Search results for: Pseudo-hyperbolic partial integro-differential equations

Authors: M. Karami Khorramabadi, P. Khazaeinejad

Abstract:

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

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This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

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Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers’ equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile.

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Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: M. Ghanbari, S. Hossainpour, G. Rezazadeh

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In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

Keywords: Micro-polar theory, Galerkin method, MEMS, micro-fluid.

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Authors: Débora C. G. Oliveira, Julio D. Salles, Bruna A. Moriy, João A. Rossignolo, Holmer Savastano JR.

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The objective of this study was to identify the optimal level of partial replacement of Portland cement by the ashes originating from burning straw and bagasse from sugar cane (ASB). Order to this end, were made five series of flat plates and cylindrical bodies: control and others with the partial replacement in 20, 30, 40 and 50% of ASB in relation to the mass of the Ordinary Portland cement, and conducted a mechanical testing of simple axial compression (cylindrical bodies) and the four-point bending (flat plates) and determined water absorption (WA), bulk density (BD) and apparent void volume (AVV) on both types of specimens. Based on the data obtained, it may be noted that the control treatment containing only Portland cement, obtained the best results. However, the cylindrical bodies with 20% ashes showed better results compared to the other treatments. And in the formulations plates, the treatment which showed the best results was 30% cement replacement by ashes.

Keywords: Modulus of rupture, simple axial compression, waste.

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Authors: Hans H. Diel

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This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

Keywords: Computational Modeling, Simulation of Quantum Theory, Quantum Field Theory, Quantum Electrodynamics

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

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Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: Azam Marjani, Saeed Shirazian

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This work deals with modeling and simulation of SO2 removal in a ceramic membrane by means of FEM. A mass transfer model was developed to predict the performance of SO2 absorption in a chemical solvent. The model was based on solving conservation equations for gas component in the membrane. Computational fluid dynamics (CFD) of mass and momentum were used to solve the model equations. The simulations aimed to obtain the distribution of gas concentration in the absorption process. The effect of the operating parameters on the efficiency of the ceramic membrane was evaluated. The modeling findings showed that the gas phase velocity has significant effect on the removal of gas whereas the liquid phase does not affect the SO2 removal significantly. It is also indicated that the main mass transfer resistance is placed in the membrane and gas phase because of high tortuosity of the ceramic membrane.

Keywords: Gas separation, finite element, ceramic, sulphur dioxide, simulation.

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Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: Mohan Kotamrazu

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Cyclone Hudhud which battered the city of Visakhapatnam on 12^th October, 2014, damaged many buildings, public amenities and infrastructure facilities along the Visakha- Bheemili coastal corridor. More than half the green cover of the city was wiped out. Majority of the trees along the coastal corridor suffered from complete or partial damage. In order to understand the different ways that trees incurred damage during the cyclone, a damage assessment study was carried out by the author. The areas covered by this study included two university campuses, several parks and residential colonies which bore the brunt of the cyclone. Post disaster attempts have been made to restore many of the trees that have suffered from partial or complete damage from the effects of extreme winds. This paper examines the various ways that trees incurred damage from the cyclone Hudhud and presents some examples of the restoration efforts carried out by educational institutions, public parks and religious institutions of the city of Visakhapatnam in the aftermath of the devastating cyclone.

Keywords: Defoliation, restoration, salt spray damage, wind throw.

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Authors: Chun-Ta Chen, Te-Tan Liao, Hoang-Vuong Pham

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In this paper motion analysis on a winding stair-climbing is investigated using our proposed rotational arm type of robotic wheelchair. For now, the robotic wheelchair is operated in an open mode to climb winding stairs by a dynamic turning, therefore, the dynamics model is required to ensure a passenger-s safety. Equations of motion based on the skid-steering analysis are developed for the trajectory planning and motion analysis on climbing winding stairs. Since the robotic wheelchair must climb a winding staircase stably, the winding trajectory becomes a constraint equation to be followed, and the Baumgarte-s method is used to solve for the constrained dynamics equations. Experimental results validate the behavior of the prototype as it climbs a winding stair.

Keywords: Climb, robotic wheelchair, skid-steering, windingstair .

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Authors: Christian Mosch, Reiner Anderl, Antonio Álvaro de Assis Moura, Klaus Schützer

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Due to short product life cycles, increasing variety of products and short cycles of leap innovations manufacturing companies have to increase the flexibility of factory structures. Flexibility of factory structures is based on defined factory planning processes in which product, process and resource data of various partial domains have to be considered. Thus factory planning processes can be characterized as iterative, interdisciplinary and participative processes [1]. To support interdisciplinary and participative character of planning processes, a federative factory data management (FFDM) as a holistic solution will be described. FFDM is already implemented in form of a prototype. The interim results of the development of FFDM will be shown in this paper. The principles are the extracting of product, process and resource data from documents of various partial domains providing as web services on a server. The described data can be requested by the factory planner by using a FFDM-browser.

