Search results for: Block floating point arithmetic
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2368

Search results for: Block floating point arithmetic

2128 Copolymers of Pyrrole and α,ω-Dithienyl Terminated Poly(ethylene glycol)

Authors: Nesrin Köken, Esin A. Güvel, Nilgün Kızılcan

Abstract:

This work presents synthesis of α,ω-dithienyl terminated poly(ethylene glycol) (PEGTh) capable for further chain extension by either chemical or electrochemical polymeriztion. PEGTh was characterized by FTIR and 1H-NMR. Further copolymerization of PEGTh and pyrrole (Py) was performed by chemical oxidative polymerization using ceric (IV) salt as an oxidant (PPy-PEGTh). PEG without end group modification was used directly to prepare copolymers with Py by Ce (IV) salt (PPy-PEG). Block copolymers with mole ratio of pyrrole to PEGTh (PEG) 50:1 and 10:1 were synthesized. The electrical conductivities of copolymers PPy-PEGTh and PPy-PEG were determined by four point probe technique. Influence of the synthetic route and content of the insulating segment on conductivity and yield of the copolymers were investigated.

Keywords: Chemical oxidative polymerization, conducting copolymer, poly(ethylene glycol), polypyrrole.

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2127 Note to the Global GMRES for Solving the Matrix Equation AXB = F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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2126 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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2125 Effect of Hartmann Number on Free Convective Flow in a Square Cavity with Different Positions of Heated Square Block

Authors: Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin

Abstract:

This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

Keywords: Finite element method, free convection, Hartmann number, square cavity.

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2124 Reversible Watermarking for H.264/AVC Videos

Authors: Yih-Chuan Lin, Jung-Hong Li

Abstract:

In this paper, we propose a reversible watermarking scheme based on histogram shifting (HS) to embed watermark bits into the H.264/AVC standard videos by modifying the last nonzero level in the context adaptive variable length coding (CAVLC) domain. The proposed method collects all of the last nonzero coefficients (or called last level coefficient) of 4×4 sub-macro blocks in a macro block and utilizes predictions for the current last level from the neighbor block-s last levels to embed watermark bits. The feature of the proposed method is low computational and has the ability of reversible recovery. The experimental results have demonstrated that our proposed scheme has acceptable degradation on video quality and output bit-rate for most test videos.

Keywords: Reversible data hiding, H.264/AVC standard, CAVLC, Histogram shifting

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2123 Intra Prediction using Weighted Average of Pixel Values According to Prediction Direction

Authors: Kibaek Kim, Dongjin Jung, Jinik Jang, Jechang Jeong

Abstract:

In this paper, we proposed a method to reduce quantization error. In order to reduce quantization error, low pass filtering is applied on neighboring samples of current block in H.264/AVC. However, it has a weak point that low pass filtering is performed regardless of prediction direction. Since it doesn-t consider prediction direction, it may not reduce quantization error effectively. Proposed method considers prediction direction for low pass filtering and uses a threshold condition for reducing flag bit. We compare our experimental result with conventional method in H.264/AVC and we can achieve the average bit-rate reduction of 1.534% by applying the proposed method. Bit-rate reduction between 0.580% and 3.567% are shown for experimental results.

Keywords: Coding efficiency, H.264/AVC, Intra prediction, Low pass filter

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2122 Motion Prediction and Motion Vector Cost Reduction during Fast Block Motion Estimation in MCTF

Authors: Karunakar A K, Manohara Pai M M

Abstract:

In 3D-wavelet video coding framework temporal filtering is done along the trajectory of motion using Motion Compensated Temporal Filtering (MCTF). Hence computationally efficient motion estimation technique is the need of MCTF. In this paper a predictive technique is proposed in order to reduce the computational complexity of the MCTF framework, by exploiting the high correlation among the frames in a Group Of Picture (GOP). The proposed technique applies coarse and fine searches of any fast block based motion estimation, only to the first pair of frames in a GOP. The generated motion vectors are supplied to the next consecutive frames, even to subsequent temporal levels and only fine search is carried out around those predicted motion vectors. Hence coarse search is skipped for all the motion estimation in a GOP except for the first pair of frames. The technique has been tested for different fast block based motion estimation algorithms over different standard test sequences using MC-EZBC, a state-of-the-art scalable video coder. The simulation result reveals substantial reduction (i.e. 20.75% to 38.24%) in the number of search points during motion estimation, without compromising the quality of the reconstructed video compared to non-predictive techniques. Since the motion vectors of all the pair of frames in a GOP except the first pair will have value ±1 around the motion vectors of the previous pair of frames, the number of bits required for motion vectors is also reduced by 50%.

