Search results for: Distribution function

Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The objective of positioning the fixture elements in the fixture is to make the workpiece stiff, so that geometric errors in the manufacturing process can be reduced. Most of the work for optimal fixture layout used the minimization of the sum of the nodal deflection normal to the surface as objective function. All deflections in other direction have been neglected. We propose a new method for fixture layout optimization in this paper, which uses the element strain energy. The deformations in all the directions have been considered in this way. The objective function in this method is to minimize the sum of square of element strain energy. Strain energy and stiffness are inversely proportional to each other. The optimization problem is solved by the sequential quadratic programming method. Three different kinds of case studies are presented, and results are compared with the method using nodal deflections as objective function to verify the propose method.

Keywords: Fixture layout, optimization, strain energy, quadratic programming.

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Authors: B. Skrabic, N. Tomic-Plazibat

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In this paper real money demand function is analyzed within multivariate time-series framework. Cointegration approach is used (Johansen procedure) assuming interdependence between money demand determinants, which are nonstationary variables. This will help us to understand the behavior of money demand in Croatia, revealing the significant influence between endogenous variables in vector autoregrression system (VAR), i.e. vector error correction model (VECM). Exogeneity of the explanatory variables is tested. Long-run money demand function is estimated indicating slow speed of adjustment of removing the disequilibrium. Empirical results provide the evidence that real industrial production and exchange rate explains the most variations of money demand in the long-run, while interest rate is significant only in short-run.

Keywords: Cointegration, Long-run equilibrium, Money demand function, Vector error correction model.

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Authors: Min Sun, Zhenyu Liu

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

Keywords: variational inequalities, monotone function, global convergence.

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Authors: María I. Jiménez, Alberto Izquierdo, Juan J. Villacorta, Lara del Val, Mariano Raboso

Abstract:

There are very complex communication systems, as the multifunction radar, MFAR (Multi-Function Array Radar), where functions are integrated all together, and simultaneously are performed the classic functions of tracking and surveillance, as all the functions related to the communication, countermeasures, and calibration. All these functions are divided into the tasks to execute. The task scheduler is a key element of the radar, since it does the planning and distribution of energy and time resources to be shared and used by all tasks. This paper presents schedulers based on the use of multiple queue. Several schedulers have been designed and studied, and it has been made a comparative analysis of different performed schedulers. The tests and experiments have been done by means of system software simulation. Finally a suitable set of radar characteristics has been selected to evaluate the behavior of the task scheduler working.

Keywords: Queue Theory, Radar, Scheduler, Task.

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Authors: R. Fatehi, M.A. Fayazbakhsh, M.T. Manzari

Abstract:

Discretization of spatial derivatives is an important issue in meshfree methods especially when the derivative terms contain non-linear coefficients. In this paper, various methods used for discretization of second-order spatial derivatives are investigated in the context of Smoothed Particle Hydrodynamics. Three popular forms (i.e. "double summation", "second-order kernel derivation", and "difference scheme") are studied using one-dimensional unsteady heat conduction equation. To assess these schemes, transient response to a step function initial condition is considered. Due to parabolic nature of the heat equation, one can expect smooth and monotone solutions. It is shown, however in this paper, that regardless of the type of kernel function used and the size of smoothing radius, the double summation discretization form leads to non-physical oscillations which persist in the solution. Also, results show that when a second-order kernel derivative is used, a high-order kernel function shall be employed in such a way that the distance of inflection point from origin in the kernel function be less than the nearest particle distance. Otherwise, solutions may exhibit oscillations near discontinuities unlike the "difference scheme" which unconditionally produces monotone results.

Keywords: Heat conduction, Meshfree methods, Smoothed ParticleHydrodynamics (SPH), Second-order derivatives.

