Search results for: partial derivatives

Authors: Yaw-Juen Wang, Po-Chun Hsu

Abstract:

This paper presents an equivalent circuit model based on piecewise linear parallel branches (PLPB) to study solar cell modules which are partially shaded. The PLPB model can easily be used in circuit simulation software such as the ElectroMagnetic Transients Program (EMTP). This PLPB model allows the user to simulate several different configurations of solar cells, the influence of partial shadowing on a single or multiple cells, the influence of the number of solar cells protected by a bypass diode and the effect of the cell connection configuration on partial shadowing.

Keywords: Cell Connection Configurations, EMTP, Equivalent Circuit, Partial Shading, Photovoltaic Module

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Authors: R. Sarathi, G. Koperundevi

Abstract:

Design of Converter transformer insulation is a major challenge. The insulation of these transformers is stressed by both AC and DC voltages. Particle contamination is one of the major problems in insulation structures, as they generate partial discharges leading it to major failure of insulation. Similarly corona discharges occur in transformer insulation. This partial discharge due to particle movement / corona formation in insulation structure under different voltage wave shapes, are different. In the present study, UHF technique is adopted to understand the discharge activity and could be realized that the characteristics of UHF signal generated under low and high fields are different. In the case of corona generated signal, the frequency content of the UHF sensor output lies in the range 0.3-1.2 GHz and is not much varied except for its increase in magnitude of discharge with the increase in applied voltage. It is realized that the current signal injected due to partial discharges/corona is about 4ns duration measured for first one half cycle. Wavelet technique is adopted in the present study. It allows one to identify the frequency content present in the signal at different instant of time. The STD-MRA analysis helps one to identify the frequency band in which the energy content of the UHF signal is maximum.

Keywords: Contamination, Insulation, Partial Discharges, Transformer oil, UHF sensors.

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Authors: Akbar Zamaniyan, Alireza Behroozsarand, Hadi Ebrahimi

Abstract:

Partial oxidation (POX) of light hydrocarbons (e.g. methane) is occurred in the first part of the autothermal reformer (ATR). The results of the detailed modeling of the reformer based on the thermodynamic model of the POX and 1D heterogeneous catalytic model for the fixed bed section are considered here. According to the results, the overall performance of the ATR can be improved by changing the important feed parameters.

Keywords: Autothermal Reformer, Partial Oxidation, Mathematical Modeling, Process Simulation, Syngas.

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Authors: Jalal M. Abdallah

Abstract:

There is a great problem in testing and investigations the reliability of different type of transformers insulation materials. It summarized in how to create and simulate the real conditions of working transformer and testing its insulation materials for Partial Discharge PD, typically as in the working mode. A lot of tests may give untrue results as the physical behavior of the insulation material differs under tests from its working condition. In this work, the real working conditions were simulated, and a large number of specimens have been tested. The investigations first stage, begin with choosing samples of different types of insulation materials (papers, pressboards, etc.). The second stage, the samples were dried in ovens at 105 C⁰and 0.01bar for 48 hours, and then impregnated with dried and gasless oil (the water content less than 6 ppm.) at 105 C⁰and 0.01bar for 48 hours, after so specimen cooling at room pressure and temperature for 24 hours. The third stage is investigating PD for the samples using ICM PD measuring device. After that, a continuous test on oil-impregnated insulation materials (paper, pressboards) was developed, and the phase resolved partial discharge pattern of PD signals was measured. The important of this work in providing the industrial sector with trusted high accurate measuring results based on real simulated working conditions. All the PD patterns (results) associated with a discharge produced in well-controlled laboratory condition. They compared with other previous and other laboratory results. In addition, the influence of different temperatures condition on the partial discharge activities was studied.

Keywords: Transformers, insulation materials, voids, partial discharge (PD).

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Sylvia Encheva

Abstract:

The importance of hints in an intelligent tutoring system is well understood. The problems however related to their delivering are quite a few. In this paper we propose delivering of hints to be based on considering their usefulness. By this we mean that a hint is regarded as useful to a student if the student has succeeded to solve a problem after the hint was suggested to her/him. Methods from the theory of partial orderings are further applied facilitating an automated process of offering individualized advises on how to proceed in order to solve a particular problem.

