Search results for: propagation equation

Authors: Mahmoud Hassanlourad, Mehran Naghizadehrokni, Vahid Molaei

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In this study, the seismic behavior of a shallow tunnel with square cross section is investigated in a two layered and elastic heterogeneous environment using numerical method. To do so, FLAC finite difference software was used. Behavioral model of the ground and tunnel structure was assumed linear elastic. Dynamic load was applied to the model for 0.2 seconds from the bottom in form of a square pulse with maximum acceleration of 1 m/s². The interface between the two layers was considered at three different levels of crest, middle, and bottom of the tunnel. The stiffness of the two upper and lower layers was considered to be varied from 10 MPa to 1000 MPa. Deformation of cross section of the tunnel due to dynamic load propagation, as well as the values of axial force and bending moment created in the tunnel structure, were examined in the three states mentioned above. The results of analyses show that heterogeneity of the environment, its stratification, and positioning of the interface of the two layers with respect to tunnel height and the stiffness ratio of the two layers have significant effects on the value of bending moment, axial force, and distortion of tunnel cross-section.

Keywords: Dynamic analysis, shallow-buried tunnel, two-layered ground.

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Authors: Olatinwo M. O., Oyeleke Olaosebikan, David Henry O.

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Rain attenuation plays a lot of roles in the design of satellite and terrestrial microwave radio links, hence a good knowledge of its effect is of great interest to Engineers and scientists in that it is often required to give a high level of accuracy of the rainrate distribution that expresses rainrate from the lowest value to the highest. This study proposes a model to express rainrate parameters alpha (α) and beta (β) as a function of geographical location at 0.01% of the time. The tropical locations used in the development of the effect were Ilorin, Ile-Ife, Douala, Dar-es-Selam, Nairobi, Lusaka, and Brazilia.

This expression clearly confirms the variability of rainfall from place to place. When consistency test was carried out using the expression to generate rainrate for each location examined, the result obtained was reliable for rain intensities between 5mm/h and 200mm/h. The variability of α and β with latitude also shows that different latitudes have different cumulative rain distribution. The model proposed in this study would be one of the useful tools to Radio Engineers since the precipitation effect in the design of satellite and terrestrial microwave radio links is among the factors to consider when designing communication systems.

Keywords: Rain rate, attenuation, geographical location.

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Authors: Basudev Ghosh, Sreyasi Banerjee

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Using the pseudopotential technique the Sagdeev potential equation has been derived in a plasma consisting of twotemperature nonisothermal electrons, negatively charged dust grains and warm positive ions. The study shows that the presence of nonisothermal two-temperature electrons and charged dust grains have significant effects on the excitation and structure of the ionacoustic double layers in the model plasma under consideration. Only compressive type double layer is obtained in the present plasma model. The double layer solution has also been obtained by including higher order nonlinearity and nonisothermality, which is shown to modify the amplitude and deform the shape of the double layer.

Keywords: Two temperature non-isothermal electrons and charged dust grains.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: Farai Nyabadza

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The functional response of an infective is the relationship between an infected individual-s infection rate and the abundance of the number of susceptibles that one can potentially be infected. In this paper, we consider defensive attitudes for HIV prevention (primary prevention) while at the same time emphasizing on offensive attitudes that reduce infection for those infected (secondary prevention). We look at how defenses can protect an uninfected individual in the case where high risk groups such as commercial sex workers and those who deliberately go out to look for partners. We propose an infection cycle that begins with a search, then an encounter, a proposal and contact. The infection cycle illustrates the various steps an infected individual goes through to successfully infect a susceptible. For heterogeneous transmission of HIV, there will be no infection unless there is contact. The ability to avoid an encounter, detection, proposal and contact constitute defense.

Keywords: Functional response, Infection cycle, Prevention, Defences, SSS equation.

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Authors: Chalermsak Leetrakool, Komson Jirapattarasilp

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This research was to study effect of rotational speed and eccentric factors, which were affected on looseness of bearing. The experiment was conducted on three rotational speeds and five eccentric distances with 5 replications. The results showed that influenced factor affected to looseness of bearing was rotational speed and eccentric distance which showed statistical significant. Higher rotational speed would cause on high looseness. Moreover, more eccentric distance, more looseness of bearing. Using bearing at high rotational with high eccentric of shaft would be affected bearing fault more than lower rotational speed. The prediction equation of looseness was generated by regression analysis. The prediction has an effected to the looseness of bearing at 91.5%.

