Search results for: neutral Rayleigh equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1316

Search results for: neutral Rayleigh equation

566 Algorithms for the Fast Computation of PWL and PHL Transforms

Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

Abstract:

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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565 A Genetic Algorithm Approach for Solving Fuzzy Linear and Quadratic Equations

Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃2 + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃b . In this proposed method the final reached x̃b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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564 Bernstein-Galerkin Approach for Perturbed Constant-Coefficient Differential Equations, One-Dimensional Analysis

Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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563 Shear Behaviour of RC Deep Beams with Openings Strengthened with Carbon Fiber Reinforced Polymer

Authors: Mannal Tariq

Abstract:

Construction industry is making progress at a high pace. The trend of the world is getting more biased towards the high rise buildings. Deep beams are one of the most common elements in modern construction having small span to depth ratio. Deep beams are mostly used as transfer girders. This experimental study consists of 16 reinforced concrete (RC) deep beams. These beams were divided into two groups; A and B. Groups A and B consist of eight beams each, having 381 mm (15 in) and 457 mm (18 in) depth respectively. Each group was further subdivided into four sub groups each consisting of two identical beams. Each subgroup was comprised of solid/control beam (without opening), opening above neutral axis (NA), at NA and below NA. Except for control beams, all beams with openings were strengthened with carbon fibre reinforced polymer (CFRP) vertical strips. These eight groups differ from each other based on depth and location of openings. For testing sake, all beams have been loaded with two symmetrical point loads. All beams have been designed based on strut and tie model concept. The outcome of experimental investigation elaborates the difference in the shear behaviour of deep beams based on depth and location of circular openings variation. 457 mm (18 in) deep beam with openings above NA show the highest strength and 381 mm (15 in) deep beam with openings below NA show the least strength. CFRP sheets played a vital role in increasing the shear capacity of beams.

Keywords: CFRP, deep beams, openings in deep beams, strut and tie model, shear behaviour.

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562 Elucidating the Influence of Demographics and Psychological Traits on Investment Biases

Authors: Huei-Wen Lin

Abstract:

This study explored the relationship between psychological traits, demographics and financial behavioral biases for individual investors in Taiwan stock market. By using questionnaire survey method conducted in 2010, there are 554 valid convenient samples collected to examine the determinants of three types of behavioral biases. Based on literature review, two hypothesized models are constructed and further used to evaluate the effects of big five personality traits and demographic variables on investment biases through Structural Equation Model (SEM) analysis. The results showed that investment biases of individual investors are significantly related to four personality traits as well as some demographics.

Keywords: Behavioral finance, Big Five, Disposition effect, Herding, Overconfidence, Personality traits.

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561 How the Kinematic Swimming of European Eel Anguilla Anguilla Changes from Axial to Non-axial Velocity Flow

Authors: Younes Matar, Fabien Candelier, Camille Solliec

Abstract:

The aim of this study is to investigate the kinematics of undulatory elongated fish swimming against a velocity flow. We perform the experiments on European eel Anguilla Anguilla swimming in a hydrodynamic re-circulating tank with the velocity flow fixed at 0.2 m/s. We find that the undulating shape of overall eel body changes when it swims slantwise from the flow direction, by comparison to axial undulation shape. We examine this kinematics and we propose a general equation describing the lateral position of undulation body taking into account the direction of the eel-s swimming.

Keywords: Undulatory swimming, maneuver, eel Anguilla Anguilla, biomechanic.

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560 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller

Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi

Abstract:

In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.

Keywords: Chaotic system, Fuzzy control, Lorenz equation.

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559 Knowledge Acquisition, Absorptive Capacity, and Innovation Capability: An Empirical Study of Taiwan's Knowledge-Intensive Industries

Authors: Shu-Hsien. Liao, Chi-Chuan. Wu, Da-Chian. Hu, Guang An. Tsuei

Abstract:

This study investigates the roles of knowledge acquisition, absorptive capacity, and innovation capability in finance and manufacturing industries. With 362 valid questionnaires from manufactures and financial industries in Taiwan, we examine the relationships between absorptive capacity, knowledge acquisition and innovation capability using a structural equation model. The results indicate that absorptive capacity is the mediator between knowledge acquisition and innovation capability, and that knowledge acquisition has a positive effect on absorptive capacity.

Keywords: Absorptive capacity, knowledge acquisition, innovation capability.