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Authors: Mário C. Ricci

Abstract:

A new, rapidly convergent, numerical procedure for internal loading distribution computation in statically loaded, singlerow, angular-contact ball bearings, subjected to a known combined radial and thrust load, which must be applied so that to avoid tilting between inner and outer rings, is used to find the load distribution differences between a loaded unfitted bearing at room temperature, and the same loaded bearing with interference fits that might experience radial temperature gradients between inner and outer rings. For each step of the procedure it is required the iterative solution of Z + 2 simultaneous nonlinear equations – where Z is the number of the balls – to yield exact solution for axial and radial deflections, and contact angles.

Keywords: Ball, Bearing, Static, Load, Iterative, Numerical, Method, Temperature, Fit.

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Authors: Jiann-Ming Wu, Hsiao-Chang Chen, Chun-Chang Wu, Pei-Hsun Hsu

Abstract:

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

Keywords: Blind image deconvolution, linear shift-invariant(LSI), linear image degradation model, radial basis functions (rbf), recursive function, annealed Hopfield neural networks.

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Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

Abstract:

Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic.

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Authors: Y. Z. Zhu, S. P. Meng, W. W. Sun

Abstract:

The influence of eccentric discharge of stored solids in squat silos has been highly valued by many researchers. However, calculation method of lateral pressure under eccentric flowing still needs to be deeply studied. In particular, the lateral pressure distribution on vertical wall could not be accurately recognized mainly because of its asymmetry. In order to build mechanical model of lateral pressure, flow channel and flow pattern of stored solids in squat silo are studied. In this passage, based on Janssen-s theory, the method for calculating lateral static pressure in squat silos after eccentric discharge is proposed. Calculative formulae are deduced for each of three possible cases. This method is also focusing on unsymmetrical distribution characteristic of silo wall normal pressure. Finite element model is used to analysis and compare the results of lateral pressure and the numerical results illustrate the practicability of the theoretical method.

Keywords: Squat silo, eccentric discharge, lateral pressure, asymmetric distribution

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Kittipong Tripetch

Abstract:

This paper proposes a study of input impedance of 2 types of CMOS active inductors. It derives 2 input impedance formulas. The first formula is the input impedance of the grounded active inductor. The second formula is the input impedance of the floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of the fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption. 

Keywords: Grounded active inductor, floating active inductor, Fully differential bandpass amplifier.

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Authors: Kanyarat Bussaban, Siriporn Poolsuwan

Abstract:

This study is conducted with the objective to prove how the distorted distribution of welfare affects the quality of school-age children lives differently in the case ofan urban community in Bangkok. 334 samples are households from Suan Oi and Ratchapatubtim communities. The study of sample communities found the difference between two communityareasthatare close. The people of Suan Oi community are economically better off people than the people of the Ratchapatubtim community. They share the benefits of using most services except the welfare of a child’s education.The resulting analysis of the variability in quality of life of the school age children indicate that heads of the households are women looking for quality of life benefits when the compulsory school age is less.A study of the two communities suggests that the inequality in incomedistribution currently affects the quality of life of school-age children.

Keywords: Inequality, Income distribution, Quality of school-age children lives, Welfare state.

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Authors: Donglan Zha, Jiansong Si

Abstract:

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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Authors: Yinchang Du, Yangfang Li

Abstract:

In this work, we used the single Langmuir probe to measure the plasma density distribution in an geometrically asymmetric capacitive coupled plasma discharge system. Because of the frame structure of powered electrode, the plasma density was not homogeneous in the discharge volume. It was higher under the frame, but lower in the centre. Finite element simulation results showed a good agreement with the experiment results. To increase the electron density in the central volume and improve the homogeneity of the plasma, we added an auxiliary electrode, powered by DC voltage, in the simulation geometry. The simulation results showed that the auxiliary electrode could alter the potential distribution and improve the density homogeneity effectively.

Keywords: Capacitive coupled discharge, asymmetric discharge, homogeneous plasma.

