Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1733

Search results for: locus equation

1733 Some Properties of Cut Locus of a Flat Torus

Authors: Pakkinee Chitsakul


In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: cut locus, flat torus, geodesics

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1732 Automatic Vowel and Consonant's Target Formant Frequency Detection

Authors: Othmane Bouferroum, Malika Boudraa


In this study, a dual exponential model for CV formant transition is derived from locus theory of speech perception. Then, an algorithm for automatic vowel and consonant’s target formant frequency detection is developed and tested on real speech. The results show that vowels and consonants are detected through transitions rather than their small stable portions. Also, vowel reduction is clearly observed in our data. These results are confirmed by the observations made in perceptual experiments in the literature.

Keywords: acoustic invariance, coarticulation, formant transition, locus equation

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1731 Molecular Characterization of Ardi Goat Assisted by Microsatellite Markers

Authors: M. F. Elzarei, A. M. Alseaf


Hundred uncorrelated animal and thirty six markers were used in this study to study the molecular characterization of Saudi native Ardi goat (BM18189, ILSTS030, INRA005, OarFCB48, BM2113, ILSTS033, INRA023, RM088, CSRD247, ILSTS034, INRA063, SRCRSP1, ILSTS002, ILSTS044, INRA172, SRCRSP5, ILSTS005, ILSTS049, MAF70, SRCRSP8, ILSTS011, ILSTS058, OarAE54, SRCRSP9, ILSTS019, ILSTS059, OARCP34, TGLA53, ILSTS022, ILSTS082, OARE129, TGLA73, ILSTS029, ILSTS087, OARE193, and RM004). Ardi goat showed high variability. The mean number of alleles per locus ranged from 5 in SRCRSP1 locus to 13.5 in CSRD247 locus. Gene diversities varied within a wide range, from 0.53 in ILSTS002 locus to 0.86 in RM088 locus. Hardy-Weinberg equilibrium was tested in order to evaluate the significance of inbreeding occurring in each locus in Ardi population. Only SRCRSP9, INRA005, ILSTS030 loci showed significance in this way.

Keywords: molecular characterization, microsatellite markers, Ardi goats, Hardy-Weinberg equilibrium

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1730 Vibration Analysis of Pendulum in a Viscous Fluid by Analytical Methods

Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin


In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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1729 Predictors of Behavior Modification Prior to Bariatric Surgery

Authors: Rosemarie Basile, Maria Loizos, John Pallarino, Karen Gibbs


Given that complications can be significant following bariatric surgery and with rates of long-term success measured in excess weight loss varying as low as 33% after five years, an understanding of the psychological factors that may mitigate findings and increase success and result in better screening and supports prior to surgery are critical. An internally oriented locus of control (LOC) has been identified as a predictor for success in obesity therapy, but has not been investigated within the context of bariatric surgery. It is hypothesized that making behavioral changes prior to surgery which mirror those that are required post-surgery may ultimately predict long-term success. 122 subjects participated in a clinical interview and completed self-report measures including the Multidimensional Health Locus of Control Scale, Overeating Questionnaire (OQ), and Lifestyle Questionnaire (LQ). Pearson correlations were computed between locus of control orientation and likelihood to make behavior changes prior to surgery. Pearson correlations revealed a positive correlation between locus of control and likelihood to make behavior changes r = 0.23, p < .05. As hypothesized, there was a significant correlation between internal locus of control and likelihood to make behavior changes. Participants with a higher LOC believe that they are able to make decisions about their own health. Future research will focus on whether this positive correlation is a predictor for future bariatric surgery success.

Keywords: bariatric surgery, behavior modification, health locus of control, overeating questionnaire

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1728 The Locus of Action - Tinted Windows

Authors: Devleminck Steven, Debackere Boris


This research is about the ways artists and scientists deal with (and endure) new meaning and comprehend and construct the world. The project reflects on the intense connection between comprehension and construction and their place of creation – the ‘locus of action’. It seeks to define a liquid form of understanding and analysis capable of approaching our complex liquid world as discussed by Zygmunt Bauman. The aim is to establish a multi-viewpoint theoretical approach based on the dynamic concept of the Flâneur as introduced by Baudelaire, replacing single viewpoint categorization. This is coupled with the concept of thickening as proposed by Clifford Geertz with its implication of interaction between multi-layers of meaning. Here walking and looking is introduced as a method or strategy, a model or map, providing a framework of understanding in conditions of hybridity and change.

