlated with postural variable only in the elderly men. This result suggests that the gender should be considered when normalizing postural variables.

Keywords: body characteristics, postural balance, elderly, gender difference

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Authors: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

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The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Baghdad Said

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Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces.

Keywords: SFDE, SD, UHRS, MNCs, FPT

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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Authors: Matevž Breška, Iztok Peruš, Vlado Stankovski

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Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database, peak ground acceleration

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Nawal A. Abu-Shady, Ibrahim M. I. Hamoda, Ahmed R. Z. Baghdadi, Mohammed K. Mohamed

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Background: The aim of this work was to investigate the efficacy of Transcranial Magnetic Therapy (TMT) on balance in hemiparetic stroke patients. It was conducted in outpatient clinic and in BIODEX balance system lab in Faculty of Physical Therapy, Cairo University. Subjects and Methods: Thirty hemiparetic stroke patients from both sexes represent the sample of this study. The patients' ages ranged from 45 to 55 years. They were assigned randomly into two equal groups; the study group (GA) and the control group (GB). control group treated by selected therapeutic physical therapy program. GA treated by the same program of treatment as the GB in addition to TMT. The duration of treatment was six weeks, three times weekly.day after day. The different aspects of dynamic balance (overall stability, anteroposterior stability and mediolateral stability indices) were assessed pre and post treatment objectively by Biodex balance system and clinically by Short Form of Berg Balance Scale (SFBBS) in both groups. Results: Comparison of each variable pre and post treatment in each group revealed a significant improvement in all different parameters in both groups ( p < 0.01), however comparison between post results revealed that the GA showed a high significant improvement higher than the GB in all different variables.

Keywords: stroke, TMT, SFBBS, biodex balance system

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Authors: Jiashu Shen

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Objectives: Spirometry is a basic reference for health evaluation which is widely used in clinical. Previous reference of spirometry is not applicable because of drastic changes of social and natural circumstance in China. A new reference values for the spirometry of the Chinese population is extremely needed. Method: Spirometric reference value was established using the statistical modeling method Generalized Additive Models for Location, Scale and Shape for forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), FEV1/FVC, and maximal mid-expiratory flow (MMEF). Results: Data from 236,606 healthy non-smokers aged 4–90 years was collected from the MJ Health Check database. Spirometry equations for FEV1, FVC, MMEF, and FEV1/FVC were established, including the predicted values and lower limits of normal (LLNs) by sex. The predictive equations that were developed for the spirometric results elaborated the relationship between spirometry and age, and they eliminated the effects of height as a variable. Most previous predictive equations for Chinese spirometry were significantly overestimated (to be exact, with mean differences of 22.21% in FEV1 and 31.39% in FVC for males, along with differences of 26.93% in FEV1 and 35.76% in FVC for females) or underestimated (with mean differences of -5.81% in MMEF and -14.56% in FEV1/FVC for males, along with a difference of -14.54% in FEV1/FVC for females) the results of lung function measurements as found in this study. Through cross-validation, our equations were established as having good fit, and the means of the measured value and the estimated value were compared, with good results. Conclusions: Our study updates the spirometric reference equations for Chinese people of all ages and provides comprehensive values for both physical examination and clinical diagnosis.

Keywords: Chinese, GAMLSS model, reference values, spirometry

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Authors: Abubakar Sadiq Mensah

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The Knowledge of the population growth of a nation is paramount to national planning. The population of a place is studied and a model developed over a period of time, Matrices is used to form model for population growth. The eigenvalue ƛ of the matrix A and its corresponding eigenvector X is such that AX = ƛX is calculated. The stable age distribution of the population is obtained using the eigenvalue and the characteristic polynomial. Hence, estimation could be made using eigenvalues and eigenvectors.

Keywords: eigenvalues, eigenvectors, population, growth/stability

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Authors: Yousef S. Kh. S. Hashem

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Accurate estimation of initial gas in place (IGIP) plays an important factor in the decision to develop a gas field. One of the methods that are available in the industry to estimate the IGIP is material balance. This method required that the well has to be shut-in while pressure is measured as it builds to average reservoir pressure. Since gas demand is high and shut-in well surveys are very expensive, flowing gas material balance (FGMB) is sometimes used instead of material balance. This work investigated the effect of reservoir properties (pressure, permeability, and reservoir size) on the estimation of IGIP when using FGMB. A gas reservoir simulator that accounts for friction loss, wellbore storage, and the non-Darcy effect was used to simulate 165 different possible causes (3 pressures, 5 reservoir sizes, and 11 permeabilities). Both tubing pressure and bottom-hole pressure were analyzed using FGMB. The results showed that the FGMB method is very sensitive for tied reservoirs (k < 10). Also, it showed which method is best to be used for different reservoir properties. This study can be used as a guideline for the application of the FGMB method.