Keywords: Motion Compensated Temporal Filtering, predictivemotion estimation, lifted wavelet transform, motion vector

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2121 Information Measures Based on Sampling Distributions

Authors: Om Parkash, A. K. Thukral, C. P. Gandhi

Abstract:

Information theory and Statistics play an important role in Biological Sciences when we use information measures for the study of diversity and equitability. In this communication, we develop the link among the three disciplines and prove that sampling distributions can be used to develop new information measures. Our study will be an interdisciplinary and will find its applications in Biological systems.

Keywords: Entropy, concavity, symmetry, arithmetic mean, diversity, equitability.

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2120 Effect of Thermal Radiation on Temperature Variation in 2-D Stagnation-Point flow

Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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2119 Multi Switched Split Vector Quantizer

Authors: M. Satya Sai Ram, P. Siddaiah, M. Madhavi Latha

Abstract:

Vector quantization is a powerful tool for speech coding applications. This paper deals with LPC Coding of speech signals which uses a new technique called Multi Switched Split Vector Quantization, This is a hybrid of two product code vector quantization techniques namely the Multi stage vector quantization technique, and Switched split vector quantization technique,. Multi Switched Split Vector Quantization technique quantizes the linear predictive coefficients in terms of line spectral frequencies. From results it is proved that Multi Switched Split Vector Quantization provides better trade off between bitrate and spectral distortion performance, computational complexity and memory requirements when compared to Switched Split Vector Quantization, Multi stage vector quantization, and Split Vector Quantization techniques. By employing the switching technique at each stage of the vector quantizer the spectral distortion, computational complexity and memory requirements were greatly reduced. Spectral distortion was measured in dB, Computational complexity was measured in floating point operations (flops), and memory requirements was measured in (floats).

Keywords: Unconstrained vector quantization, Linear predictiveCoding, Split vector quantization, Multi stage vector quantization, Switched Split vector quantization, Line Spectral Frequencies.

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2118 Combined Analysis of Sudoku Square Designs with Same Treatments

Authors: A. Danbaba

Abstract:

Several experiments are conducted at different environments such as locations or periods (seasons) with identical treatments to each experiment purposely to study the interaction between the treatments and environments or between the treatments and periods (seasons). The commonly used designs of experiments for this purpose are randomized block design, Latin square design, balanced incomplete block design, Youden design, and one or more factor designs. The interest is to carry out a combined analysis of the data from these multi-environment experiments, instead of analyzing each experiment separately. This paper proposed combined analysis of experiments conducted via Sudoku square design of odd order with same experimental treatments.

Keywords: Sudoku designs, combined analysis, multi-environment experiments, common treatments.

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2117 Applications of Cascade Correlation Neural Networks for Cipher System Identification

Authors: B. Chandra, P. Paul Varghese

Abstract:

Crypto System Identification is one of the challenging tasks in Crypt analysis. The paper discusses the possibility of employing Neural Networks for identification of Cipher Systems from cipher texts. Cascade Correlation Neural Network and Back Propagation Network have been employed for identification of Cipher Systems. Very large collection of cipher texts were generated using a Block Cipher (Enhanced RC6) and a Stream Cipher (SEAL). Promising results were obtained in terms of accuracy using both the Neural Network models but it was observed that the Cascade Correlation Neural Network Model performed better compared to Back Propagation Network.

Keywords: Back Propagation Neural Networks, CascadeCorrelation Neural Network, Crypto systems, Block Cipher, StreamCipher.

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2116 Order Penetration Point Location using Fuzzy Quadratic Programming

Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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2115 Research on Urban Point of Interest Generalization Method Based on Mapping Presentation

Authors: Chengming Li, Yong Yin, Peipei Guo, Xiaoli Liu

Abstract:

Without taking account of the attribute richness of POI (point of interest) data and spatial distribution limited by roads, a POI generalization method considering both attribute information and spatial distribution has been proposed against the existing point generalization algorithm merely focusing on overall information of point groups. Hierarchical characteristic of urban POI information expression has been firstly analyzed to point out the measurement feature of the corresponding hierarchy. On this basis, an urban POI generalizing strategy has been put forward: POIs urban road network have been divided into three distribution pattern; corresponding generalization methods have been proposed according to the characteristic of POI data in different distribution patterns. Experimental results showed that the method taking into account both attribute information and spatial distribution characteristics of POI can better implement urban POI generalization in the mapping presentation.