Keywords: action, art, liquid, locus, negotiation, place, science

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1727 USA Commercial Pilots’ Views of Crew Resource Management, Social Desirability, and Safety Locus of Control

Authors: Stephen Vera, Tabitha Black, Charalambos Cleanthous, Ryan Sain


A gender comparison of USA commercial pilots’ demographics and views of CRM, social desirability and locus of control were surveyed. The Aviation safety locus of control (ASLOC) was used to measure external (ASLOC-E) or internal (ASLOC-I) aviation safety locus of control. The gender differences were explored using the ASLOC scores as a categorical variable. A differential comparison of crew resource management (CRM), based on the Federal Aviation Administration’s (FAA) guidelines was conducted. The results indicated that the proportion of female to male respondents matches the current ratio of USA commercial pilots. Moreover, there were no significant differences regarding overall education and the total number of communication classes one took. Regarding CRM issues, there were no significant differences on their views regarding the roles of the PIC, stress, time management, and managing a flight team. The females scored significantly lower on aeronautical decision making (ADM) and communications. There were no significant differences on either the Balanced Inventory of Desirable Responding (BIDR) impression management (IM) or self-deceptive enhancement (SDE). Although there were no overall significant differences on the ASLOC, the females did score higher on the internal subscale than did the males. An additional comparison of socially desirable responding indicates that all scores may be invalid, especially from the female respondents.

Keywords: social desirability, safety locus of control, crew resource management, commercial pilots

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1726 Locus of Control and Sense of Happiness: A Mediating Role of Self-Esteem

Authors: Ivanna Shubina


Background/Objectives and Goals: Recent interest in positive psychology is reflected in a plenty of studies conducted on its basic constructs (e.g. self-esteem and happiness) in interrelation with personality features, social rules, business and technology development. The purpose of this study is to investigate the mediating role of self-esteem, exploring the relationships between self-esteem and happiness, self-esteem and locus of control (LOC). It hypothesizes that self-esteem may be interpreted as a predictor of happiness and mediator in the locus of control establishment. A plenty of various empirical studies results have been analyzed in order to collect data for this theoretical study, and some of the analysed results can be considered as arguable or incoherent. However, the majority of results indicate a strong relationship between three considered concepts: self-esteem, happiness, the locus of control. Methods: In particular, this study addresses the following broad research questions: i) Is self-esteem just an index of global happiness? ii) May happiness be possible or realizable without a healthy self-confidence and self-acceptance? iii) To what extent does self-esteem influence on the level of happiness? iv) Is high self-esteem a sufficient condition for happiness? v) Is self-esteem is a strong predictor of internal locus of control maintenance? vi) Is high self-esteem related to internal LOC, while low self-esteem to external LOC? In order to find the answers for listed questions, 60 reliable sources have been analyzed, results of what are discussed more detailed below. Expected Results/Conclusion/Contribution:It is recognized that the relationship between self-esteem, happiness, locus of control is complex: internal LOC is contributing to happiness, but it is not directly related to it; self-esteem is a powerful and important psychological factor in mental health and well-being; the feelings of being worthy and empowered are associated with significant achievements and high self-esteem; strong and appropriate self-esteem (when the discrepancy between “ideal” and “real” self is balanced) is correlated with more internal LOC (when the individual tends to believe that personal achievements depend on possessed features, vigor, and persistence). Despite the special attention paid to happiness, the locus of control and self-esteem, independently, theoretical and empirical equivocations within each literature foreclose many obvious predictions about the nature of their empirical distinction. In terms of theoretical framework, no model has achieved consensus as an ultimate theoretical background for any of the mentioned constructs. To be able to clarify the relationship between self-esteem, happiness, and locus of control more interdisciplinary studies have to take place in order to get data on heterogeneous samples, provided from various countries, cultures, and social groups.

Keywords: happiness, locus of control, self-esteem, mediation

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1725 Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation

Authors: Jian-Jun Shu


It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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1724 A Study on Multidimensional Locus of Control and the Procrastinating Behavior in Employees

Authors: Richa Mishra, Sonia Munjal


In this increasingly hectic and competitive climate, employees are expected to manage the resources available to them to perform their work. However, many are wasting the most precious and scarce resource at their disposal, time, by procrastinating on tasks and thereby costing themselves and their organizations. As timely performance is a requirement of most jobs, procrastination is particularly problematic in the workplace. Evidence suggests that procrastination and poor performance go hand-in-hand, as procrastinators miss more deadlines than non-procrastinators and make more errors and work at a slower speed than non-procrastinators when performing timed tasks. This research is hence an effort to add a little in the sparse knowledge base. It is an effort to throw light on the relationship of Levenson’s multi dimensions of locus of control and also an effort to identify if it is one of the causes and of employees procrastination which have not been explored earlier. The study also explores the effect and relationship of multidimensional locus of control and various levels of stress on procrastination. The results of the research have ascertained that there is significant impact of LOC dimensions on the procrastinating behavior of the employees. One of the major findings to emerge from the current research that managers with powerful others as their LOC dimensions were least procrastinating, contradicts the previous research results that external procrastinate more than internals.