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558 DTC-SVM Scheme for Induction Motors Fedwith a Three-level Inverter

Authors: Ehsan Hassankhan, Davood A. Khaburi

Abstract:

Direct Torque Control is a control technique in AC drive systems to obtain high performance torque control. The conventional DTC drive contains a pair of hysteresis comparators. DTC drives utilizing hysteresis comparators suffer from high torque ripple and variable switching frequency. The most common solution to those problems is to use the space vector depends on the reference torque and flux. In this Paper The space vector modulation technique (SVPWM) is applied to 2 level inverter control in the proposed DTC-based induction motor drive system, thereby dramatically reducing the torque ripple. Then the controller based on space vector modulation is designed to be applied in the control of Induction Motor (IM) with a three-level Inverter. This type of Inverter has several advantages over the standard two-level VSI, such as a greater number of levels in the output voltage waveforms, Lower dV/dt, less harmonic distortion in voltage and current waveforms and lower switching frequencies. This paper proposes a general SVPWM algorithm for three-level based on standard two-level SVPWM. The proposed scheme is described clearly and simulation results are reported to demonstrate its effectiveness. The entire control scheme is implemented with Matlab/Simulink.

Keywords: Direct torque control, space vector Pulsewidthmodulation(SVPWM), neutral point clamped(NPC), two-levelinverter.

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557 Soil Organic Carbon Pool Assessment and Chemical Evaluation of Soils in Akure North and South Local Government Area of Ondo State

Authors: B. F. Dada, B. S. Ewulo, M. A. Awodun, S. O. Ajayi

Abstract:

Aggregate soil carbon distribution and stock in the soil in the form of a carbon pool is important for soil fertility and sequestration. The amount of carbon pool and other nutrients statues of the soil are to benefit plants, animal and the environment in the long run. This study was carried out at Akure North and South Local Government; the study area is one of the 18 Local Government Areas of Ondo State in the Southwest geo-political zone of Nigeria. The sites were divided into Map Grids and geo-referenced with Global Positioning System (GPS). Horizons were designated and morphological description carried out on the field. Pedons were characterized and classified according to USDA soil taxonomy. The local government area shares boundaries with; Ikere Local Government (LG) in the North, Ise Orun LG in the northwest, Ifedore LG in the northeast Akure South LG in the East, Ose LG in the South East, and Owo LG in the South. SOC-pool at Federal College of Agriculture topsoil horizon A2 is significantly higher than all horizons, 67.83 th⁻¹. The chemical properties of the pedons have shown that the soil is very strongly acidic to neutral reaction (4.68 – 6.73). The nutrients status of the soil topsoil A1 and A2 generally indicates that the soils have a low potential for retaining plant nutrients, and therefore call for adequate soil management.

Keywords: Soil organic carbon, horizon, pedon, Akure.

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556 The Impact of Parent Involvement in Preschool Disabled Children

Authors: Sheng-Min Cheng

Abstract:

The purpose of this study was to investigate the relationship between parent involvement and preschool disabled children’s development. Parents of 3 year old disabled children (N=440) and 5 year old disabled children (N=937) participating in the Special Needs Education Longitudinal Study were interviewed or answered the web design questionnaire about their actions in parenting their disabled children. These children’s developments were also evaluated by their teachers. Data were analyzed using Structural Equation Modeling. Results were showed by tables and figures. Based on the results, the researcher made some suggestions for future studies.

Keywords: Child development, longitudinal data analysis, parent involvement, preschool disabled children.

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555 The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data

Authors: Jiashang Jiang, Yongxin Yuan

Abstract:

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords: Model updating, damped gyroscopic system, partially prescribed spectral information.

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554 A Clock Skew Minimization Technique Considering Temperature Gradient

Authors: Se-Jin Ko, Deok-Min Kim, Seok-Yoon Kim

Abstract:

The trend of growing density on chips has increases not only the temperature in chips but also the gradient of the temperature depending on locations. In this paper, we propose the balanced skew tree generation technique for minimizing the clock skew that is affected by the temperature gradients on chips. We calculate the interconnect delay using Elmore delay equation, and find out the optimal balanced clock tree by modifying the clock trees generated through the Deferred Merge Embedding(DME) algorithm. The experimental results show that the distance variance of clock insertion points with and without considering the temperature gradient can be lowered below 54% and we confirm that the skew is remarkably decreased after applying the proposed technique.

Keywords: clock, clock-skew, temperature, thermal.

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553 Defect Modes in Multilayered Piezoelectric Structures

Authors: D. G. Piliposyan

Abstract:

Propagation of electro-elastic waves in a piezoelectric waveguide with finite stacks and a defect layer is studied using a modified transfer matrix method. The dispersion equation for a periodic structure consisting of unit cells made up from two piezoelectric materials with metallized interfaces is obtained. An analytical expression, for the transmission coefficient for a waveguide with finite stacks and a defect layer, that is found can be used to accurately detect and control the position of the passband within a stopband. The result can be instrumental in constructing a tunable waveguide made of layers of different or identical piezoelectric crystals and separated by metallized interfaces.

