Search results for: Neugebauer Color Equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1544

Search results for: Neugebauer Color Equation

1424 Numerical Study of Some Coupled PDEs by using Differential Transformation Method

Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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1423 Local Mesh Co-Occurrence Pattern for Content Based Image Retrieval

Authors: C. Yesubai Rubavathi, R. Ravi

Abstract:

This paper presents the local mesh co-occurrence patterns (LMCoP) using HSV color space for image retrieval system. HSV color space is used in this method to utilize color, intensity and brightness of images. Local mesh patterns are applied to define the local information of image and gray level co-occurrence is used to obtain the co-occurrence of LMeP pixels. Local mesh co-occurrence pattern extracts the local directional information from local mesh pattern and converts it into a well-mannered feature vector using gray level co-occurrence matrix. The proposed method is tested on three different databases called MIT VisTex, Corel, and STex. Also, this algorithm is compared with existing methods, and results in terms of precision and recall are shown in this paper.

Keywords: Content-based image retrieval system, HSV color space, gray level co-occurrence matrix, local mesh pattern.

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1422 One Some Effective Solutions of Stokes Axisymmetric Equation for a Viscous Fluid

Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

Abstract:

The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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1421 Comparative Evaluation of Color-Based Video Signatures in the Presence of Various Distortion Types

Authors: Aritz Sánchez de la Fuente, Patrick Ndjiki-Nya, Karsten Sühring, Tobias Hinz, Karsten Müller, Thomas Wiegand

Abstract:

The robustness of color-based signatures in the presence of a selection of representative distortions is investigated. Considered are five signatures that have been developed and evaluated within a new modular framework. Two signatures presented in this work are directly derived from histograms gathered from video frames. The other three signatures are based on temporal information by computing difference histograms between adjacent frames. In order to obtain objective and reproducible results, the evaluations are conducted based on several randomly assembled test sets. These test sets are extracted from a video repository that contains a wide range of broadcast content including documentaries, sports, news, movies, etc. Overall, the experimental results show the adequacy of color-histogram-based signatures for video fingerprinting applications and indicate which type of signature should be preferred in the presence of certain distortions.

Keywords: color histograms, robust hashing, video retrieval, video signature

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1420 The Pell Equation x2 − (k2 − k)y2 = 2t

Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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1419 The Relationship of Anthocyanins with Color of Organically and Conventionally Cultivated Potatoes

Authors: I. Murniece, L. Tomsone, I. Skrabule, A. Vaivode

Abstract:

Many of the compounds present in potato are important because of their beneficial effects on health, therefore, are highly desirable in the human diet. Potato tubers contain significant amounts of anthocyanins. The aim of this research was to determine the content of anthocyanins and its relationship with the colour of organically and conventionally cultivated potato varieties. In the research eight potato samples of three potato varieties were analyzed on anthocyanins, dry matter content and color. Obtained results show that there was no significant influence on amount of anthocyanins between different cultivation environments (p>0.05) while between varieties – significant difference (p<0.05). Strong correlation between the amount of anthocyanins and color was determined.

Keywords: Potato variety, anthocyanins, organic, conventional, dry matter.

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1418 Support Vector Machines For Understanding Lane Color and Sidewalks

Authors: Hoon Lee, Soonyoung Park, Kyoungho Choi

Abstract:

Understanding road features such as lanes, the color of lanes, and sidewalks in a live video captured from a moving vehicle is essential to build video-based navigation systems. In this paper, we present a novel idea to understand the road features using support vector machines. Various feature vectors including color components of road markings and the difference between two regions, i.e., chosen AOIs, and so on are fed into SVM, deciding colors of lanes and sidewalks robustly. Experimental results are provided to show the robustness of the proposed idea.

Keywords: video-based navigation system, lane detection, SVMs, autonomous vehicles

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1417 Some Complexiton Type Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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1416 Verification of K-ω SST Turbulence Model for Supersonic Internal Flows

Authors: J. Kolář, V. Dvořák

Abstract:

In this work, we try to find the best setting of Computational Fluid Dynamic solver available for the problems in the field of supersonic internal flows. We used the supersonic air-toair ejector to represent the typical problem in focus. There are multiple oblique shock waves, shear layers, boundary layers and normal shock interacting in the supersonic ejector making this device typical in field of supersonic inner flows. Modeling of shocks in general is demanding on the physical model of fluid, because ordinary conservation equation does not conform to real conditions in the near-shock region as found in many works. From these reasons, we decided to take special care about solver setting in this article by means of experimental approach of color Schlieren pictures and pneumatic measurement. Fast pressure transducers were used to measure unsteady static pressure in regimes with normal shock in mixing chamber. Physical behavior of ejector in several regimes is discussed. Best choice of eddy-viscosity setting is discussed on the theoretical base. The final verification of the k-ω SST is done on the base of comparison between experiment and numerical results.