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Authors: R. Varalakshmi

Abstract:

For the last decade, researchers have started to focus their interest on Multicast Group Key Management Framework. The central research challenge is secure and efficient group key distribution. The present paper is based on the Bit model based Secure Multicast Group key distribution scheme using the most popular absolute encoder output type code named Gray Code. The focus is of two folds. The first fold deals with the reduction of computation complexity which is achieved in our scheme by performing fewer multiplication operations during the key updating process. To optimize the number of multiplication operations, an O(1) time algorithm to multiply two N-bit binary numbers which could be used in an N x N bit-model of reconfigurable mesh is used in this proposed work. The second fold aims at reducing the amount of information stored in the Group Center and group members while performing the update operation in the key content. Comparative analysis to illustrate the performance of various key distribution schemes is shown in this paper and it has been observed that this proposed algorithm reduces the computation and storage complexity significantly. Our proposed algorithm is suitable for high performance computing environment.

Keywords: Multicast Group key distribution, Bit model, Integer Multiplications, reconfigurable mesh, optimal algorithm, Gray Code, Computation Complexity, Storage Complexity.

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Authors: Won-Ho Kim, Chang-Ho Hyun, Moon-Jung Kim

Abstract:

In this paper, zigbee communication based wireless energy surveillance system is presented. The proposed system consists of multiple energy surveillance devices and an energy surveillance monitor. Each different standby power-off value of electric device is set automatically by using learning function of energy surveillance device. Thus adaptive standby power-off function provides user convenience and it maximizes the energy savings. Also, power consumption monitoring function is helpful to reduce inefficient energy consumption in home. The zigbee throughput simulator is designed to evaluate minimum transmission power and maximum allowable information quantity in the proposed system. The test result of prototype has been satisfied all the requirements. The proposed system has confirmed that can be used as an intelligent energy surveillance system for energy savings in home or office.

Keywords: Energy monitoring system, Energy surveillance system, Energy sensor network, Energy savings.

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Authors: Wen-Lung Huang, Shih-Pin Chen

Abstract:

This paper investigates the optimization problem of multi-product aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh-s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level a is formulated to calculate the bounds of the optimal performance measure at a . Then the membership function of the optimal performance measure is constructed by enumerating different values of a . Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.

Keywords: fuzzy data, aggregate production planning, membership function, parametric programming

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Authors: Jin-Hong Kim

Abstract:

Roles of the vegetation to mitigate the erosion of the stream bed or to facilitate the deposition of the fine sediments by the species of the aquatic plants were presented. Field investigation on the estimation of the change of the bed level and the estimation of the flow characteristics were performed. The results showed that Phragmites japonica has the mitigation function of 0.3m-0.4m of the erosion in the range of higher than 1.0m/s of flow velocity at the vegetated region. Phragmites communis has the mitigation function of 0.2m-0.3m of the erosion in the range of higher than 0.7m/s of flow velocity at the vegetated region. Salix gracilistyla has greater role than Phragmites japonica and Phragmites communis to sustain the stable channel. It has the mitigation function of 0.4m-0.5m of the erosion in the range of higher than 1.4m/s of flow velocity. Miscanthus sacchariflorus has a weak role compared with that of Phragmites japonica and Salix gracilistyla, but it has still function for sustaining the stable bed. From these results, the vegetation has effective roles to mitigate the erosion or to facilitate the deposition of the stream bed.

Keywords: Aquatic plants, Phragmites japonica, Phragmites communis, Miscanthus sacchariflorus, Salix gracilistyla.

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Authors: Malinwo Estone Ayikpa

Abstract:

With the rapid increase of grid-connected PV systems over the last decades, genuine challenges have arisen for engineers and professionals of energy field in the planning and operation of existing distribution networks with the integration of new generation sources. However, the conventional distribution network, in its design was not expected to receive other generation outside the main power supply. The tools generally used to analyze the networks become inefficient and cannot take into account all the constraints related to the operation of grid-connected PV systems. Some of these constraints are voltage control difficulty, reverse power flow, and especially voltage unbalance which could be due to the poor distribution of single-phase PV systems in the network. In order to analyze the impact of the connection of small and large number of PV systems to the distribution networks, this paper presents an efficient optimization tool that minimizes voltage unbalance in three-phase distribution networks with active and reactive power injections from the allocation of single-phase and three-phase PV plants. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. Good reduction of voltage unbalance can be achieved by reactive power control of the PV systems. The presented tool is based on the three-phase current injection method and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems.