Keywords: flowing material balance, gas reservoir, reserves, gas simulator

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Authors: Ghada Mohamed Rashad, Doaa Ayoub Elimy, Mohamed Hussein Elgendy, Ahmed Mohamed Fathi Elshiwi, Mahmoud Ghazy

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Background: Flat feet cause changes in foot mobility, foot posture, and load distribution under the foot which influences dynamic balance, that is essential in activities of daily living and for optimal performance in sports activity. Purpose: To investigate the effect of flat feet on dynamic balance including overall stability index (OAI), anteroposterior stability index (APSI) and mediolateral stability index (MLSI). Study Design: The design of the study was an experimental design. Subjects: Forty subjects from both sexes were selected from the Faculty of Physical Therapy, Cairo University, their mean age (23.55 ± 1.74 ) years, divided into two groups, group A (8 males and 12 females) with flat feet, and group B (9 males and 11 females) with normal feet. Methods: The Navicular Drop Test was used to determine if the feet were pronated and Biodex Balance System was used to assess dynamic balance at level 8 and level 4 for both groups. Results: There was no significant difference in dynamic balance including (OSI, APSI and MLSI) of the Biodex at stability level (8) (most stable) (p = 0.56). While there was a significant difference between both groups in all dependent variables at stability level (4) (less stable level) (p = 0.0001). Conclusion: It may be concluded that flat feet have an effect on dynamic balance and there is balance affection in subjects with flat feet.

Keywords: flat feet, dynamic balance, postural stability, types of flat feet, eversion strength

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Authors: Badriah Alayidi, Emad Alyahya

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Background: Most people with Multiple Sclerosis (MS) report worsening balance as the condition progresses. Poor balance control is also well known to be a significant risk factor for both falling and fear of falling. The increased risk of falls with disease progression thus makes balance control an essential target of gait rehabilitation amongst people with MS. Intervention programs have developed various methods to improve balance control, and accumulating evidence suggests that exercise programs may help people with MS improve their balance. Among these methods, virtual reality (VR) is growing in popularity as a balance-training technique owing to its potential benefits, including better compliance and greater user happiness. However, it is not clear if a VR environment will induce different balance control mechanisms in MS as compared to healthy individuals or traditional environments. Therefore, this study aims to examine how individuals with MS control their balance in a VR setting. Methodology: The proposed study takes an empirical approach to estimate and determine the role of balance response in persons with MS using a VR environment. It will use primary data collected through patient observations, physiological and biomechanical evaluation of balance, and data analysis. Results: The preliminary systematic review and meta-analysis indicated that there was variability in terms of the outcome assessing balance response in people with MS. The preliminary results of these assessments have the potential to provide essential indicators of the progression of MS and contribute to the individualization of treatment and evaluation of the interventions’ effectiveness. The literature describes patients who have had the opportunity to experiment in VR settings and then used what they have learned in the real world, suggesting that this VR setting could be more appealing than conditional settings. The findings of the proposed study will be beneficial in estimating and determining the effect of VR on balance control in persons with MS. In previous studies, VR was shown to be an interesting approach to neurological rehabilitation, but more data are needed to support this approach in MS. Conclusions: The proposed study enables an assessment of balance and evaluations of a variety of physiological implications related to neural activity as well as biomechanical implications related to movement analysis.

Keywords: multiple sclerosis, virtual reality, postural control, balance

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Authors: Neda Dekamei, Mostafa Sarabzadeh, Masoumeh Bigdeli

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Backward running is commonly used in different sports conditioning, motor learning, and neurological purposes, and even more commonly in physical rehabilitation. The present study evaluated the effects of six weeks backward and forward running methods on balance promotion adaptation in students. 12 male and female preseniors with the age range of 45-60 years participated and were randomly classified into two groups of backward running (n: 6) and forward running (n: 6) training interventions. During six weeks, 3 sessions per week, all subjects underwent stated different models of backward and forward running training on treadmill (65-80 of HR max). Pre and post-tests were performed by force plate and electromyogram, two times before and after intervention. Data were analyzed using by T test. On the basis of obtained data, significant differences were recorded on balance and plantar flexion force in backward running (BR) and no difference for forward running (FR). It seems the training model of backward running can generate more stimulus to achieve better plantar flexion force and strengthening ankle protectors which leads to balance improvement in pre aging period. It can be recommended as an effective method to promote seniors life quality especially in balance neuromuscular parameters.