Keywords: CFD simulations, color Schlieren, k-ω SST, supersonic flows, shock waves.

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1415 An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes

Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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1414 Explicit Solutions and Stability of Linear Differential Equations with multiple Delays

Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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1413 Reliability Analysis of P-I Diagram Formula for RC Column Subjected to Blast Load

Authors: Masoud Abedini, Azrul A. Mutalib, Shahrizan Baharom, Hong Hao

Abstract:

This study was conducted published to investigate there liability of the equation pressure-impulse (PI) reinforced concrete column inprevious studies. Equation involves three different levels of damage criteria known as D =0. 2, D =0. 5 and D =0. 8.The damage criteria known as a minor when 0-0.2, 0.2-0.5is known as moderate damage, high damage known as 0.5-0.8, and 0.8-1 of the structure is considered a failure. In this study, two types of reliability analyzes conducted. First, using pressure-impulse equation with different parameters. The parameters involved are the concrete strength, depth, width, and height column, the ratio of longitudinal reinforcement and transverse reinforcement ratio. In the first analysis of the reliability of this new equation is derived to improve the previous equations. The second reliability analysis involves three types of columns used to derive the PI curve diagram using the derived equation to compare with the equation derived from other researchers and graph minimum standoff versus weapon yield Federal Emergency Management Agency (FEMA). The results showed that the derived equation is more accurate with FEMA standards than previous researchers.

Keywords: Blast load, RC column, P-I curve, Analytical formulae, Standard FEMA.

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1412 A New Color Image Database for Benchmarking of Automatic Face Detection and Human Skin Segmentation Techniques

Authors: Abdallah S. Abdallah, Mohamad A bou El-Nasr, A. Lynn Abbott

Abstract:

This paper presents a new color face image database for benchmarking of automatic face detection algorithms and human skin segmentation techniques. It is named the VT-AAST image database, and is divided into four parts. Part one is a set of 286 color photographs that include a total of 1027 faces in the original format given by our digital cameras, offering a wide range of difference in orientation, pose, environment, illumination, facial expression and race. Part two contains the same set in a different file format. The third part is a set of corresponding image files that contain human colored skin regions resulting from a manual segmentation procedure. The fourth part of the database has the same regions converted into grayscale. The database is available on-line for noncommercial use. In this paper, descriptions of the database development, organization, format as well as information needed for benchmarking of algorithms are depicted in detail.

Keywords: Image database, color image analysis, facedetection, skin segmentation.

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1411 Adomian Decomposition Method Associated with Boole-s Integration Rule for Goursat Problem

Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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1410 Effect of Blanching on the Quality of Microwave Vacuum Dried Dill (Anethum graveolens L.)

Authors: Evita Straumite, Zanda Kruma, Ruta Galoburda, Kaiva Saulite

Abstract:

Dill (Anethum graveolens L.) is a popular herb used in many regions, including Baltic countries. Dill is widely used for flavoring foods and beverages due to its pleasant spicy aroma. The aim of this work was to determine the best blanching method for processing of dill prior to microwave vacuum drying based on sensory properties, color and volatile compounds in dried product. Two blanching mediums were used – water and steam, and for part of samples microwave pretreatment was additionally used. Evaluation of dried dill volatile aroma compounds, color changes and sensory attributes was performed. Results showed that blanching significantly influences the quality of dried dill. After evaluation of volatile aroma compounds, color and sensory properties of microwave vacuum dried dill, as the best method for dill pretreatment was established blanching at 90 °C for 30 s.