Keywords: Decision support services, uncertainty management, partial orderings.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: Nelly К. Akhmatova, Оlga V. Lebedinskaya, Stanislav G. Markushin, Elvin А. Akhmatov, Lidiya A. Geiderova, Еlena А. Lebedinskaya, Vera M. Axenova, Аnatoliy P. Godovalov

Abstract:

The study of cytokine expression in mice under the influence of inactivated poliovirus and Imovaks polio vaccine in combination with derivatives of chitosan shows various kinds of processes. There is a significant increase in IL-12 in the serum of immunized animals, which should stimulate the production of IFN-γ NK-cells and T-cells and polarize the immune response to Th1 type. Thus, the derivatives of chitosan can promote cell component of the immune response, providing a full antiviral immunity.

Keywords: Poliovirus, chitosan, cytokine expression, antiviral immunity.

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Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

Abstract:

To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: Waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II.

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Authors: H. Bagheri, H. Emami, M. R. Pakravan

Abstract:

Crosstalk is the major limiting issue in very high bit-rate digital subscriber line (VDSL) systems in terms of bit-rate or service coverage. At the central office side, joint signal processing accompanied by appropriate power allocation enables complex multiuser processors to provide near capacity rates. Unfortunately complexity grows with the square of the number of lines within a binder, so by taking into account that there are only a few dominant crosstalkers who contribute to main part of crosstalk power, the canceller structure can be simplified which resulted in a much lower run-time complexity. In this paper, a multiuser power control scheme, namely iterative waterfilling, is combined with previously proposed partial crosstalk cancellation approaches to demonstrate the best ever achieved performance which is verified by simulation results.

Keywords: iterative waterfilling, partial crosstalk cancellation, run-time complexity, VDSL.

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Authors: Jingming Wu, Ruikang Hu, Junqi Yue, Zhaoguang Yang, Lifeng Zhang

Abstract:

Fecal sterol has been proposed as a chemical indicator of human fecal pollution even when fecal coliform populations have diminished due to water chlorination or toxic effects of industrial effluents. This paper describes an improved derivatization procedure for simultaneous determination of four fecal sterols including coprostanol, epicholestanol, cholesterol and cholestanol using gas chromatography-mass spectrometry (GC-MS), via optimization study on silylation procedures using N-O-bis (trimethylsilyl)-trifluoroacetamide (BSTFA), and N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA), which lead to the formation of trimethylsilyl (TMS) and tert-butyldimethylsilyl (TBS) derivatives, respectively. Two derivatization processes of injection-port derivatization and water bath derivatization (60 oC, 1h) were inspected and compared. Furthermore, the methylation procedure at 25 oC for 2h with trimethylsilydiazomethane (TMSD) for fecal sterols analysis was also studied. It was found that most of TMS derivatives demonstrated the highest sensitivities, followed by methylated derivatives. For BSTFA or MTBSTFA derivatization processes, the simple injection-port derivatization process could achieve the same efficiency as that in the tedious water bath derivatization procedure.

Keywords: Fecal Sterols, Methylation, Silylation, BSTFA, MTBSTFA, TMSD, GC-MS.

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Authors: Jingming Wu, Ruikang Hu, Junqi Yue, Zhaoguang Yang, Lifeng Zhang

Abstract:

Fecal sterol has been proposed as a chemical indicator of human fecal pollution even when fecal coliform populations have diminished due to water chlorination or toxic effects of industrial effluents. This paper describes an improved derivatization procedure for simultaneous determination of four fecal sterols including coprostanol, epicholestanol, cholesterol and cholestanol using gas chromatography-mass spectrometry (GC-MS), via optimization study on silylation procedures using N-O-bis (trimethylsilyl)-trifluoroacetamide (BSTFA), and N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA), which lead to the formation of trimethylsilyl (TMS) and tert-butyldimethylsilyl (TBS) derivatives, respectively. Two derivatization processes of injection-port derivatization and water bath derivatization (60 oC, 1h) were inspected and compared. Furthermore, the methylation procedure at 25 oC for 2h with trimethylsilydiazomethane (TMSD) for fecal sterols analysis was also studied. It was found that most of TMS derivatives demonstrated the highest sensitivities, followed by methylated derivatives. For BSTFA or MTBSTFA derivatization processes, the simple injection-port derivatization process could achieve the same efficiency as that in the tedious water bath derivatization procedure.

Keywords: Fecal Sterols, Methylation, Silylation, BSTFA, MTBSTFA, TMSD, GC-MS.

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: Kartini, K., Rohaidah, M.N., Zuraini, ZA.