Keywords: Bearing, Looseness, Rotational speed, Eccentric

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Authors: Vera Pujani

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The purpose of this study is to investiagte the use of the ecommerce website in Indonesia as a developing country. The ecommerce website has been identified having the significant impact on business activities in particular solving the geographical problem for islanded countries likes Indonesia. Again, website is identified as a crucial marketing tool. This study presents the effect of quality and features on the use and user satisfaction employing ecommerce websites. Survey method for 115 undergraduate students of Management Department in Andalas University who are attending Management Information Systems (SIM) class have been undertaken. The data obtained is analyzed using Structural Equation Modeling (SEM) using SmartPLS program. This result found that quality of system and information, feature as well satisfaction influencing the use ecommerce website in Indonesia contexts.

Keywords: Use, Developing Country, Satisfaction, Website

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Authors: Abdelrahman A. H. Abdelrahim, Gharib Subhi Mahmoud, Sherzod Turaev, Azeddine Messikh

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Quantum gates are the basic building blocks in the quantum circuits model. These gates can be implemented using adiabatic or non adiabatic processes. Adiabatic models can be controlled using auxiliary qubits, whereas non adiabatic models can be simplified by using one single-shot implementation. In this paper, the controlled adiabatic evolutions is combined with the single-shot implementation to obtain quantum gates with controlled non adiabatic evolutions. This is an important improvement which can speed the implementation of quantum gates and reduce the errors due to the long run in the adiabatic model. The robustness of our scheme to different types of errors is also investigated.

Keywords: Adiabatic evolutions, non adiabatic evolutions, controlled adiabatic evolutions, quantum rotation gates, dephasing rates, master equation.

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Authors: Kazuo Komatsu, Hitoshi Takata

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This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: S. Karabulut, A. Güllü, A. Güldas, R. Gürbüz

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This study investigates the effects of the lead angle and chip thickness variation on surface roughness during the machining of compacted graphite iron using ceramic cutting tools under dry cutting conditions. Analytical models were developed for predicting the surface roughness values of the specimens after the face milling process. Experimental data was collected and imported to the artificial neural network model. A multilayer perceptron model was used with the back propagation algorithm employing the input parameters of lead angle, cutting speed and feed rate in connection with chip thickness. Furthermore, analysis of variance was employed to determine the effects of the cutting parameters on surface roughness. Artificial neural network and regression analysis were used to predict surface roughness. The values thus predicted were compared with the collected experimental data, and the corresponding percentage error was computed. Analysis results revealed that the lead angle is the dominant factor affecting surface roughness. Experimental results indicated an improvement in the surface roughness value with decreasing lead angle value from 88° to 45°.

Keywords: CGI, milling, surface roughness, ANN, regression, modeling, analysis.

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

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Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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Authors: Ebru Kavak Akpinar, Seda Toraman

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In the present work, the effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick-s diffusion equation. The results showed that increasing drying temperature accelerated the drying process. All drying experiments had only falling rate period. The average effective moisture diffusivity values varied from 2.807x10-10 to 6.977x10-10m2 s_1 over the temperature and velocity range. The temperature dependence of the effective moisture diffusivity for the thin layer drying of the ginger slices was satisfactorily described by an Arrhenius-type relationship with activation energy values of 19.313- 22.722 kJ.mol-1 within 40–70 °C and 0.8-3 ms-1 temperature range.

Keywords: Ginger, Drying, Activation energy, Moisture diffusivity.

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

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In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

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A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Abdul Wasy, Balakrishnan G., Yi Qi Wang, Atta Ur Rehman, Jung Il Song

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Vickers indentation is used to measure the hardness of materials. In this study, numerical simulation of Vickers indentation experiment was performed for Diamond like Carbon (DLC) coated materials. DLC coatings were deposited on stainless steel 304 substrates with Chromium buffer layer using RF Magnetron and T-shape Filtered Cathodic Vacuum Arc Dual system The objective of this research is to understand the elastic plastic properties, stress strain distribution, ring and lateral crack growth and propagation, penetration depth of indenter and delamination of coating from substrate with effect of buffer layer thickness. The effect of Poisson-s ratio of DLC coating was also analyzed. Indenter penetration is more in coated materials with thin buffer layer as compared to thicker one, under same conditions. Similarly, the specimens with thinner buffer layer failed quickly due to high residual stress as compared to the coated materials with reasonable thickness of 200nm buffer layer. The simulation results suggested the optimized thickness of 200 nm among the prepared specimens for durable and long service.

Keywords: Thin film, buffer layer. Diamond like Carbon, Vickers indentation, Poisson's ratio, Finite element.