Keywords: dried dill, sensory panel, sensory properties, aroma compounds, color

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1409 Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations

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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1408 Role of Lemna minor Lin. in Treating the Textile Industry Wastewater

Authors: D. Sivakumar

Abstract:

Textile industry processes are among the most environmentally unfriendly industrial processes; because, they produce color wastewater that is heavily polluted the environment. Therefore, textile industry wastewater has to be treated before being discharged into the environment. In this study, experiments were conducted for different process parameters like nutrient dosage and dilution ratio against the pH and contact time to remove COD and color in a textile industrial wastewater using aquatic macrophytes Lemna minor L. The experimental results showed that the maximum percentage reduction of COD and color in a textile industry wastewater by Lemna minor L. was obtained at an optimum nutrient dosage of 50g, dilution ratio of 8, pH of 8 and contact time of 4 days. Similarly, the results of validation experiments showed that the experiments were able to reproduce the obtained optimum process parameters. The maximum removal percentage of color in an aqueous solution (86.35%) is higher than the removal of color in a textile industry wastewater (82.85). Further, the first order kinetic model was fitted well with the experimental data of this present study. Finally, this study concluded that Lemna minor L. may be used for removing all types of parameters in any type of textile industry wastewater.

Keywords: Aquatic Macrophyte, Process Parameters, Textile Industry Wastewater.

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1407 A Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers

Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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1406 Dyeing Properties of Natural Dyes on Silk Treated with ß-Cyclodextrin

Authors: Samera Salimpour Abkenar

Abstract:

In this work, silk yarns were treated using ß-cyclodextrin (ß-CD) and cross-linked with citric acid (CA) via pad-dry-cure method. Elemental and FESEM analyses confirmed the presence of ß-CD on the treated silk samples even after five washing cycles. Then, the treated samples were dyed using natural dyes (carrot, orange and tomato). Results showed that the color strength (K/S) of the treated samples had been markedly enhanced compared with the control sample (after treatment with metal mordant). Finally, the color strength (K/S value) and color fastness (fading, staining and light fastness) of the treated samples with ß-CD were investigated and compared.

Keywords: ß-cyclodextrin, dyeing, natural dyes, silk yarn.

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1405 An Expectation of the Rate of Inflation According to Inflation-Unemployment Interaction in Croatia

Authors: Zdravka Aljinović, Snježana Pivac, Boško Šego

Abstract:

According to the interaction of inflation and unemployment, expectation of the rate of inflation in Croatia is estimated. The interaction between inflation and unemployment is shown by model based on three first-order differential i.e. difference equations: Phillips relation, adaptive expectations equation and monetary-policy equation. The resulting equation is second order differential i.e. difference equation which describes the time path of inflation. The data of the rate of inflation and the rate of unemployment are used for parameters estimation. On the basis of the estimated time paths, the stability and convergence analysis is done for the rate of inflation.

Keywords: Differencing, inflation, time path, unemployment.

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1404 Visual Object Tracking in 3D with Color Based Particle Filter

Authors: Pablo Barrera, Jose M. Canas, Vicente Matellan

Abstract:

This paper addresses the problem of determining the current 3D location of a moving object and robustly tracking it from a sequence of camera images. The approach presented here uses a particle filter and does not perform any explicit triangulation. Only the color of the object to be tracked is required, but not any precisemotion model. The observation model we have developed avoids the color filtering of the entire image. That and the Monte Carlotechniques inside the particle filter provide real time performance.Experiments with two real cameras are presented and lessons learned are commented. The approach scales easily to more than two cameras and new sensor cues.

Keywords: Monte Carlo sampling, multiple view, particle filters, visual tracking.

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1403 Improved Processing Speed for Text Watermarking Algorithm in Color Images

Authors: Hamza A. Al-Sewadi, Akram N. A. Aldakari

Abstract:

Copyright protection and ownership proof of digital multimedia are achieved nowadays by digital watermarking techniques. A text watermarking algorithm for protecting the property rights and ownership judgment of color images is proposed in this paper. Embedding is achieved by inserting texts elements randomly into the color image as noise. The YIQ image processing model is found to be faster than other image processing methods, and hence, it is adopted for the embedding process. An optional choice of encrypting the text watermark before embedding is also suggested (in case required by some applications), where, the text can is encrypted using any enciphering technique adding more difficulty to hackers. Experiments resulted in embedding speed improvement of more than double the speed of other considered systems (such as least significant bit method, and separate color code methods), and a fairly acceptable level of peak signal to noise ratio (PSNR) with low mean square error values for watermarking purposes.