Keywords: BRAGECRIM, Factory Planning Process, FactoryData Management, Web Services

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Authors: Mihai Lungu

Abstract:

The paper presents the design of a mini-UAV attitude controller using the backstepping method. Starting from the nonlinear dynamic equations of the mini-UAV, by using the backstepping method, the author of this paper obtained the expressions of the elevator, rudder and aileron deflections, which stabilize the UAV, at each moment, to the desired values of the attitude angles. The attitude controller controls the attitude angles, the angular rates, the angular accelerations and other variables that describe the UAV longitudinal and lateral motions. To design the nonlinear controller, by using the backstepping technique, the nonlinear equations and the Lyapunov analysis have been directly used. The designed controller has been implemented in Matlab/Simulink environment and its effectiveness has been tested with a campaign of numerical simulations using data from the UAV flight tests. The obtained results are very good and they are better than the ones found in previous works.

Keywords: Attitude angles, Backstepping, Controller, UAV.

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Authors: M. Palanivel, R. Uthayakumar

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In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous Weibull distribution deteriorating items with power demand pattern is presented. In this model, the holding cost per unit of the item per unit time is assumed to be an increasing linear function of time spent in storage. Here the retailer is allowed a trade-credit offer by the supplier to buy more items. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimizing the total inventory cost by finding the optimal time interval and finding the optimal order quantity. The optimal solution of the model is illustrated with the help of numerical examples. Finally sensitivity analysis and graphical representations are given to demonstrate the model.

Keywords: Power demand pattern, Partial backlogging, Time dependent holding cost, Trade credit, Weibull deterioration.

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Authors: Chien-Jen Liu, Shu Ching Yang

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Using the technology acceptance model (TAM), this study examined the external variables of technological complexity (TC) to acquire a better understanding of the factors that influence the acceptance of computer application courses by learners at Active Aging Universities. After the learners in this study had completed a 27-hour Facebook course, 44 learners responded to a modified TAM survey. Data were collected to examine the path relationships among the variables that influence the acceptance of Facebook-mediated community learning. The partial least squares (PLS) method was used to test the measurement and the structural model. The study results demonstrated that attitudes toward Facebook use directly influence behavioral intentions (BI) with respect to Facebook use, evincing a high prediction rate of 58.3%. In addition to the perceived usefulness (PU) and perceived ease of use (PEOU) measures that are proposed in the TAM, other external variables, such as TC, also indirectly influence BI. These four variables can explain 88% of the variance in BI and demonstrate a high level of predictive ability. Finally, limitations of this investigation and implications for further research are discussed.

Keywords: Technology acceptance model (TAM), technological complexity, partial least squares (PLS), perceived usefulness.

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Authors: M. H. Kargarnovin, K. Momeni

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The study of the stress distribution on a hollow cylindrical fiber placed in a composite material is considered in this work and an analytical solution for this stress distribution has been constructed. Finally some parameters such as fiber-s thickness and fiber-s length are considered and their effects on the distribution of stress have been investigated. For finding the governing relations, continuity equations for the axisymmetric problem in cylindrical coordinate (r,o,z) are considered. Then by assuming some conditions and solving the governing equations and applying the boundary conditions, an equation relates the stress applied to the representative volume element with the stress distribution on the fiber has been found.

Keywords: Axial Loading, Composite, Hollow CylindricalFiber, Stress Distribution.

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Authors: Arunesh Chandra, Pankaj Chandna, Surinder Deswal, Rajesh Kumar Mishra, Rajender Kumar

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The arm length, hand length, hand breadth and middle finger length of 1540 right-handed industrial workers of Haryana state was used to assess the relationship between the upper limb dimensions and stature. Initially, the data were analyzed using basic univariate analysis and independent t-tests; then simple and multiple linear regression models were used to estimate stature using SPSS (version 17). There was a positive correlation between upper limb measurements (hand length, hand breadth, arm length and middle finger length) and stature (p < 0.01), which was highest for hand length. The accuracy of stature prediction ranged from ± 54.897 mm to ± 58.307 mm. The use of multiple regression equations gave better results than simple regression equations. This study provides new forensic standards for stature estimation from the upper limb measurements of male industrial workers of Haryana (India). The results of this research indicate that stature can be determined using hand dimensions with accuracy, when only upper limb is available due to any reasons likewise explosions, train/plane crashes, mutilated bodies, etc. The regression formula derived in this study will be useful for anatomists, archaeologists, anthropologists, design engineers and forensic scientists for fairly prediction of stature using regression equations.

Keywords: Anthropometric dimensions, Forensic identification, Industrial workers, Stature prediction.

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Authors: Tawfig Eltaif, Hesham A. Bakarman, N. Alsowaidi, M. R. Mokhtar, Malek Harbawi

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Multiple User Interference (MUI) considers the primary problem in Optical Code-Division Multiple Access (OCDMA), which resulting from the overlapping among the users. In this article we aim to mitigate this problem by studying an interference cancellation scheme called successive interference cancellation (SIC) scheme. This scheme will be tested on two different detection schemes, spectral amplitude coding (SAC) and direct detection systems (DS), using partial modified prime (PMP) as the signature codes. It was found that SIC scheme based on both SAC and DS methods had a potential to suppress the intensity noise, that is to say it can mitigate MUI noise. Furthermore, SIC/DS scheme showed much lower bit error rate (BER) performance relative to SIC/SAC scheme for different magnitude of effective power. Hence, many more users can be supported by SIC/DS receiver system.