Keywords: Defect mode, Bloch waves, periodic phononic crystal, piezoelectric composite waveguide.

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552 Oman’s Position in U.S. Tourists’ Mind: The Use of Importance-Performance Analysis on Destination Attributes

Authors: Mohammed Gamil Montasser, Angelo Battaglia

Abstract:

Tourism is making its presence felt across the Sultanate of Oman. The story is one of the most recognized phenomena as a sustainable solid growth and is considered a remarkable outcome for any destination. The competitive situation and challenges within the tourism industry worldwide entail a better understanding of the destination position and its image to achieve Oman’s aspiration to retain its international reputation as one of the most desirable destinations in the Middle East. To access general perceptions of Oman’s attributes, their importance and their influences among U.S. tourists, an online survey was conducted with 522 American travelers who have traveled internationally, including non-visitors, virtual-visitors and visitors to Oman. This research involved a total of 36 attributes in the survey. Participants were asked to rate their agreement on how each attribute represented Oman and how important each attribute was for selecting destinations on 5- point Likert Scale. They also indicated if each attribute has a positive, neutral or negative influence on their destination selection. Descriptive statistics and importance performance analysis (IPA) were conducted. IPA illustrated U.S. tourists’ perceptions of Oman’s destination attributes and their importance in destination selection on a matrix with four quadrants, divided by actual mean value in each grid for importance (M=3.51) and performance (M=3.57). Oman tourism organizations and destination managers may use these research findings for future marketing and management efforts toward the U.S. travel market.

Keywords: Analysis of importance and performance, destination attributes, Oman’s position, U.S. tourists.

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551 Nonlinear Stability of Convection in a Thermally Modulated Anisotropic Porous Medium

Authors: M. Meenasaranya, S. Saravanan

Abstract:

Conditions corresponding to the unconditional stability of convection in a mechanically anisotropic fluid saturated porous medium of infinite horizontal extent are determined. The medium is heated from below and its bounding surfaces are subjected to temperature modulation which consists of a steady part and a time periodic oscillating part. The Brinkman model is employed in the momentum equation with the Bousinessq approximation. The stability region is found for arbitrary values of modulational frequency and amplitude using the energy method. Higher order numerical computations are carried out to find critical boundaries and subcritical instability regions more accurately.

Keywords: Convection, porous medium, anisotropy, temperature modulation, nonlinear stability.

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550 The Effect of Slow Variation of Base Flow Profile on the Stability of Slightly Curved Mixing Layers

Authors: Irina Eglite, Andrei A. Kolyshkin

Abstract:

The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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549 Effect of Ionic Strength on Mercury Adsorption on Contaminated Soil

Authors: G. Petruzzelli, F. Pedron, I. Rosellini, E. Tassi, F. Gorini, B. Pezzarossa, M. Barbafieri

Abstract:

Mercury adsorption on soil was investigated at different ionic strengths using Ca(NO3)2 as a background electrolyte. Results fitted the Langmuir equation and the adsorption isotherms reached a plateau at higher equilibrium concentrations. Increasing ionic strength decreased the sorption of mercury, due to the competition of Ca ions for the sorption sites in the soils. The influence of ionic strength was related to the mechanisms of heavy metal sorption by the soil. These results can be of practical importance both in the agriculture and contaminated soils since the solubility of mercury in soils are strictly dependent on the adsorption and release process.

Keywords: Heavy metals, bioavailability, remediation, competitive sorption.

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548 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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547 A Constitutive Model for Time-Dependent Behavior of Clay

Authors: T. N. Mac, B. Shahbodaghkhan, N. Khalili

Abstract:

A new elastic-viscoplastic (EVP) constitutive model is proposed for the analysis of time-dependent behavior of clay. The proposed model is based on the bounding surface plasticity and the concept of viscoplastic consistency framework to establish continuous transition from plasticity to rate dependent viscoplasticity. Unlike the overstress based models, this model will meet the consistency condition in formulating the constitutive equation for EVP model. The procedure of deriving the constitutive relationship is also presented. Simulation results and comparisons with experimental data are then presented to demonstrate the performance of the model.

Keywords: Bounding surface, consistency theory, constitutive model, viscosity.