Keywords: POI, Road network, spatial information expression, selection method, distribution pattern.

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2114 A Reconfigurable Processing Element Implementation for Matrix Inversion Using Cholesky Decomposition

Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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2113 Analytical Model of Connection Establishment Duration Calculation in Wireless Networks

Authors: Y. Chaiko

Abstract:

It is important to provide possibility of so called “handover" for the mobile subscriber from GSM network to Wi-Fi network and back. To solve specified problem it is necessary to estimate connection time between base station and wireless access point. Difficulty to estimate this parameter is that it doesn-t described in specifications of the standard and, hence, no recommended value is given. In this paper, the analytical model is presented that allows the estimating connection time between base station and IEEE 802.11 access point.

Keywords: Access point, connection procedure, Wi-Fi network.

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2112 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

Authors: Menglong Su, Shaoyun Shi, Qing Xu

Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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2111 Some (v + 1, b + r + λ + 1, r + λ + 1, k, λ + 1) Balanced Incomplete Block Designs (BIBDs) from Lotto Designs (LDs)

Authors: Oluwaseun. A. Alawode, Timothy. A. Bamiduro, Adekunle. A. Eludire

Abstract:

The paper considered the construction of BIBDs using potential Lotto Designs (LDs) earlier derived from qualifying parent BIBDs. The study utilized Li’s condition  pr t−1  ( t−1 2 ) + pr− pr t−1 (t−1) 2  < ( p 2 ) λ, to determine the qualification of a parent BIBD (v, b, r, k, λ) as LD (n, k, p, t) constrained on v ≥ k, v ≥ p, t ≤ min{k, p} and then considered the case k = t since t is the smallest number of tickets that can guarantee a win in a lottery. The (15, 140, 28, 3, 4) and (7, 7, 3, 3, 1) BIBDs were selected as parent BIBDs to illustrate the procedure. These BIBDs yielded three potential LDs each. Each of the LDs was completely generated and their properties studied. The three LDs from the (15, 140, 28, 3, 4) produced (9, 84, 28, 3, 7), (10, 120, 36, 3, 8) and (11, 165, 45, 3, 9) BIBDs while those from the (7, 7, 3, 3, 1) produced the (5, 10, 6, 3, 3), (6, 20, 10, 3, 4) and (7, 35, 15, 3, 5) BIBDs. The produced BIBDs follow the generalization (v + 1, b + r + λ + 1, r +λ+1, k, λ+1) where (v, b, r, k, λ) are the parameters of the (9, 84, 28, 3, 7) and (5, 10, 6, 3, 3) BIBDs. All the BIBDs produced are unreduced designs.

Keywords: Balanced Incomplete Block Designs, Lotto Designs, Unreduced Designs, Lottery games.

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2110 Production of Biodiesel from Different Edible Oils

Authors: Amir Shafeeq, Ayyaz Muhammad, Noman Hassan, Rofice Dickson

Abstract:

Different vegetable oil based biodiesel (FAMES) were prepared by alkaline transesterification using refined oils as well as waste frying oil (WFO). Methanol and sodium hydroxide are used as catalyst under similar reaction conditions. To ensure the quality of biodiesel produced, a series of different ASTM Standard tests were carried out. In this context, various testwere done including viscosity, carbon residue, specific gravity, corrosion test, flash point, cloud point and pour point. Results revealed that characteristics of biodiesel depend on the feedstock and it is far better than petroleum diesel.

Keywords: Biodiesel, Edible oils, Separation.

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2109 Water Boundary Layer Flow Over Rotating Sphere with Mass Transfer

Authors: G. Revathi, P. Saikrishnan

Abstract:

An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.

Keywords: Boundary layer, suction, mass transfer, rotating sphere.

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2108 Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options

Authors: R.Balamurugan, S.Subramanian

Abstract:

This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.

Keywords: Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.

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2107 Positive Solutions for Discrete Third-order Three-point Boundary Value Problem

Authors: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

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2106 Integration of Virtual Learning of Induction Machines for Undergraduates

Authors: Rajesh Kumar, Puneet Aggarwal

Abstract:

In context of understanding problems faced by undergraduate students while carrying out laboratory experiments dealing with high voltages, it was found that most of the students are hesitant to work directly on machine. The reason is that error in the circuitry might lead to deterioration of machine and laboratory instruments. So, it has become inevitable to include modern pedagogic techniques for undergraduate students, which would help them to first carry out experiment in virtual system and then to work on live circuit. Further advantages include that students can try out their intuitive ideas and perform in virtual environment, hence leading to new research and innovations. In this paper, virtual environment used is of MATLAB/Simulink for three-phase induction machines. The performance analysis of three-phase induction machine is carried out using virtual environment which includes Direct Current (DC) Test, No-Load Test, and Block Rotor Test along with speed torque characteristics for different rotor resistances and input voltage, respectively. Further, this paper carries out computer aided teaching of basic Voltage Source Inverter (VSI) drive circuitry. Hence, this paper gave undergraduates a clearer view of experiments performed on virtual machine (No-Load test, Block Rotor test and DC test, respectively). After successful implementation of basic tests, VSI circuitry is implemented, and related harmonic distortion (THD) and Fast Fourier Transform (FFT) of current and voltage waveform are studied.

Keywords: Block rotor test, DC test, no-load test, virtual environment, VSI.

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2105 Maximum Power Point Tracking Using FLC Tuned with GA

Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

Abstract:

The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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2104 Ten Limit Cycles in a Quintic Lyapunov System

Authors: Li Feng

Abstract:

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.

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2103 Cooling Turbine Blades using Exciting Boundary Layer

Authors: Ali Ghobadi, Seyed Mohammad Javadi, Behnam Rahimi

Abstract:

The present study is concerned with the effect of exciting boundary layer on cooling process in a gas-turbine blades. The cooling process is numerically investigated. Observations show cooling the first row of moving or stable blades leads to increase their life-time. Results show that minimum temperature in cooling line with exciting boundary layer is lower than without exciting. Using block in cooling line of turbines' blade causes flow pattern and stability in boundary layer changed that causes increase in heat transfer coefficient. Results show at the location of block, temperature of turbines' blade is significantly decreased. The k-ε turbulence model is used.

Keywords: Cooling, Exciting Boundary Layer, Heat Transfer, Turbine Blade.

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2102 A Rigid Point Set Registration of Remote Sensing Images Based on Genetic Algorithms and Hausdorff Distance

Authors: F. Meskine, N. Taleb, M. Chikr El-Mezouar, K. Kpalma, A. Almhdie

Abstract:

Image registration is the process of establishing point by point correspondence between images obtained from a same scene. This process is very useful in remote sensing, medicine, cartography, computer vision, etc. Then, the task of registration is to place the data into a common reference frame by estimating the transformations between the data sets. In this work, we develop a rigid point registration method based on the application of genetic algorithms and Hausdorff distance. First, we extract the feature points from both images based on the algorithm of global and local curvature corner. After refining the feature points, we use Hausdorff distance as similarity measure between the two data sets and for optimizing the search space we use genetic algorithms to achieve high computation speed for its inertial parallel. The results show the efficiency of this method for registration of satellite images.

Keywords: Feature extraction, Genetic algorithms, Hausdorff distance, Image registration, Point registration.

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2101 Building an Arithmetic Model to Assess Visual Consistency in Townscape

Authors: Dheyaa Hussein, Peter Armstrong

Abstract:

The phenomenon of visual disorder is prominent in contemporary townscapes. This paper provides a theoretical framework for the assessment of visual consistency in townscape in order to achieve more favourable outcomes for users. In this paper, visual consistency refers to the amount of similarity between adjacent components of townscape. The paper investigates parameters which relate to visual consistency in townscape, explores the relationships between them and highlights their significance. The paper uses arithmetic methods from outside the domain of urban design to enable the establishment of an objective approach of assessment which considers subjective indicators including users’ preferences. These methods involve the standard of deviation, colour distance and the distance between points. The paper identifies urban space as a key representative of the visual parameters of townscape. It focuses on its two components, geometry and colour in the evaluation of the visual consistency of townscape. Accordingly, this article proposes four measurements. The first quantifies the number of vertices, which are points in the three-dimensional space that are connected, by lines, to represent the appearance of elements. The second evaluates the visual surroundings of urban space through assessing the location of their vertices. The last two measurements calculate the visual similarity in both vertices and colour in townscape by the calculation of their variation using methods including standard of deviation and colour difference. The proposed quantitative assessment is based on users’ preferences towards these measurements. The paper offers a theoretical basis for a practical tool which can alter the current understanding of architectural form and its application in urban space. This tool is currently under development. The proposed method underpins expert subjective assessment and permits the establishment of a unified framework which adds to creativity by the achievement of a higher level of consistency and satisfaction among the citizens of evolving townscapes.

Keywords: Townscape, Urban Design, Visual Assessment, Visual Consistency.

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2100 Numerical Study of a Class of Nonlinear Partial Differential Equations

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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2099 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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