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Authors: Nisha Goyal, R.K. Gupta

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Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Yi Chao Ma, Cheng Siong Chin, Wai Lok Woo

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Since the last decade, there has been a rapid growth in digital multimedia, such as high-resolution media files and threedimentional movies. Hence, there is a need for large digital storage such as Hard Disk Drive (HDD). As such, users expect to have a quieter HDD in their laptop. In this paper, a jury test has been conducted on a group of 34 people where 17 of them are students who are the potential consumer, and the remaining are engineers who know the HDD. A total 13 HDD sound samples have been selected from over hundred HDD noise recordings. These samples are selected based on an agreed subjective feeling. The samples are played to the participants using head acoustic playback system, which enabled them to experience as similar as possible the same environment as have been recorded. Analysis has been conducted and the obtained results have indicated different group has different perception over the noises. Two neural network-based acoustic annoyance models are established based on back propagation neural network. Four psychoacoustic metrics, loudness, sharpness, roughness and fluctuation strength, are used as the input of the model, and the subjective evaluation results are taken as the output. The developed models are reasonably accurate in simulating both training and test samples.

Keywords: Hard disk drive noise, jury test, neural network model, psychoacoustic annoyance.

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Authors: Noor Atinah Ahmad, Shazia Javed

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We present a discussion of three adaptive filtering algorithms well known for their one-step termination property, in terms of their relationship with the minimal residual method. These algorithms are the normalized least mean square (NLMS), Affine Projection algorithm (APA) and the recursive least squares algorithm (RLS). The NLMS is shown to be a result of the orthogonality condition imposed on the instantaneous approximation of the Wiener equation, while APA and RLS algorithm result from orthogonality condition in multi-dimensional minimal residual formulation. Further analysis of the minimal residual formulation for the RLS leads to a triangular system which also possesses the one-step termination property (in exact arithmetic)

Keywords: Adaptive filtering, minimal residual method, projection method.

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Authors: Saeed Sarabadan, Kamal Rashedi

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This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Mohammad Jamil Abd AlGhani

Abstract:

The natural native antioxidants N,N-P-methyl phenyl acetone and N,N-phenyl acetone were isolated from the Iraqi crude oil region of Kirkuk by ion exchange and their structure was characterized by spectral and chemical analysis methods. Tetraline was used as a liquid hydrocarbon to detect the efficiency of isolated molecules at elevated temperature (393 K) that it has physicochemical specifications and structure closed to hydrocarbons fractionated from crude oil. The synthesized universal antioxidant 2,6-ditertiaryisobutyl-p-methyl phenol (Unol) with known stochiometric coefficient of inhibition equal to (2) was used as a model for comparative evaluation at the same conditions. Modified chemiluminescence method was used to find the amount of absorbed oxygen and the induction periods in and without the existence of isolated antioxidants molecules. The results of induction periods and quantity of absorbed oxygen during the oxidation process were measured by manometric installation. It was seen that at specific equal concentrations of N,N-phenyl acetone and N, N-P-methyl phenyl acetone in comparison with Unol at 393 K were with (2) and (2.5) times efficient than do Unol. It means that they had the ability to inhibit the formation of new free radicals and prevent the chain reaction to pass from the propagation to the termination step rather than decomposition of formed hydroperoxides.

Keywords: Antioxidants, chemiluminescence, inhibition, unol.

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Authors: D. H. Kim, Y. H. Kim, T. Kim

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A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle.

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Authors: Hashim Mohammed Alhassan, Johnnie Ben-Edigbe

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Traffic flow in adverse weather conditions have been investigated in this study for general traffic, week day and week end traffic. The empirical evidence is strong in support of the view that rainfall affects macroscopic traffic flow parameters. Data generated from a basic highway section along J5 in Johor Bahru, Malaysia was synchronized with 161 rain events over a period of three months. This revealed a 4.90%, 6.60% and 11.32% reduction in speed for light rain, moderate rain and heavy rain conditions respectively. The corresponding capacity reductions in the three rainfall regimes are 1.08% for light rain, 6.27% for moderate rain and 29.25% for heavy rain. In the week day traffic, speed drops of 8.1% and 16.05% were observed for light and heavy conditions. The moderate rain condition speed increased by 12.6%. The capacity drops for week day traffic are 4.40% for light rain, 9.77% for moderate rain and 45.90% for heavy rain. The weekend traffic indicated speed difference between the dry condition and the three rainy conditions as 6.70% for light rain, 8.90% for moderate rain and 13.10% for heavy rain. The capacity changes computed for the weekend traffic were 0.20% in light rain, 13.90% in moderate rain and 16.70% in heavy rain. No traffic instabilities were observed throughout the observation period and the capacities reported for each rain condition were below the norain condition capacity. Rainfall has tremendous impact on traffic flow and this may have implications for shock wave propagation.

Keywords: Highway Capacity, Dry condition, Rainfall Intensity, Rainy condition, Traffic Flow Rate.

