Search results for: the structural equation

Authors: Yuan Yan Tang, Lina Yang, Hong Li

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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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Authors: Fety Nurlia Muzayanah, Arif Imam Suroso, Mukhamad Najib

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The market share of organic food in Indonesia just reaches 0.5-2 percents from the entire of agricultural products. The aim of this research is to analyze the relation of gender, work, age and final education toward the buying interest of organic food, to identify the factors influencing the resistance of the purchase of organic food, and to identify the market education process. The analysis result of Structural Equation Modeling (SEM) shows the factors causing the resistance of the purchase of organic food are the negative attitude toward organic food, the lack of affordable in range for organic food product and the lack of awareness toward organic food, while the subjective norms have no significant effect toward the buying interest. The market education process which can be done is the education about the use of the health of organic food, the organic certification and the economic value.

Keywords: market education, organic food, consumer behavior, structural equation modeling

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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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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Authors: Wei Lu

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With the development of information technology in China, network consumption is becoming more and more popular. As a special group, college students have a high degree of education and distinct opinions and personalities. In the future, the key groups of network consumption have gradually become the focus groups of network consumption. Studying college students’ online consumption behavior has important theoretical significance and practical value. Based on the Stimulus-Organism-Response (SOR) driving model and the structural equation model, this paper establishes the influencing factors model of College students’ online consumption behavior, evaluates and amends the model by using SPSS and AMOS software, analyses and determines the positive factors of marketing college students’ consumption, and provides an effective basis for guiding and promoting college student consumption.

Keywords: college students, online consumption, stimulate-organism-reaction driving model, structural equation model

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Authors: Halima Akhtar, Abhijeet Chandra

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The paper attempts to analyze the factors that influence the Consumer Behavior to purchase apparel through the internet. The intentions to buy apparels online were based on in terms of user style, orientation, size and reputation of the merchant, social influence, perceived information utility, perceived ease of use, perceived pleasure and attractiveness and perceived trust and risk. The basic framework used was Technology acceptance model to explain apparels acceptance. A survey was conducted to gather the data from 200 people. The measures and hypotheses were analyzed using Correlation testing and would be further validated by the Structural Equation Modelling. The implications of the findings for theory and practice could be used by marketers of online apparel websites. Based on the values obtained, we can conclude that the factors such as social influence, Perceived information utility, attractiveness and trust influence the decision for a user to buy apparels online. The major factors which are found to influence an online apparel buying decision are ease of use, attractiveness that a website can offer and the trust factor which a user shares with the website.

Keywords: E-tailers, consumer behaviour, technology acceptance model, structural modelling

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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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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Authors: Shittu Ahmed Tajudeen

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This study examines student-teachers’ attitude and intention towards cell-phone use for learning. The study involves one hundred and ninety (190) trainee teachers in one of the Institutes of Education in Nigeria. The data of the study was collected through a questionnaire on a rating of seven point likert-type Scale. The data collected was used to test the hypothesized model of the study using Structural Equation Modeling approach. The finding of the study revealed that Perceived Usefulness (PU), Perceived Ease of Use (PEU), Subjective Norm (SN) and Attitude significantly influence students’ intention towards adoption of cell-phone for learning. The study showed that perceived ease of use stands to be the strongest predictor of cell-phone use. The model of the study exhibits a good-fit with the data and provides an explanation on student- teachers’ attitude and intention towards cell-phone for learning.