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546 Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space

Authors: Melih Turgut, Süha Yılmaz

Abstract:

In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

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545 Investigating the Usability of a University Website from the Users’ Perspective: An Empirical Study of Benue State University Website

Authors: Abraham Undu, Stephen Akuma

Abstract:

Websites are becoming a major component of an organization’s success in our ever globalizing competitive world. The website symbolizes an organization, interacting or projecting an organization’s principles, culture, values, vision, and perspectives. It is an interface connecting organizations and their clients. The university, as an academic institution, makes use of a website to communicate and offer computing services to its stakeholders (students, staff, host community, university management etc). Unfortunately, website designers often give more consideration to the technology, organizational structure and business objectives of the university than to the usability of the site. Website designers end up designing university websites which do not meet the needs of the primary users. This empirical study investigated the Benue State University website from the point view of students. This research was realized by using a standardized website usability questionnaire based on the five factors of usability defined by WAMMI (Website Analysis and Measurement Inventory): attractiveness, controllability, efficiency, learnability and helpfulness. The result of the investigation showed that the university website (https://portal.bsum.edu.ng/) has neutral usability level because of the usability issues associated with the website. The research recommended feasible solutions to improve the usability of the website from the users’ perspective and also provided a modified usability model that will be used for better evaluation of the Benue State University website.

Keywords: Usability, usability factors, university websites, user’s perspective, WAMMI, modified usability model, Benue State University.

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544 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory

Authors: Ping Liu, Yongkun Li

Abstract:

This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.

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543 Velocity Distribution in Open Channels: Combination of Log-law and Parabolic-law

Authors: Snehasis Kundu, Koeli Ghoshal

Abstract:

In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

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542 Adsorption of Paracetamol Using Activated Carbon of Dende and Babassu Coconut Mesocarp

Authors: R. C. Ferreira, H. H. C. De Lima, A. A. Cândido, O. M. Couto Junior, P. A. Arroyo, K. Q De Carvalho, G. F. Gauze, M. A. S. D. Barros

Abstract:

Removal of the widespread used drug paracetamol from water was investigated using activated carbon originated from dende coconut mesocarp and babassu coconut mesocarp. Kinetic and equilibrium data were obtained at different values of pH. Both activated carbons showed high efficiency when pH ≤ pHPZC as the carbonil group of paracetamol molecule are adsorbed due to positively charged carbon surface. Microporosity also played an important role in such process. Pseudo-second order model was better adjusted to the kinetic results. Equilibrium data may be represented by Langmuir equation.

Keywords: Adsorption, activated carbon, babassu, dende.

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541 An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli System

Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou

Abstract:

The aim of this work is to study the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step, the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: Boundary control, exact controllability, finite difference methods, functional optimization.

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540 Entrepreneurs’ Perceptions of the Economic, Social and Physical Impacts of Tourism

Authors: Oktay Emir

Abstract:

The objective of this study is to determine how entrepreneurs perceive the economic, social and physical impacts of tourism. The study was conducted in the city of Afyonkarahisar, Turkey, which is rich in thermal tourism resources and investments. A survey was used as the data collection method, and the questionnaire was applied to 472 entrepreneurs. A simple random sampling method was used to identify the sample. Independent sampling t-tests and ANOVA tests were used to analyse the data obtained. Additionally, some statistically significant differences (p<0.05) were found based on the participants’ demographic characteristics regarding their opinions about the social, economic and physical impacts of tourism activities.

Keywords: Tourism, perception, entrepreneurship, entrepreneurs, structural equation modelling.

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539 Influence of Artificial Roughness on Heat Transfer in the Rotating Flow

Authors: T. Magrakvelidze, N. Bantsadze, N. Lekveishvili, Kh. Lomidze

Abstract:

The results of an experimental study of the process of convective and boiling heat transfer in the vessel with stirrer for smooth and rough ring-shaped pipes are presented. It is established that creation of two-dimensional artificial roughness on the heated surface causes the essential (~100%) intensification of convective heat transfer. In case of boiling the influence of roughness appears on the initial stage of boiling and in case of fully developed nucleate boiling there was no intensification of heat transfer. The similitude equation for calculating convective heat transfer coefficient, which generalizes well experimental data both for the smooth and the rough surfaces is proposed.

Keywords: boiling, heat transfer, roughness.

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538 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra

Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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537 Dynamic Stability of Beams with Piezoelectric Layers Located on a Continuous Elastic Foundation

Authors: A. R. Nezamabadi, M. Karami Khorramabadi

Abstract:

This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Dynamic stability, Homogeneous graded beam-Piezoelectric layer, Harmonic balance method.

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