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Authors: C. P. Providakis, G. M. Angeli, M. J. Favvata, N. A. Papadopoulos, C. E. Chalioris, C. G. Karayannis

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An effort for the detection of damages in the  reinforcement bars of reinforced concrete members using PZTs is  presented. The damage can be the result of excessive elongation of  the steel bar due to steel yielding or due to local steel corrosion. In  both cases the damage is simulated by considering reduced diameter  of the rebar along the damaged part of its length. An integration  approach based on both electromechanical admittance methodology  and guided wave propagation technique is used to evaluate the  artificial damage on the examined longitudinal steel bar. Two  actuator PZTs and a sensor PZT are considered to be bonded on the  examined steel bar. The admittance of the Sensor PZT is calculated  using COMSOL 3.4a. Fast Furrier Transformation for a better  evaluation of the results is employed. An effort for the quantification  of the damage detection using the root mean square deviation  (RMSD) between the healthy condition and damage state of the  sensor PZT is attempted. The numerical value of the RSMD yields a  level for the difference between the healthy and the damaged  admittance computation indicating this way the presence of damage  in the structure. Experimental measurements are also presented.

 

Keywords: Concrete reinforcement, damage detection, electromechanical admittance, experimental measurements, finite element method, guided waves, PZT.

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Authors: A. Khourgami, M. Rafiee, H. Jafari, Z. Bitarafan

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To study the effect of suitable methods for propagation of True Potato Seed (TPS) progenies, transplant and selection of the best progenies, a factorial experiment base on a randomized complete block design was carried out in the research field of Sahneh region, Kermanshah, Iran during 2009-2010. Five selective progenies from CIP (International Potato Center) including CIP.994013, CIP.994002, CIP.994014, CIP.888006, and CIP.994001 and two transplant preparation methods (Paper pot preparation for mechanical cultivation and preparation in transplant trays for manual cultivation) were studied in three replications. Results showed that different progenies had no significant effect on plant height (cm) and tuber yield (t ha-1), whereas had a significant effect on number of tubers per unit area (m2). There was significant difference between transplant preparation methods for plant height and tuber yield. The interaction effect of progenies and transplant preparation method was not significant for these traits. CIP.888006 progeny and paper pot preparation method produced the highest tuber yields. Also CIP.994002 and CIP.994014 progenies considered as the best progenies under paper pot preparation method due to high yields.

Keywords: Potato, Solanum tuberosum, TPS progenies, Transplant preparation method

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

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In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

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Authors: Weihua Ruan, Kuan-Chou Chen

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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: Choon Ki Ahn, Jung Hun Park, Wook Hyun Kwon

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CEMTool is a command style design and analyzing package for scientific and technological algorithm and a matrix based computation language. In this paper, we present new 2D & 3D finite element method (FEM) packages for CEMTool. We discuss the detailed structures and the important features of pre-processor, solver, and post-processor of CEMTool 2D & 3D FEM packages. In contrast to the existing MATLAB PDE Toolbox, our proposed FEM packages can deal with the combination of the reserved words. Also, we can control the mesh in a very effective way. With the introduction of new mesh generation algorithm and fast solving technique, our FEM packages can guarantee the shorter computational time than MATLAB PDE Toolbox. Consequently, with our new FEM packages, we can overcome some disadvantages or limitations of the existing MATLAB PDE Toolbox.

Keywords: CEMTool, Finite element method (FEM), Numericalanalysis, Partial differential equation (PDE)

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Authors: A. F. Ali, D. M. Shawky

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Discovering new biological knowledge from the highthroughput biological data is a major challenge to bioinformatics today. To address this challenge, we developed a new approach for protein classification. Proteins that are evolutionarily- and thereby functionally- related are said to belong to the same classification. Identifying protein classification is of fundamental importance to document the diversity of the known protein universe. It also provides a means to determine the functional roles of newly discovered protein sequences. Our goal is to predict the functional classification of novel protein sequences based on a set of features extracted from each protein sequence. The proposed technique used datasets extracted from the Structural Classification of Proteins (SCOP) database. A set of spectral domain features based on Fast Fourier Transform (FFT) is used. The proposed classifier uses multilayer back propagation (MLBP) neural network for protein classification. The maximum classification accuracy is about 91% when applying the classifier to the full four levels of the SCOP database. However, it reaches a maximum of 96% when limiting the classification to the family level. The classification results reveal that spectral domain contains information that can be used for classification with high accuracy. In addition, the results emphasize that sequence similarity measures are of great importance especially at the family level.

Keywords: Bioinformatics, Artificial Neural Networks, Protein Sequence Analysis, Feature Extraction.

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Authors: Shan Gao

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In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.

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