Keywords: cell-phone, adoption, structural equation modeling, technology acceptance model

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Authors: Sy, Melecio Jr

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The decision to adopt vertical integration (VI) is firm-specific, but there is a common practice among businesses in an industry to maximize the massive potential benefits of VI. This study aims to determine VI adoption in the restaurant industry in Davao City. Using a two-step sampling process, the study used a validated survey questionnaire among 264 restaurant owners and managers randomly selected and geographically classified. It is a quantitative study where the data were subjected to a structural equation model (SEM). The results revealed that VI is present but limited to procurement, production, restaurant services, and online marketing. Raw materials were outsourced while delivery to customers through third-party delivery services. VI slowly increased over ten years except for online marketing, which has grown significantly in a few years. The endogenous and exogenous variables were correlated and established the linear regression model. The SEM's best fit model revealed that strategic motives (SMOT) and market factors (MFAC) influenced VI adoption while MFAC is the best predictor. Favorable market factors may lead restaurants to adopt VI. It is, thus, recommended for restaurants to institutionalize strategic management, quantify the impact of double marginalization in future studies as a reason for VI and conduct this study during the new normal to see the influence of business efficiencies and firm economies on VI adoption.

Keywords: business efficiencies, business management, davao city, firm economies, market factors, philippines, strategic motives, structural equation model, supply chain, vertical integration adoption

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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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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Authors: Sherry Ann Ganase, Sandra Sookram

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This study examines adaptation measures and factors that influence adaptation decisions in Bequia by using multiple linear regression and a structural equation model. Using survey data, the results suggest that households are knowledgeable and concerned about climate change but lack knowledge about the measures needed to adapt. The findings from the SEM suggest that a positive relationship exist between vulnerability and adaptation, vulnerability and perception, along with a negative relationship between perception and adaptation. This suggests that being aware of the terms associated with climate change and knowledge about climate change is insufficient for implementing adaptation measures; instead the risk and importance placed on climate change, vulnerability experienced with household flooding, drainage and expected threat of future sea level are the main factors that influence the adaptation decision. The results obtained in this study are beneficial to all as adaptation requires a collective effort by stakeholders.

Keywords: adaptation, Bequia, multiple linear regression, structural equation model

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

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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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Authors: Taehyun Kim, Hyunjoo Park, Taehyun Kim

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Since the rapid economic development, Korea has recently entered a period of low growth due to population decline and aging. Due to the urbanization around the metropolitan area and the hollowing of local cities, the ecological capacity of a city is decreasing while ecological footprints are increasing, requiring a compact space plan for maintaining urban functions. The purpose of this study is to analyze the relationship between urban spatial structure and residents' ecological footprints for sustainable spatial planning. To do this, we try to analyze the relationship between intra-urban spatial structure, such as net/gross density and service accessibility, and resident ecological footprints of food, housing, transportation, goods and services through survey and structural equation modeling. The results of the study will be useful in establishing an implementation plan for sustainable development goals (SDGs), especially for sustainable cities and communities (SDG 11) and responsible consumption and production (SDG 12) in the future.

Keywords: ecological footprint, structural equation modeling, survey, sustainability, urban spatial structure

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Authors: Muna Alghabshi, Edmana Krishnan

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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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Authors: Benedict Barnes, Anthony Y. Aidoo

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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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Authors: Sayed Kifayat Shah, Tang Zhongjun, Mohammad Ahmad, Sohaib Mostafa

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This article investigates consumer’s intention to shift to 5G in the light of disruptive technology innovation. To switch from 4G (Existing) technology to 5G (Disruptive) technology requires not just economic benefits and costs but involves other values too, which aren't yet experienced in the framework of technology innovation. This study extended the valued adaptation (VAM) model by proposing the sustainability values (SVs) construct. The model was examined on data from 361 Chinese consumers using the partial least squares-based structural equation modelling (PLS-SEM) technique. The outcomes prove the significant correlation of sustainability values (SVs) which influences consumer’s switching intentions toward 5G disruptive technology. The findings of this research will be helpful to telecoms firms in developing consumer retention strategies. Some limitations and the importance of the research for scholars and managers are also discussed.

