Search results for: Estler face motionreversal method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8481

Search results for: Estler face motionreversal method

8271 Calculation of Heating Load for an Apartment Complex with Unit Building Method

Authors: Ju-Seok Kim, Sun-Ae Moon, Tae-Gu Lee, Seung-Jae Moon, Jae-Heon Lee

Abstract:

As a simple to method estimate the plant heating energy capacity of an apartment complex, a new load calculation method has been proposed. The method which can be called as unit building method, predicts the heating load of the entire complex instead of summing up that of each apartment belonging to complex. Comparison of the unit heating load for various floor sizes between the present method and conventional approach shows a close agreement with dynamic load calculation code. Some additional calculations are performed to demonstrate it-s application examples.

Keywords: Unit Building Method, Unit Heating Load, TFMLoad.

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8270 The Effects of Knowledge Management on Human Capital towards Organizational Innovation

Authors: Wan Norhayate Wan Daud, Fakhrul Anwar Zainol, Maslina Mansor

Abstract:

The study was conducted to produce case studies from the Malaysian public universities stands point East Coast of Malaysia. The aim of this study is to analyze the effects of knowledge management on human capital toward organizational innovation. The focus point of this study is on the management member in the faculties of these three Malaysian Public Universities in the East Coast state of Peninsular Malaysia. In this case, respondents who agreed to further participate in the research will be invited to a one-hour face-to-face semi-structured, in-depth interview. As a result, the sample size for this study was 3 deans of Faculty of Management. Lastly, this study tries to recommend the framework of organizational innovation in Malaysian Public Universities.

Keywords: Human Capital, Knowledge Management, Organizational Innovation, Public University.

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8269 Organizational Commitment of Anadolu University Open Education Faculty Students

Authors: Emine Demiray, Şensu Curabay

Abstract:

Distance education program is a dimension of contemporary and new education technologies. Concepts and applications in this field are the results of a series of educational demands and developments in various communication and education technologies. Distance education applications have some conceptual bases. These are creating new education opportunities, realizing work-education unity, getting democratic in education, lifelong education, tendency to individual matters, effective use of institutions, integration of technology and education, tendency to individual and social needs, taking three dimensional integration as the main principle (publishing, printed materials and face to face education), reaching maximum mass, individual and mass education integrity and education demand and financial matters balance. Economics, Business Administration and Open Education faculties, which have been giving education within Anadolu University since 1982 in Turkey, are carrying on education with nearly 1.000.000 students. The aim of this study is to determine organizational commitment levels of students who have been studying at Anadolu University Economics, Business Administration and Open Education faculties in the scope of affective, continuance and nominative commitment in Allen&Meyer model. In the study, organizational commitment of the Economics, Business Administration and Open Education faculty students, who are receiving education by means of distance education, to their faculties is dealt after introducing Anadolu University Distance Education system which gives higher education via distance education method in Turkey. In order to increase the success level of faculties it is required for students to have high level of organizational commitment to their faculties. A questionnaire has been applied by using “Organizational Commitment Scale", developed by Meyer&Allen to determine organizational commitments of Economics, Business Administration and Open Education students. Organizational commitment is dealt with as affective, continuance and nominative commitment. The questionnaire was applied face to face to randomly chosen 500 students living in Eskişehir and the data was downloaded to the computer by using SPSS program and the results were analyzed in terms of demographic features (gender, age, marital status, years of study, work and income level) of students by using frequency test, ttest and ANOVA test. As a result of these analyses, when the comments of Open Education Faculty students on levels of affective, continuance and nominative commitment to their faculties were examined, it has been revealed that continuance commitment level has the highest rate. Among the female participants; continuance commitment is high in the age range of 30-40, for normative commitment it is 17-22. However no dominant age range was defined for affective commitment. Regarding the marital status; continuance commitment average is higher among married participants; but nominative affective commitment average is higher among single participants. As to the years of study, affective and continuance commitment is higher among senior students while normative commitment is higher among junior students. Moreover; in terms of continuance, affective and normative commitment, those who do not work and have low income have higher level of all there commitment types than those who work and have relatively high income.