Abstract:

Demolitions of buildings have created a lot of waste and one of it is clay bricks. The waste clay bricks were ground to roughly cement fineness and used to partially replaced cement at 10%, 20% and 30% with w/b ratio of 0.6 and tested at 7, 28, 60, 90 and 120 days. The result shows that the compressive strength of GCB concrete increases over age however, decreases as the level of replacements increases. It was also found that 10% replacement of GCB gave the highest compressive strength, however for optimum replacement, 30% was chosen as it still attained strength of grade 30 concrete. In terms of durability performances, results show that GCB replacement up to 30% was found to be efficient in reducing water absorption as well as water permeability. These studies show that GCB has the potential to be used as partial cement replacement in making concrete.

Keywords: Compressive Strength, Ground Clay Bricks, Partial Cement Replacement, Water Absorption and Permeability

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Authors: Sarah Fahad Alajmi, Tamer Ezzat Youssef

Abstract:

Here, we report a simple method for the direct conversion of 6-Nitro-1H-indole into N-substituted indoles via electrochemical dehydrogenative reaction with halogenated reagents under strongly basic conditions through N–R bond formation. The N-protected indoles have been prepared under moderate and scalable electrolytic conditions. The conduct of the reactions was performed in a simple divided cell under constant current without oxidizing reagents or transition-metal catalysts. The synthesized products have been characterized via UV/Vis spectrophotometry, 1H-NMR, and FTIR spectroscopy. A possible reaction mechanism is discussed based on the N-protective products. This methodology could be applied to the synthesis of various biologically active N-substituted indole derivatives.

Keywords: Green chemistry, 1H-indole, NH-containing heteroaromatic, organic electrosynthesis.

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Authors: Gu-Fang Mou, Ting-Zhu Huang

Abstract:

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

Keywords: Matrix completion, matrix completion, N10 -matrix, non-combinatorially symmetric, cycle, digraph.

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Authors: Kazuyoshi MORI

Abstract:

The two-stage compensator designs of linear system are investigated in the framework of the factorization approach. First, we give “full feedback" two-stage compensator design. Based on this result, various types of the two-stage compensator designs with partial feedbacks are derived.

Keywords: Linear System, Factorization Approach, Two-Stage Compensator Design, Parametrization of Stabilizing Controllers.

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Authors: M. Habchi, S. M. Mesli, M. Kotbi

Abstract:

A structural study of an aqueous electrolyte whose experimental results are available. It is a solution of LiCl-6H2O type at glassy state (120K) contrasted with pure water at room temperature by means of Partial Distribution Functions (PDF) issue from neutron scattering technique. Based on these partial functions, the Reverse Monte Carlo method (RMC) computes radial and angular correlation functions which allow exploring a number of structural features of the system. The obtained curves include some artifacts. To remedy this, we propose to introduce a screened potential as an additional constraint. Obtained results show a good matching between experimental and computed functions and a significant improvement in PDFs curves with potential constraint. It suggests an efficient fit of pair distribution functions curves.

Keywords: RMC simulation; Screened potential; partial and pair distribution functions; glassy and liquid state

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Authors: I. Algul, G. Akgun, H. Kurtaran

Abstract:

Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: Generalized differential quadrature method, doubly curved panels, laminated composite materials, small displacement.

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Authors: J. Arneric, A. Rozga

Abstract:

In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1,1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1,1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla stocks (information-s-communications industry).

Keywords: Heteroscedasticity, Log-likelihood Maximization, Quasi-Newton iteration procedure, Volatility.

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Authors: R. Fan, Q. Wan, H. Chen, Y.L. Liu, Y.P. Liu

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This paper considers a robust recovery of sparse frequencies from partial phase-only measurements. With the proposed method, sparse frequencies can be reconstructed, which makes full use of the sparse distribution in the Fourier representation of the complex-valued time signal. Simulation experiments illustrate the proposed method-s advantages over conventional methods in both noiseless and additive white Gaussian noise cases.

Keywords: Sparse signal recovery, phase-only measurements, Compressive sensing, convex relaxation.

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Authors: Ji Hyung Park, Dong-Hyun Seo, Young-Jin Jung, Han Sung Kim

Abstract:

The aim of this study is to evaluate the effects of the laser and partial vibration stimulation on the mice tibia with morphological characteristics. Twenty female C57BL/6 mice (12 weeks old) were used for the experiment. The study was carried out on four groups of animals each consisting of five mice. Four groups of mice were ovariectomized. Animals were scanned at 0 and 2 weeks after ovariectomy by using micro computed tomography to estimate morphological characteristics of tibial trabecular bone. Morphological analysis showed that structural parameters of multi-stimuli group appear significantly better phase in BV/TV, BS/BV, Tb.Th, Tb.N, Tb.Sp, and Tb.pf than single stimulation groups. However, single stimulation groups didn’t show significant effect on tibia with Sham group. This study suggests that multi-stimuli may restrain the change as the degenerate phase on osteoporosis in the mice tibia.