Keywords: value adaptation model (VAM), sustainability values (SVs), disruptive 5G technology, switching intentions (SI), partial least squares-based structural equation modelling (PLS-SEM)

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Authors: Lunliang Zhong, Bin Duan

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The undergraduate graduation project is a vital part of the higher education curriculum, crucial for engineering accreditation. Current evaluations often summarize data without identifying underlying issues. This study applies the Peter-Clark algorithm to analyze causal relationships within the graduation project data of an Electronics and Information Engineering program, creating a causal model. Structural equation modeling confirmed the model's validity. The analysis reveals key teaching stages affecting project success, uncovering problems in the process. Introducing causal discovery and inference into project evaluation helps identify issues and propose targeted improvement measures. The effectiveness of these measures is validated by comparing the learning outcomes of two student cohorts, stratified by confounding factors, leading to improved teaching quality.

Keywords: causal discovery, causal inference, continuous improvement, Peter-Clark algorithm, structural equation modeling

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Authors: Vimi Jham

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The banking sector has undergone tremendous change in all forms of service it provides to its customers. The efforts of the banks is to avoid customer defection and lead to customer satisfaction. The purpose of the study was to examine the linkages among the constructs such as customer perceived service quality, perceived service recovery quality and customer satisfaction in the banking industry. The moderating effect of negative brand perception due to service failure on recovery satisfaction were investigated. Random sampling methods are used to draw the sample from the population. Data was collected from 262 banking customers and were analyzed with the help of structural equation modelling approach using Smart PLS to understand the relationship among variables being studied. The results of the study contribute to the research by proving that customer service recovery satisfaction is dependent on customer perceived service quality and the moderating effect of negative brand perception due to service failure was insignificant.

Keywords: service recovery satisfaction, perceived service recovery quality, perceived service quality, structural equation modelling

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Authors: Divine Agozie, Muesser Nat, Eric Afful-Dadzie

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This examination attempts an analysis of the effect of business intelligence and analytics (BI&A) capabilities on organizational role stressors and the implications of such an effect on performance. Two hundred twenty-eight responses gathered from seventy-six firms across Ghana were analyzed using the Partial Least Squares Structural Equation Modelling (PLS-SEM) approach to validate the hypothesized relationships identified in the research model. Findings suggest both endogenous and exogenous dependencies of the sensing capability on the multiple role requirements of personnel. Further, transforming capability increases role conflict, whereas driving capability of BI&A systems impacts role conflict and role ambiguity. This study poses many practical insights to firms seeking to acquire analytics capabilities to drive performance and data-driven decision-making. It is important for firms to consider balancing role changes and task requirements before implementing and post-implementation stages of BI&A innovations.

Keywords: business intelligence and analytics, dynamic capabilities view, organizational stressors, structural equation modelling

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Authors: Sonal H. Singh, Bhaskar Bhowmick

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The research hypothesis formulated in this paper examines the importance of microfinance provision for entrepreneurship development by engendering a high level of entrepreneurial orientation among the grassroots entrepreneurs. A theoretically well supported empirical framework is proposed to identify the influence of financial services and non-financial services provided by microfinance institutes in strengthening the impact of grassroots innovation on entrepreneurial orientation under resource constraints. In this paper, Grassroots innovation is perceived in three dimensions: new learning practice, localized solution, and network development. The study analyzes the moderating effect of microfinance provision on the relationship between grassroots innovation and entrepreneurial orientation. The paper employed structural equation modelling on 400 data entries from the grassroots entrepreneurs in India. The research intends to help policymakers, entrepreneurs and microfinance providers to promote the innovative design of microfinance services for the well-being of grassroots entrepreneurs and to foster sustainable entrepreneurship development.

Keywords: entrepreneurship development, grassroots innovation, India, structural equation model

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

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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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Authors: Yen-Ku Kuo, Chie-Bein Chen, Jyh-Yi Shih, Kuang-Yi Lin, Chien-Han Peng

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This study is primarily concerned with exploring what factors affect the consumer’s intention of using mobile phone e-book. In developing research structure, we adopted technology acceptance model (TAM) and Innovation Diffusion Theory (IDT) as a foundation. The analysis method of structural equation model (SEM) was used to carry out this study. Subjects were 261 users who are using or used the mobile phone e-book. The findings can be summed up as follows: (1) The subjective norm and job relevance has non-significant and positive influence to the perceived usefulness. This represents now the user are still in a small number and most of them used it in non-work related purpose. (2) The output quality, result demonstrability and perceived ease of use were confirmed to have positive and significant influence to the perceived usefulness. (3) The moderator “innovative diffusion” affects the relationship between the attitude and behavior intention. These findings could be a reference for the practice and future study to make further exploration.