Keywords: Multiple User Interference (MUI), Optical Code-Division Multiple Access (OCDMA), Partial Modified Prime Code (PMP), Spectral Amplitude Coding (SAC), Successive Interference Cancellation (SIC).

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Authors: Arun Goel

Abstract:

The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free overfall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, Support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, Support vector machine (Polynomial and rbf) models and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free overfall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: Air entrainment rate, dissolved oxygen, regression, SVM, weir.

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Authors: Jamal A. Gledan, Othman A. Azzeidani

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During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three – parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: Geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: A. T. Eswara

Abstract:

This paper analyses the unsteady, two-dimensional stagnation point flow of an incompressible viscous fluid over a flat sheet when the flow is started impulsively from rest and at the same time, the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. The partial differential equations governing the laminar boundary layer forced convection flow are non-dimensionalised using semi-similar transformations and then solved numerically using an implicit finitedifference scheme known as the Keller-box method. Results pertaining to the flow and heat transfer characteristics are computed for all dimensionless time, uniformly valid in the whole spatial region without any numerical difficulties. Analytical solutions are also obtained for both small and large times, respectively representing the initial unsteady and final steady state flow and heat transfer. Numerical results indicate that the velocity ratio parameter is found to have a significant effect on skin friction and heat transfer rate at the surface. Furthermore, it is exposed that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state (large time solution).

Keywords: Forced flow, Keller-box method, Stagnation point, Stretching flat sheet, Unsteady laminar boundary layer, Velocity ratio parameter.

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Authors: Ioan Popa, Cristiana Tudor, Radu Lupu

Abstract:

The interdependences among stock market indices were studied for a long while by academics in the entire world. The current financial crisis opened the door to a wide range of opinions concerning the understanding and measurement of the connections considered to provide the controversial phenomenon of market integration. Using data on the log-returns of 17 stock market indices that include most of the CEE markets, from 2005 until 2009, our paper studies the problem of these dependences using a new methodological tool that takes into account both the volatility clustering effect and the stochastic properties of these linkages through a Dynamic Conditional System of Simultaneous Equations. We find that the crisis is well captured by our model as it provides evidence for the high volatility – high dependence effect.

Keywords: Stock market interdependences, Dynamic System ofSimultaneous Equations, financial crisis

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Authors: José Luis Oslinger, Luis Carlos Castro

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Measurements of capacitance C and dissipation factor tand of the stator insulation system provide useful information about internal defects within the insulation. The index k is defined as the proportionality constant between the changes at high voltage of capacitance DC and of the dissipation factor Dtand . DC and Dtand values were highly correlated when small flat defects were within the insulation and that correlation was lost in the presence of large narrow defects like electrical treeing. The discrimination between small and large defects is made resorting to partial discharge PD phase angle analysis. For the validation of the results, C and tand measurements were carried out in a 15MVA 4160V steam turbine turbogenerator placed in a sugar mill. In addition, laboratory test results obtained by other authors were analyzed jointly. In such laboratory tests, model coil bars subjected to thermal cycling resulted highly degraded and DC and Dtand values were not correlated. Thus, the index k could not be calculated.

Keywords: Aging, capacitance, dissipation factor, electrical treeing, insulation condition, partial discharge.

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Authors: Nnamdi N. Omehe, Chibuzo Emeruwa

Abstract:

ZnIn2Se4 and ZnIn2Te4 are vacancy defect materials whose properties have been investigated using Density Functional Theory (DFT) framework. The pseudopotential method in conjunction with the LDA+U technique and the Projector Augmented Wave (PAW) was used to calculate the electronic band structure, total density of state, and the partial density of state; while the norm-conserving pseudopotential was used to calculate the dielectric response function with scissors shift. Both ZnIn2Se4 and ZnIn2Te4 were predicted to be semiconductors with energy band gap of 1.66 eV and 1.33 eV respectively, and they both have direct energy band gap at the gamma point of high symmetry. The topmost valence subband for ZnIn2Se4 and ZnIn2Te4 has an energy width of 5.7 eV and 6.0 eV respectively. The calculations of partial density of state (PDOS) show that for ZnIn2Se4, the top of the valence band is dominated by Se-4p orbital, while the bottom of the conduction band is composed of In-5p, In-5s, and Zn-4s states. PDOS for ZnIn2Te4, shows that the top of the valence band is mostly of Te-5p states, while its conduction band bottom is composed mainly of Zn-4s, Te-5p, Te-5s, and In-5s states. Dielectric response function calculation yielded (0) of 11.9 and 36 for ZnIn2Se4 and ZnIn2Te4 respectively.

Keywords: Optoelectronic, Dielectric Response Function, LDA+U, band structure calculation.

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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