Keywords: Photovoltaic generation, primal-dual interior point method, three-phase optimal power flow, unbalanced system.

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Authors: I. Omerhodzic, S. Avdakovic, A. Nuhanovic, K. Dizdarevic

Abstract:

In this paper, a wavelet-based neural network (WNN) classifier for recognizing EEG signals is implemented and tested under three sets EEG signals (healthy subjects, patients with epilepsy and patients with epileptic syndrome during the seizure). First, the Discrete Wavelet Transform (DWT) with the Multi-Resolution Analysis (MRA) is applied to decompose EEG signal at resolution levels of the components of the EEG signal (δ, θ, α, β and γ) and the Parseval-s theorem are employed to extract the percentage distribution of energy features of the EEG signal at different resolution levels. Second, the neural network (NN) classifies these extracted features to identify the EEGs type according to the percentage distribution of energy features. The performance of the proposed algorithm has been evaluated using in total 300 EEG signals. The results showed that the proposed classifier has the ability of recognizing and classifying EEG signals efficiently.

Keywords: Epilepsy, EEG, Wavelet transform, Energydistribution, Neural Network, Classification.

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Authors: Tomohiro Hachino, Kenji Shimoda, Hitoshi Takata

Abstract:

This paper presents a method of model selection and identification of Hammerstein systems by hybridization of the genetic algorithm (GA) and particle swarm optimization (PSO). An unknown nonlinear static part to be estimated is approximately represented by an automatic choosing function (ACF) model. The weighting parameters of the ACF and the system parameters of the linear dynamic part are estimated by the linear least-squares method. On the other hand, the adjusting parameters of the ACF model structure are properly selected by the hybrid algorithm of the GA and PSO, where the Akaike information criterion is utilized as the evaluation value function. Simulation results are shown to demonstrate the effectiveness of the proposed hybrid algorithm.

Keywords: Hammerstein system, identification, automatic choosing function model, genetic algorithm, particle swarm optimization.

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Authors: Mohammad Mashud, S. M. Nahid Hasan

Abstract:

The aim of the research work is to modify the NACA 4215 airfoil with flap and rotary cylinder at the leading edge of the airfoil and experimentally study the static pressure distribution over the airfoil completed with flap and leading-edge vortex generator. In this research, NACA 4215 wing model has been constructed by generating the profile geometry using the standard equations and design software such as AutoCAD and SolidWorks. To perform the experiment, three wooden models are prepared and tested in subsonic wind tunnel. The experiments were carried out in various angles of attack. Flap angle and momentum injection rate are changed to observe the characteristics of pressure distribution. In this research, a new concept of flow separation control mechanism has been introduced to improve the aerodynamic characteristics of airfoil. Control of flow separation over airfoil which experiences a vortex generator (rotating cylinder) at the leading edge of airfoil is experimentally simulated under the effects of momentum injection. The experimental results show that the flow separation control is possible by the proposed mechanism, and benefits can be achieved by momentum injection technique. The wing performance is significantly improved due to control of flow separation by momentum injection method.

Keywords: Airfoil, momentum injection, flap and pressure distribution.

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Authors: K. Hosseini, MD., R. Mazaheri, MD., H.R. Khoddami Vishteh, MD., M.A. Mansournia, MD., H. Angoorani, MD

Abstract:

Background: Tissue Doppler Echocardiography (TDE) assesses diastolic function more accurately than routine pulse Doppler echo. Assessment of the effects of dynamic and static exercises on the heart by using TDE can provides new information about the athlete-s heart syndrome. Methods: This study was conducted on 20 elite wrestlers, 14 endurance runners at national level and 21 non-athletes as the control group. Participants underwent two-dimensional echocardiography, standard Doppler and TDE. Results: Wrestlers had the highest left ventricular mass index, enddiastolic inter-ventricular septum thickness and left ventricular Posterior wall thickness. Runners had the highest Left ventricular end-diastolic volume, LV ejection fraction, stroke volume and cardiac output. In TDE, the early diastolic velocity of mitral annulus to the late diastolic velocity ratio in athletic groups was greater than the controls with no significant difference. Conclusion: In spite of cardiac morphological changes in athletes, TDE shows that cardiac diastolic function won-t be adversely affected.