Keywords: Open education, Organizational commitment, Distance education.

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8268 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

Abstract:

In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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8267 Enhancing the Connectedness in Ad–hoc Mesh Networks using the Terranet Technology

Authors: Obeidat I., Bsoul M., Khasawneh A., Kilani Y.

Abstract:

This paper simulates the ad-hoc mesh network in rural areas, where such networks receive great attention due to their cost, since installing the infrastructure for regular networks in these areas is not possible due to the high cost. The distance between the communicating nodes is the most obstacles that the ad-hoc mesh network will face. For example, in Terranet technology, two nodes can communicate if they are only one kilometer far from each other. However, if the distance between them is more than one kilometer, then each node in the ad-hoc mesh networks has to act as a router that forwards the data it receives to other nodes. In this paper, we try to find the critical number of nodes which makes the network fully connected in a particular area, and then propose a method to enhance the intermediate node to accept to be a router to forward the data from the sender to the receiver. Much work was done on technological changes on peer to peer networks, but the focus of this paper will be on another feature which is to find the minimum number of nodes needed for a particular area to be fully connected and then to enhance the users to switch on their phones and accept to work as a router for other nodes. Our method raises the successful calls to 81.5% out of 100% attempt calls.

Keywords: Adjacency matrix, Ad-hoc mesh network, Connectedness, Terranet technology

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8266 Online Collaborative Learning System Using Speech Technology

Authors: Sid-Ahmed. Selouani, Tang-Ho Lê, Chadia Moghrabi, Benoit Lanteigne, Jean Roy

Abstract:

A Web-based learning tool, the Learn IN Context (LINC) system, designed and being used in some institution-s courses in mixed-mode learning, is presented in this paper. This mode combines face-to-face and distance approaches to education. LINC can achieve both collaborative and competitive learning. In order to provide both learners and tutors with a more natural way to interact with e-learning applications, a conversational interface has been included in LINC. Hence, the components and essential features of LINC+, the voice enhanced version of LINC, are described. We report evaluation experiments of LINC/LINC+ in a real use context of a computer programming course taught at the Université de Moncton (Canada). The findings show that when the learning material is delivered in the form of a collaborative and voice-enabled presentation, the majority of learners seem to be satisfied with this new media, and confirm that it does not negatively affect their cognitive load.

Keywords: E-leaning, Knowledge Network, Speech recognition, Speech synthesis.

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8265 A New Preconditioned AOR Method for Z-matrices

Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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8264 A Family of Improved Secant-Like Method with Super-Linear Convergence

Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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8263 Interaction between Environmental Performance and Logistic System: A Case Study of International Company

Authors: T. Tambovceva, A. Tambovcevs

Abstract:

The activities which are mostly related to the environmental performance need to be pointed, especially how logistics systems influence on environmental performance. This paper analyses how company could lead the initiative in this area by incorporating environmental management principles into their daily activities. The analysis is based on literature review about logistics and environment, the information from company R website as well as face-to-face interviews. A case study is given to show how they can turn practices into green while simultaneously meet the efficiency objectives. The research results show that the adoption of EMS and ISO 14001 certification is an effective tool for the logistics management. Such practices simultaneously reduce the negative contribute to better company performance. The results also show that the emissions to air and water, and energy consumption are the main logistics impacts to the environment.

Keywords: environmental management system, green logistics, information technology, information systems.