Keywords: Multidimensional Locus of Control, workplace procrastination, employee behaviour, manufacturing industry

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1723 An Analytical Method for Solving General Riccati Equation

Authors: Y. Pala, M. O. Ertas


In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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1722 The Correlation between Emotional Intelligence and Locus of Control: Empirical Study on Lithuanian Youth

Authors: Dalia Antiniene, Rosita Lekaviciene


The qualitative methodology based study is designed to reveal a connection between emotional intelligence (EI) and locus of control (LC) within the population of Lithuanian youth. In the context of emotional problems, the locus of control reflects how one estimates the causes of his/her emotions: internals (internal locus of control) associate their emotions with their manner of thinking, whereas externals (external locus of control) consider emotions to be evoked by external circumstances. On the other hand, there is little empirical data about this connection, and the results in disposition are often contradictory. In the conducted study 1430 young people, aged 17 to 27, from various regions of Lithuania were surveyed. The subjects were selected by quota sampling, maintaining natural proportions of the general Lithuanian youth population. To assess emotional intelligence the EI-DARL test (i.e. self-report questionnaire consisting of 75 items) was implemented. The emotional intelligence test, created applying exploratory factor analysis, reveals four main dimensions of EI: understanding of one’s own emotions, regulation of one’s own emotions, understanding other’s emotions, and regulation of other’s emotions (subscale reliability coefficients fluctuate between 0,84 and 0,91). An original 16-item internality/externality scale was used to examine the locus of control (internal consistency of the Externality subscale - 0,75; Internality subscale - 0,65). The study has determined that the youth understands and regulates other people’s emotions better than their own. Using the K-mean cluster analysis method, it was established that there are three groups of subjects according to their EI level – people with low, medium and high EI. After comparing means of subjects’ favorability of statements on the Internality/Externality scale, a predominance of internal locus of control in the young population was established. The multiple regression models has shown that a rather strong statistically significant correlation exists between total EI, EI subscales and LC. People who tend to attribute responsibility for the outcome of their actions to their own abilities and efforts have higher EI and, conversely, the tendency to attribute responsibility to external forces is related more with lower EI. While pursuing their goals, young people with high internality have a predisposition to analyze perceived emotions and, therefore, gain emotional experience: they learn to control their natural reactions and to act adequately in a situation at hand. Thus the study unfolds, that a person’s locus of control and emotional intelligence are related phenomena and allows us to draw a conclusion, that a person’s internality/externality is a reliable predictor of total EI and its components.

Keywords: emotional intelligence, externality, internality, locus of control

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1721 Associations between Mindfulness, Temporal Discounting, Locus of Control, and Reward-Based Eating in a Sample of Overweight and Obese Adults

Authors: Andrea S. Badillo-Perez, Alexis D. Mitchell, Sara M. Levens


Overeating, and obesity have been associated with addictive behavior, primarily due to behaviors like reward-based eating, the tendency to overeat due to factors such as lack of control, preoccupation over food, and lack of satiation. Temporal discounting (TD), the ability to select future rewards over short term gains, and mindfulness, the process of maintaining present moment awareness, have been suggested to have significant, differential impacts on health-related behaviors. An individual’s health locus of control, the degree to which they feel that they have control over their health is also known to have an impact on health outcomes. The goal of this study was to investigate the relationship between health locus of control and reward-based eating, as well as the relation between TD and mindfulness in a sample (N = 126) of overweight or obese participants from larger health-focused study. Through the use of questionnaires (including the Five Facet Mindfulness Questionnaire (FFMQ), Reward-Based Eating Drive (RED), and Multidimensional Health Locus of Control (MHLOC)), anthropometric measurements, and a computerized TD task, a series of regressions tested the association between subscales of these measures. Results revealed differences in how the mindfulness subscales are associated with TD measures. Specifically the ‘Observing’ (beta =-.203) and ‘Describing’ (beta =.26) subscales were associated with lower TD rates and a longer subjective devaluation time-frame respectively. In contrast, the ‘Acting with Awareness’ subscale was associated with a shorter subjective devaluation timeframe (beta =-.23). These findings suggest that the reflective perspective initiated through the observing and describing components of mindfulness may facilitate delay of gratification, whereas the acting with awareness component of mindfulness, which focuses on the present moment, may make delay of gratification more challenging. Results also indicated that a higher degree of reward-based eating was associated with a higher degree of an external health locus of control based on the power of chance (beta =.10). However, an external locus of control based on the power of others had no significant association with reward-based eating. This finding implies that the belief that health is due to chance is associated with greater reward-based eating behavior, suggesting that interventions that focus on locus of control may be helpful. Overall, findings demonstrate that weight loss interventions may benefit from health locus of control and mindfulness exercises, but caution should be taken as the components of mindfulness appear to have different effects on increasing or decreasing delay of gratification.