Keywords: backward running, balance, plantar flexion, pre seniors

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: S. Benbia, W. Bouafia, D. Khellaf, A. Chennaf, M. Yahia

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Our study was designed to highlight changes in certain biochemical parameters (CH, TG, HDL, GOT, GPT, LDL, and CRP), obese women infertile fertile witnesses and research potential pathophysiological link between obesity and infertility in this population of women. This practical work was focused on a population of 24 obese women infertile, compared to controls, subjects without any pathology causing disruption of parameters to be studied to determine the contribution of obesity in the etiology of infertility. The assay results revealed a highly significant difference between the two groups in serum CH, TG, HDL, TGO and TGP (P < 0.0001) and in the rate of LDL (p = 0.0017) and CRP (p = 0.02). The hormonal balance also shows a significant difference between the two groups (P < 0.0001).The present study indicates that obesity is associated with infertility, but there is no direct pathophysiological link between obesity and infertility has not been determined. Further in-depth studies are needed to determine the exact mechanism by which overweight leads to female infertility.

Keywords: obesity, fertility, infertility, biochemical, women

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Authors: Serdar Kucuk, Redwan Alqasemi

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In this paper, the generic kinematic equations of 1-Degrees-Of-Freedom (DOF), 2-DOF, and 3-DOF above-knee prosthetic legs are derived using the mathematical tools used in science of robotics. As it is known, since the human leg performs rotational motions in the knee joint and foot-ankle joint, the axial rotational motions in the above-knee prosthetic legs are performed by using one or more revolute joints. When deriving the kinematic equations of the 1-DOF, 2-DOF, and 3-DOF above-knee prosthetic legs, the foot-ankle is treated as if there were a fixed non-rotating joint, a revolute joint, and a universal joint, respectively. The kinematic equations of the prosthetic legs presented in this article are obtained using DH method. The main advantages of this method are the easy physical interpretation of robot mechanisms and the use of 4x4 homogeneous transformation matrices, which are widely used in the literature. It is thought that the equations presented in this article contribute positively to the design, control, simulation and hence easy production of above-knee prosthetic legs.

Keywords: robotic above-knee prosthetic legs, generic kinematic equations, revolute and universal joints, DH method

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Tarik Ozmen

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The soccer players need good dynamic balance and jumping performance for dribbling, crossing rival, and to be effective in high balls during soccer game. The quadriceps angle (Q-angle) is used to assess biomechanics of the patellofemoral joint in the musculoskeletal medicine. The Q angle is formed by the intersection of two lines drawing from the anterior superior iliac spine to the centre of the patella and to the midline of the tibia tuberosity. Studies have shown that the Q angle is inversely associated with quadriceps femoris strength. The purpose of this study was to investigate relationship between dynamic balance, jumping performance and Q-angle in soccer players. Thirty male soccer players (mean ± SD: age, 15.23 ± 0.56 years, height, 170 ± 8.37 cm, weight, 61.36 ± 6.04 kg) participated as volunteer in this study. Dynamic balance of the participants were evaluated at directions of anterior (A), posteromedial (PM) and posterolateral (PL) with Star Excursion Balance Test (SEBT). Each participant was instructed to reach as far as with the non-dominant leg in each of the 3 directions while maintaining dominant leg stance. Leg length was used to normalize excursion distances by dividing the distance reached by leg length and then multiplying the result by 100. The jumping performance was evaluated by squat jump using a contact mat. A universal (standard) goniometer was used to measure the Q angle in standing position. The Q angle was not correlated with directions of SEBT (A: p = 0.32, PM: p = 0.06, PL: p = 0.37). The squat jump height was not correlated with Q-angle (p = 0.21). The findings of this study suggest that there are no significant relationships between dynamic balance, jumping performance and Q-angle in soccer players. Further studies should investigate relationship between balance ability, athletic performance and Q-angle with larger sample size in soccer players.