Keywords: Tissue Doppler Echocardiography, Diastolic function, Athlete's heart syndrome, Static exercise, Dynamic exercise

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Authors: Saleem Z. Ramadan

Abstract:

In this paper, a model is proposed to determine the life distribution parameters of the useful life region for the PV system utilizing a combination of non-parametric and linear regression analysis for the failure data of these systems. Results showed that this method is dependable for analyzing failure time data for such reliable systems when the data is scarce.

Keywords: Masking, Bathtub model, reliability, non-parametric analysis, useful life.

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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Authors: Srinath Shetty K., Shivashankar R., Rashmi P. Shetty

Abstract:

Earth reinforcing techniques have become useful and economical to solve problems related to difficult grounds and provide satisfactory foundation performance. In this context, this paper uses radial basis function neural network (RBFNN) for predicting the bearing pressure of strip footing on reinforced granular bed overlying weak soil. The inputs for the neural network models included plate width, thickness of granular bed and number of layers of reinforcements, settlement ratio, water content, dry density, cohesion and angle of friction. The results indicated that RBFNN model exhibited more than 84 % prediction accuracy, thereby demonstrating its application in a geotechnical problem.

Keywords: Bearing pressure, granular bed, radial basis function neural network, strip footing.

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

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As far as the latest technological improvements are concerned, digital systems more become popular than the past. Despite this growing demand to the digital systems, content copy and attack against the digital cinema contents becomes a serious problem. To solve the above security problem, we propose “traceable watermarking using Hash functions for digital cinema system. Digital Cinema is a great application for traceable watermarking since it uses watermarking technology during content play as well as content transmission. The watermark is embedded into the randomly selected movie frames using CRC-32 techniques. CRC-32 is a Hash function. Using it, the embedding position is distributed by Hash Function so that any party cannot break off the watermarking or will not be able to change. Finally, our experimental results show that proposed DWT watermarking method using CRC-32 is much better than the convenient watermarking techniques in terms of robustness, image quality and its simple but unbreakable algorithm.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip, traceable watermark, Hash Function, CRC-32.

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: Labiba Gilani, Asifullah Khan, Anwar M. Mirza

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This paper introduces a technique of distortion estimation in image watermarking using Genetic Programming (GP). The distortion is estimated by considering the problem of obtaining a distorted watermarked signal from the original watermarked signal as a function regression problem. This function regression problem is solved using GP, where the original watermarked signal is considered as an independent variable. GP-based distortion estimation scheme is checked for Gaussian attack and Jpeg compression attack. We have used Gaussian attacks of different strengths by changing the standard deviation. JPEG compression attack is also varied by adding various distortions. Experimental results demonstrate that the proposed technique is able to detect the watermark even in the case of strong distortions and is more robust against attacks.

Keywords: Blind Watermarking, Genetic Programming (GP), Fitness Function, Discrete Cosine Transform (DCT).

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Authors: M.kayhani, M.Nourouzi, A. Amiri Delooei

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This study presents an exact general solution for steady-state conductive heat transfer in cylindrical composite laminates. Appropriate Fourier transformation has been obtained using Sturm-Liouville theorem. Series coefficients are achieved by solving a set of equations that related to thermal boundary conditions at inner and outer of the cylinder, also related to temperature continuity and heat flux continuity between each layer. The solution of this set of equations are obtained using Thomas algorithm. In this paper, the effect of fibers- angle on temperature distribution of composite laminate is investigated under general boundary conditions. Here, we show that the temperature distribution for any composite laminates is between temperature distribution for laminates with θ = 0° and θ = 90° .

Keywords: exact solution, composite laminate, heat conduction, cylinder, Fourier transformation.

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