Keywords: health locus of control, mindfulness, obesity, reward-based eating, temporal discounting

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1720 Image Transform Based on Integral Equation-Wavelet Approach

Authors: Yuan Yan Tang, Lina Yang, Hong Li


Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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1719 Second Order Solitary Solutions to the Hodgkin-Huxley Equation

Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis


Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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1718 Study of Cahn-Hilliard Equation to Simulate Phase Separation

Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa


An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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1717 Study and Solving Partial Differential Equation of Danel Equation in the Vibration Shells

Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar


This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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1716 Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm

Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad


Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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1715 Exact Solutions of a Nonlinear Schrodinger Equation with Kerr Law Nonlinearity

Authors: Muna Alghabshi, Edmana Krishnan


A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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1714 Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation

Authors: Benedict Barnes, Anthony Y. Aidoo


A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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1713 Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach

Authors: F. U. Rahman, R. Q. Zhang


This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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1712 A Study of Non Linear Partial Differential Equation with Random Initial Condition

Authors: Ayaz Ahmad


In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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1711 Predictors of Academic Dishonesty among Serially Frustrated Students in Ogun State, Southwest, Nigeria

Authors: Oyesoji Aremu, Taiwo Williams


This study examined some factors (academic self-efficacy, locus of control, motivation and gender) that could predict academic dishonesty among serially frustrated students in Ogun State, South West, Nigeria. Serial academically frustrated students are students who are unable to attain and meet academic expectations set by themselves or significant others. A sample of 250 undergraduate students selected from two faculties from a University in Ogun State,South West Nigeria took part in the study. Multiple regression analysis was employed to determine the joint and relative contributions of the independent variables to the prediction of the dependent variable. T-test was used to test the hypothesis determining the gender difference between the independent variables (academic self-efficacy, locus of control and motivation) and academic dishonesty of serial academically frustrated male and female students. The results of the study showed all the independent variables jointly contributed to predicting academic dishonesty, while only academic self-efficacy and motivation had relative contributions to the dependent measure. There was no significant difference in the academic self-efficacy and motivation among males and females on academic dishonesty of the serial academically frustrated students but locus of control showed a significant difference between male and female students on academic dishonesty. Implications for counseling of the findings are discussed in the study.

Keywords: academic dishonesty, serially frustrated students, academic self-efficacy, locus of control

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1710 Exact Soliton Solutions of the Integrable (2+1)-Dimensional Fokas-Lenells Equation

Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov


Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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1709 Chern-Simons Equation in Financial Theory and Time-Series Analysis

Authors: Ognjen Vukovic


Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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1708 Fixed Point Iteration of a Damped and Unforced Duffing's Equation

Authors: Paschal A. Ochang, Emmanuel C. Oji


The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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1707 A Novel Method for Solving Nonlinear Whitham–Broer–Kaup Equation System

Authors: Ayda Nikkar, Roghayye Ahmadiasl


In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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1706 Body Image Dissatifaction with and Personal Behavioral Control in Obese Patients Who are Attending to Treatment

Authors: Mariela Gonzalez, Zoraide Lugli, Eleonora Vivas, Rosana Guzmán


The objective was to determine the predictive capacity of self-efficacy perceived for weight control, locus of weight control and skills of weight self-management in the dissatisfaction of the body image in obese people who attend treatment. Sectional study conducted in the city of Maracay, Venezuela, with 243 obese who attend to treatment, 173 of the feminine gender and 70 of the male, with ages ranging between 18 and 57 years old. The sample body mass index ranged between 29.39 and 44.14. The following instruments were used: The Body Shape Questionnaire (BSQ), the inventory of body weight self-regulation, The Inventory of self-efficacy in the regulation of body weight and the Inventory of the Locus of weight control. Calculating the descriptive statistics and of central tendency, coefficients of correlation and multiple regression; it was found that a low ‘perceived Self-efficacy in the weight control’ and a high ‘Locus of external control’, predict the dissatisfaction with body image in obese who attend treatment. The findings are a first approximation to give an account of the importance of the personal control variables in the study of the psychological grief on the overweight individual.

Keywords: dissatisfaction with body image, obese people, personal control, psychological variables

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1705 Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation

Authors: Sachin Kumar


Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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1704 A Posteriori Analysis of the Spectral Element Discretization of Heat Equation

Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed


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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