Keywords: Laser, Partial Vibration, Osteoporosis, in vivo micro-CT, mice.

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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Authors: Bothinah Altaf, Gary Montague, Elaine B. Martin

Abstract:

This study involves the modeling and monitoring of an ammonia synthesis fixed-bed reactor using partial least squares (PLS) and its variants. The process exhibits complex dynamic behavior due to the presence of heat recycling and feed quench. One limitation of static PLS model in this situation is that it does not take account of the process dynamics and hence dynamic PLS was used. Although it showed, superior performance to static PLS in terms of prediction, the monitoring scheme was inappropriate hence adaptive PLS was considered. A limitation of adaptive PLS is that non-conforming observations also contribute to the model, therefore, a new adaptive approach was developed, robust adaptive dynamic PLS. This approach updates a dynamic PLS model and is robust to non-representative data. The developed methodology showed a clear improvement over existing approaches in terms of the modeling of the reactor and the detection of faults.

Keywords: Ammonia synthesis fixed-bed reactor, dynamic partial least squares modeling, recursive partial least squares, robust modeling.

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Authors: Amir Badkoubeh, Guchuan Zhu

Abstract:

This paper addresses the problem of asymptotic tracking control of a linear parabolic partial differential equation with indomain point actuation. As the considered model is a non-standard partial differential equation, we firstly developed a map that allows transforming this problem into a standard boundary control problem to which existing infinite-dimensional system control methods can be applied. Then, a combination of energy multiplier and differential flatness methods is used to design an asymptotic tracking controller. This control scheme consists of stabilizing state-feedback derived from the energy multiplier method and feed-forward control based on the flatness property of the system. This approach represents a systematic procedure to design tracking control laws for a class of partial differential equations with in-domain point actuation. The applicability and system performance are assessed by simulation studies.

Keywords: Tracking Control, In-domain point actuation, PartialDifferential Equations.

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Authors: Shiraz Ahmad, Zhe-Ming Lu

Abstract:

An effective visual error concealment method has been presented by employing a robust rotation, scale, and translation (RST) invariant partial patch matching model (RSTI-PPMM) and exemplar-based inpainting. While the proposed robust and inherently feature-enhanced texture synthesis approach ensures the generation of excellent and perceptually plausible visual error concealment results, the outlier pruning property guarantees the significant quality improvements, both quantitatively and qualitatively. No intermediate user-interaction is required for the pre-segmented media and the presented method follows a bootstrapping approach for an automatic visual loss recovery and the image and video error concealment.

Keywords: Exemplar-based image and video inpainting, outlierpruning, RST-invariant partial patch matching model (RSTI-PPMM), visual error concealment.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: Integral differential equations, American options, jump–diffusion model, rational approximation.

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Authors: Rezaul Azim, Mohammad Tariqul Islam, Norbahiah Misran

Abstract:

In this paper, a planar antenna for UWB applications has been proposed. The antenna consists of a square patch, a partial ground plane and a slot on the ground plane. The proposed antenna is easy to be integrated with microwave circuitry for low manufacturing cost. The flat type antenna has a compact structure and the total size is 14.5×14.5mm2. The result shows that the impedance bandwidth (VSWR≤ 2) of the proposed antenna is 12.49 GHz (2.95 to 15.44 GHz), which is equivalent to 135.8%. Details of the proposed compact planar UWB antenna design is presented and discussed.

Keywords: Planar antenna, partial ground plane, ultrawideband(UWB) antenna.

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Authors: Rehana Naz, D. P. Mason, Fazal Mahomed

Abstract:

A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl-s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the two velocity components. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the axisymmetric liquid and free jet. The multiplier approach applied to the third-order partial differential equation for the stream function yields two local conserved vectors one of which is a non-local conserved vector for the system. One of the conserved vectors gives the conserved quantity for the axisymmetric free jet but the conserved quantity for the wall jet is not obtained from the second conserved vector. The conserved quantity for the axisymmetric wall jet is derived from a non-local conserved vector of the third-order partial differential equation for the stream function. This non-local conserved vector for the third-order partial differential equation for the stream function is obtained by using the stream function as multiplier.

Keywords: Axisymmetric jet, liquid jet, free jet, wall jet, conservation laws, conserved quantity.

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