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8262 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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8261 Improved IDR(s) Method for Gaining Very Accurate Solutions

Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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8260 Hardness Variations as Affected by Bar Diameter of AISI 4140 Steel

Authors: Hamad K. Al-Khalid, Ayman M. Alaskari, Samy E. Oraby

Abstract:

Hardness of the widely used structural steel is of vital importance since it may help in the determination of many mechanical properties of a material under loading situations. In order to obtain reliable information for design, properties homogeneity should be validated. In the current study the hardness variation over the different diameters of the same AISI 4140 bar is investigated. Measurements were taken on the two faces of the stock at equally spaced eight sectors and fifteen layers. Statistical and graphical analysis are performed to asses the distribution of hardness measurements over the specified area. Hardness measurements showed some degree of dispersion with about ± 10% of its nominal value provided by manufacturer. Hardness value is found to have a slight decrease trend as the diameter is reduced. However, an opposite behavior is noticed regarding the sequence of the sector indicating a nonuniform distribution over the same area either on the same face or considering the corresponding sector on the other face (cross section) of the same material bar.

Keywords: Hardness; Hardness variation; AISI 4140 steel; Bardiameter; Statistical Analysis.

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8259 Denosing ECG using Translation Invariant Multiwavelet

Authors: Jeong Yup Han, Su Kyung Lee, Hong Bae Park

Abstract:

In this paper, we propose a method to reduce the various kinds of noise while gathering and recording the electrocardiogram (ECG) signal. Because of the defects of former method in the noise elimination of ECG signal, we use translation invariant (TI) multiwavelet denoising method to the noise elimination. The advantage of the proposed method is that it may not only remain the geometrical characteristics of the original ECG signal and keep the amplitudes of various ECG waveforms efficiently, but also suppress impulsive noise to some extent. The simulation results indicate that the proposed method are better than former removing noise method in aspects of remaining geometrical characteristics of ECG signal and the signal-to-noise ratio (SNR).

Keywords: ECG, TI multiwavelet, denoise.

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8258 Direct Method for Converting FIR Filter with Low Nonzero Tap into IIR Filter

Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

Abstract:

In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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8257 Wavelet Based Identification of Second Order Linear System

Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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8256 Fast Search Method for Large Video Database Using Histogram Features and Temporal Division

Authors: Feifei Lee, Qiu Chen, Koji Kotani, Tadahiro Ohmi

Abstract:

In this paper, we propose an improved fast search algorithm using combined histogram features and temporal division method for short MPEG video clips from large video database. There are two types of histogram features used to generate more robust features. The first one is based on the adjacent pixel intensity difference quantization (APIDQ) algorithm, which had been reliably applied to human face recognition previously. An APIDQ histogram is utilized as the feature vector of the frame image. Another one is ordinal feature which is robust to color distortion. Combined with active search [4], a temporal pruning algorithm, fast and robust video search can be realized. The proposed search algorithm has been evaluated by 6 hours of video to search for given 200 MPEG video clips which each length is 30 seconds. Experimental results show the proposed algorithm can detect the similar video clip in merely 120ms, and Equal Error Rate (ERR) of 1% is achieved, which is more accurately and robust than conventional fast video search algorithm.

Keywords: Fast search, Adjacent pixel intensity differencequantization (APIDQ), DC image, Histogram feature.

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8255 Note to the Global GMRES for Solving the Matrix Equation AXB = F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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8254 Direct Transient Stability Assessment of Stressed Power Systems

Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

Abstract:

This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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8253 A Descent-projection Method for Solving Monotone Structured Variational Inequalities

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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8252 A GA-Based Role Assignment Approach for Web-based Cooperative Learning Environments

Authors: Yi-Chun Chang, Jian-Wei Li

Abstract:

Web-based cooperative learning focuses on (1) the interaction and the collaboration of community members, and (2) the sharing and the distribution of knowledge and expertise by network technology to enhance learning performance. Numerous research literatures related to web-based cooperative learning have demonstrated that cooperative scripts have a positive impact to specify, sequence, and assign cooperative learning activities. Besides, literatures have indicated that role-play in web-based cooperative learning environments enhances two or more students to work together toward the completion of a common goal. Since students generally do not know each other and they lack the face-to-face contact that is necessary for the negotiation of assigning group roles in web-based cooperative learning environments, this paper intends to further extend the application of genetic algorithm (GA) and propose a GA-based algorithm to tackle the problem of role assignment in web-based cooperative learning environments, which not only saves communication costs but also reduces conflict between group members in negotiating role assignments.

