Search results for: population balance equation

Authors: Mohamed A. Eid, Sobhy M. Aly, Marwa M. Ibrahim, Nadia L. Radwan

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To investigate the interaction effects of vitamin D supplementation combined with aerobic exercises (AE) and conventional physical therapy program (CPTP) on balance and physical performance in children with Down syndrome (DS).Methods: A randomized controlled trial was conducted for 38 children with DS, with ages ranging from 8 to 12 years. They were divided randomly to two groups. The control group (n=19) received the CPTP, while the study group (n=19) received the CPTP, AE, and vitamin D in the form of an oral daily dose of vitamin D3 400 IU (Cholecalciferol). Evaluation of balance by using the Biodex Stability System and physical performance by using the six-minute walk test (6MWT)was performed before and after 12 weeks of the treatment program. Findings: All groups showed a significant improvement in balance and physical performance after treatment (p < 0.05). The study group showed a significant improvement in balance and physical performancecompared with that of the control group (p < 0.05). Conclusion: Vitamin D supplementation combined with AE and CPTP could improve balance and physical performance in children with DS. Therefore, vitamin D and AEshould be considered as adjunctive to the rehabilitation program of these children.

Keywords: aerobic exercises, balance, down syndrome, physical performance, vitamin D

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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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: 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: 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: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Abdulrahman Abdulrahman

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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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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: 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: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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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: Prashant Verma, K. K. Singh, Anjali Singh, Ujjaval Srivastava

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Contraceptive policies have been derived to achieve desired reductions in the growth rate and also, applied to the data of Uttar-Pradesh, India for illustration. Using the Lotka’s integral equation for the stable population, expressions for the proportion of contraceptive users at different ages have been obtained. At the age of 20 years, 42% of contraceptive users is imperative to reduce the present annual growth rate of 0.036 to 0.02, assuming that 40% of the contraceptive users discontinue at the age of 25 years and 30% again continue contraceptive use at age 30 years. Further, presuming that 75% of women start using contraceptives at the age of 23 years, and 50% of the remaining women start using contraceptives at the age of 28 years, while the rest of them start using it at the age of 32 years. If we set a minimum age of marriage as 20 years, a reduction of 0.019 in growth rate will be obtained. This study describes how the level of contraceptive use at different age groups of women reduces the growth rate in the state of Uttar Pradesh. The article also promotes delayed marriage in the region.

Keywords: child bearing, contraceptive devices, contraceptive policies, population growth, stable population

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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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: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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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: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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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: 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: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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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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