Keywords: mobile phone e-book, technology acceptance model (TAM), innovation diffusion theory (IDT), structural equation model (SEM)

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Authors: Ayaz Ahmad

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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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Authors: Monalisa Pradhan, Ajana Dutta, Irshad Kariyattuparamb Abbas, Boby Joseph, T. N. Guru Row, Diptikanta Swain, Gopal K. Pradhan

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Compounds with the Vanthoffite crystal structure having general formula Na6M(SO₄)₄ (M= Mg, Mn, Ni , Co, Fe, Cu and Zn) display a variety of intriguing physical properties intimately related to their structural arrangements. The compound Na6Mn(SO4)4 shows antiferromagnetic ordering at low temperature where the in-plane Mn-O•••O-Mn interactions facilitates antiferromagnetic ordering via a super-exchange interaction between the Mn atoms through the oxygen atoms . The inter-atomic bond distances and angles can easily be tuned by applying external pressure and can be probed using high resolution X-ray diffraction. Moreover, because the magnetic interaction among the Mn atoms are super-exchange type via Mn-O•••O-Mn path, the variation of the Mn-O•••O-Mn dihedral angle and Mn-O bond distances under high pressure inevitably affects the magnetic properties. Therefore, it is evident that high pressure studies on the magnetically ordered materials would shed light on the interplay between their structural properties and magnetic ordering. This will indeed confirm the role of buckling of the Mn-O polyhedral in understanding the origin of anti-ferromagnetism. In this context, we carried out the pressure dependent X-ray diffraction measurement in a diamond anvil cell (DAC) up to a maximum pressure of 17 GPa to study the phase transition and determine equation of state from the volume compression data. Upon increasing the pressure, we didn’t observe any new diffraction peaks or sudden discontinuity in the pressure dependences of the d values up to the maximum achieved pressure of ~17 GPa. However, it is noticed that beyond 12 GPa the a and b lattice parameters become identical while there is a discontinuity in the β value around the same pressure. This indicates a subtle transition to a pseudo-monoclinic phase. Using the third order Birch-Murnaghan equation of state (EOS) to fit the volume compression data for the entire range, we found the bulk modulus (B0) to be 44 GPa. If we consider the subtle transition at 12 GPa, we tried to fit another equation state for the volume beyond 12 GPa using the second order Birch-Murnaghan EOS. This gives a bulk modulus of ~ 34 GPa for this phase.

Keywords: mineral, structural phase transition, high pressure XRD, spectroscopy

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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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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Authors: Ognjen Vukovic

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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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Authors: Ashley Wei-Ting Wang, Wen-Yau Hsu

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Objectives: The current study applies and expands the Tripartite Model to elaborate the link between non-suicidal self-injury (NSSI) and suicidal behavior. We propose a structural model of NSSI and suicidal risk, in which negative affect (NA) predicts both anxiety and depression, positive affect (PA) predicts depression only, anxiety is linked to NSSI, and depression is linked to suicidal risk. Method: Four hundreds and eighty seven undergraduates participated. Data were collected by administering self-report questionnaires. We performed hierarchical regression and structural equation modeling to test the proposed structural model. Results: The results largely support the proposed structural model, with one exception: anxiety was strongly associated with NSSI and to a lesser extent with suicidal risk. Conclusions: We conclude that the co-occurrence of NSSI and suicidal risk is due to NA and anxiety, and suicidal risk can be differentiated by depression. Further theoretical and practical implications are discussed.

Keywords: non-suicidal self-injury, suicidal risk, anxiety, depression, the tripartite model, hierarchical relationship

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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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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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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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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