Keywords: genetic algorithm (GA), role assignment, role-play; web-based cooperative learning.

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8251 Error Propagation in the RK5GL3 Method

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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8250 Approximate Method of Calculation of Inviscid Hypersonic Flow

Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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8249 Development of an Implicit Physical Influence Upwind Scheme for Cell-Centered Finite Volume Method

Authors: Shidvash Vakilipour, Masoud Mohammadi, Rouzbeh Riazi, Scott Ormiston, Kimia Amiri, Sahar Barati

Abstract:

An essential component of a finite volume method (FVM) is the advection scheme that estimates values on the cell faces based on the calculated values on the nodes or cell centers. The most widely used advection schemes are upwind schemes. These schemes have been developed in FVM on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed for a cell-centered FVM that uses an implicit coupled solver. Results are compared with the exponential differencing scheme (EDS) and the skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated for a lid-driven cavity flow at Re = 1000, 3200, and 5000 and a backward-facing step flow at Re = 800. Simulations show considerable differences between the results of EDS scheme with benchmarks, especially for the lid-driven cavity flow at high Reynolds numbers. These differences occur due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results for the backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in the lid-driven cavity flow can be related to its lack of sensitivity to the pressure difference between cell face and upwind points, which is critical for the prediction of such vortex dominant flows.

Keywords: Cell-centered finite volume method, physical influence scheme, exponential differencing scheme, skew upwind differencing scheme, false diffusion.

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8248 Convergence Analysis of the Generalized Alternating Two-Stage Method

Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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8247 Analysis of Distribution of Thrust, Torque and Efficiency of a Constant Chord, Constant Pitch C.R.P. Fan by H.E.S. Method

Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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8246 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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8245 Relationships among Tourists’ Needs for Uniqueness, Perceived Authenticity and Behavioral Intentions

Authors: Deniz Karagöz Yüncü

Abstract:

This study tested a structural model which investigates the relationships among tourists’ need for uniqueness, perceived authenticity (object-based authenticity and existential authenticity) and behavioral intentions to consume cultural and heritage destinations. The sample of the study comprised of 281 participants in a cultural heritage site, in Cappadocia, Turkey. The data were provided via face to face interviews in two months (September and October) which considered the high season. Structural equation modeling was employed to test the causal relationships among the hypotheses. Findings revealed tourists’ creative choice had an influence on object-based authenticity and existential authenticity. Tourists’ avoidance had an influence on object-based authenticity. The study concluded that two dimensions, namely, the object based authenticity and existential authenticity had significant impact on behavioral intentions.

Keywords: Needs for uniqueness, object-based authenticity, existential authenticity, behavioral intentions.

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8244 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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8243 Factors Influencing the Housing Price: Developers’ Perspective

Authors: Ernawati Mustafa Kamal, Hasnanywati Hassan, Atasya Osmadi

Abstract:

The housing industry is crucial for sustainable development of every country. Housing is a basic need that can enhance the quality of life. Owning a house is therefore the main aim of individuals. However, affordability has become a critical issue towards homeownership. In recent years, housing price in the main cities has increased tremendously to unaffordable level. This paper investigates factors influencing the housing price from developer’s perspective and provides recommendation on strategies to tackle this issue. Online and face-to-face survey was conducted on housing developers operating in Penang, Malaysia. The results indicate that (1) location; (2) macroeconomics factor; (3) demographic factors; (4) land/zoning and; (5) industry factors are the main factors influencing the housing price. This paper contributes towards better understanding on developers’ view on how the housing price is determined and form a basis for government to help tackle the housing affordability issue.

Keywords: Factors influencing house price, housing affordability, housing developers, Malaysia.

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8242 The Homotopy Analysis Method for Solving Discontinued Problems Arising in Nanotechnology

Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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