Keywords: balance, jump height, Q angle, soccer

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Seyed Salahedin Naghshbandi, Zahra Bozorgzadeh, Leila Zakizadeh, Siavash Hamidzadeh

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From the sport economy experts point of view, the existence of competitive balance among sport leagues and its numerous effects on league is an important and undeniable issue. In general, sport events fans are so eager to unpredictable results of competition in order to reach the top of excitement and necessary motivation for following competitions. The purpose of this research is to consider and compare the competitive balance among five provisional European football leagues (Spain, England, Italy, France and Germany) during 1966 - 2015 seasons. Research data are secondary and obtained from Premier League final tables of selected countries in 1966 - 2015 seasons. For analyzing data, C5 and C5ICB indicators used. whatever these indicators be less, more balance establishes in the league and vice-versa. The result showed that Le champion of France reached from 1,259 to 1,395; Italy Serie-A league from 1,316 to 1,432; England premier league from 1, 342 to 1,455; Germany Bundesliga from 1,238 to 1,465 and Spain La liga from 1,295 to 1,495. So by comparing C5ICB charts during 1966 - 2015 seasons, La liga of Spain moved more toward imbalance and enjoyed less balance with other European Leagues. Also, La champion of France during the mentioned season, enjoyed less imbalance and preserved its relative balance with monotonous process. It seems that football in France has been followed as stable during 1966 to 2015, and prediction of results was more difficult and competitions were so attractive for spectators, but in Italy, England, Germany, and Spain there were less balance, respectively.

Keywords: competitive balance, professional football league, competition, C5ICB

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Authors: Sheena K. J., Jyoti Badge, Sayed Mohammed Zeeshan

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A Comparative Study of Exponential and Logistic Population Growth Models in India India is the second most populous city in the world, just behind China, and is going to be in the first place by next year. The Indian population has remarkably at higher rate than the other countries from the past 20 years. There were many scientists and demographers who has formulated various models of population growth in order to study and predict the future population. Some of the models are Fibonacci population growth model, Exponential growth model, Logistic growth model, Lotka-Volterra model, etc. These models have been effective in the past to an extent in predicting the population. However, it is essential to have a detailed comparative study between the population models to come out with a more accurate one. Having said that, this research study helps to analyze and compare the two population models under consideration - exponential and logistic growth models, thereby identifying the most effective one. Using the census data of 2011, the approximate population for 2016 to 2031 are calculated for 20 Indian states using both the models, compared and recorded the data with the actual population. On comparing the results of both models, it is found that logistic population model is more accurate than the exponential model, and using this model, we can predict the future population in a more effective way. This will give an insight to the researchers about the effective models of population and how effective these population models are in predicting the future population.

Keywords: population growth, population models, exponential model, logistic model, fibonacci model, lotka-volterra model, future population prediction, demographers

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Authors: Elham Azimzadeh, Fahimeh Khorshidi, Alireza Farsi

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Balance impairment and fear of falling in older adults may reduce their quality of life. Reactive balance training could improve rapid postural responses and fall prevention in the elderly during daily tasks. Performing postural training and simultaneously cognitive dual tasks could be similar to the daily circumstances. Purpose: This study aimed to determine the effect of balance training on stable and unstable surfaces under dual cognitive task conditions on postural control and fear of falling in the elderly. Methods: Thirty non-fallers of older adults (65-75 years) were randomly assigned to two training groups: stable-surface (n=10), unstable-surface (n=10), or a control group (n=10). The intervention groups underwent six weeks of balance training either on a stable (balance board) or an unstable (wobble board) surface while performing a cognitive dual task. The control group received no balance intervention. COP displacements in the anterioposterior (AP) and mediolateral (ML) directions using a computerized balance board, functional balance using TUG, and fear of falling using FES-I were measured in all participants before and after the interventions. Summary of Results: Mixed ANOVA (3 groups * 2 times) with repeated measures and post hoc test showed a significant improvement in both intervention groups in AP index (F= 11/652, P= 0/0002) and functional balance (F= 9/961, P= 0/0001). However, the unstable surface training group had more improvement. However, the fear of falling significantly improved after training on an unstable surface (p= 0/035). All groups had no significant improvement in the ML index (p= 0/817). In the present study, there was an improvement in the AP index after balance training. Conclusion: Unstable surface training may reduce reaction time in posterior ankle muscle activity. Furthermore, focusing attention on cognitive tasks can lead to maintaining balance unconsciously. Most of the daily activities need attention distribution among several activities. So, balance training concurrent to a dual cognitive task is challenging and more similar to the real world. According to the specificity of the training principle, it may improve functional independence and fall prevention in the elderly.

Keywords: cognitive dual task, elderly, fear of falling, postural control, unstable surface

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