Keywords: Steganography, watermarking, private keys, time complexity measurements.

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1402 Reduction of False Positives in Head-Shoulder Detection Based on Multi-Part Color Segmentation

Authors: Lae-Jeong Park

Abstract:

The paper presents a method that utilizes figure-ground color segmentation to extract effective global feature in terms of false positive reduction in the head-shoulder detection. Conventional detectors that rely on local features such as HOG due to real-time operation suffer from false positives. Color cue in an input image provides salient information on a global characteristic which is necessary to alleviate the false positives of the local feature based detectors. An effective approach that uses figure-ground color segmentation has been presented in an effort to reduce the false positives in object detection. In this paper, an extended version of the approach is presented that adopts separate multipart foregrounds instead of a single prior foreground and performs the figure-ground color segmentation with each of the foregrounds. The multipart foregrounds include the parts of the head-shoulder shape and additional auxiliary foregrounds being optimized by a search algorithm. A classifier is constructed with the feature that consists of a set of the multiple resulting segmentations. Experimental results show that the presented method can discriminate more false positive than the single prior shape-based classifier as well as detectors with the local features. The improvement is possible because the presented approach can reduce the false positives that have the same colors in the head and shoulder foregrounds.

Keywords: Pedestrian detection, color segmentation, false positives, feature extraction.

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1401 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability

Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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1400 Maxwell-Cattaneo Regularization of Heat Equation

Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

Abstract:

This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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1399 A Design for Supply Chain Model by Integrated Evaluation of Design Value and Supply Chain Cost

Authors: Yuan-Jye Tseng, Jia-Shu Li

Abstract:

To design a product with the given product requirement and design objective, there can be alternative ways to propose the detailed design specifications of the product. In the design modeling stage, alternative design cases with detailed specifications can be modeled to fulfill the product requirement and design objective. Therefore, in the design evaluation stage, it is required to perform an evaluation of the alternative design cases for deciding the final design. The purpose of this research is to develop a product evaluation model for evaluating the alternative design cases by integrated evaluating the criteria of functional design, Kansei design, and design for supply chain. The criteria in the functional design group include primary function, expansion function, improved function, and new function. The criteria in the Kansei group include geometric shape, dimension, surface finish, and layout. The criteria in the design for supply chain group include material, manufacturing process, assembly, and supply chain operation. From the point of view of value and cost, the criteria in the functional design group and Kansei design group represent the design value of the product. The criteria in the design for supply chain group represent the supply chain and manufacturing cost of the product. It is required to evaluate the design value and the supply chain cost to determine the final design. For the purpose of evaluating the criteria in the three criteria groups, a fuzzy analytic network process (FANP) method is presented to evaluate a weighted index by calculating the total relational values among the three groups. A method using the technique for order preference by similarity to ideal solution (TOPSIS) is used to compare and rank the design alternative cases according to the weighted index using the total relational values of the criteria. The final decision of a design case can be determined by using the ordered ranking. For example, the design case with the top ranking can be selected as the final design case. Based on the criteria in the evaluation, the design objective can be achieved with a combined and weighted effect of the design value and manufacturing cost. An example product is demonstrated and illustrated in the presentation. It shows that the design evaluation model is useful for integrated evaluation of functional design, Kansei design, and design for supply chain to determine the best design case and achieve the design objective.

Keywords: Design evaluation, functional design, Kansei design, supply chain, design value, manufacturing cost, fuzzy analytic network process, technique for order preference by similarity to ideal solution.

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1398 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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1397 Fragile Watermarking for Color Images Using Thresholding Technique

Authors: Kuo-Cheng Liu

Abstract:

In this paper, we propose ablock-wise watermarking scheme for color image authentication to resist malicious tampering of digital media. The thresholding technique is incorporated into the scheme such that the tampered region of the color image can be recovered with high quality while the proofing result is obtained. The watermark for each block consists of its dual authentication data and the corresponding feature information. The feature information for recovery iscomputed bythe thresholding technique. In the proofing process, we propose a dual-option parity check method to proof the validity of image blocks. In the recovery process, the feature information of each block embedded into the color image is rebuilt for high quality recovery. The simulation results show that the proposed watermarking scheme can effectively proof the tempered region with high detection rate and can recover the tempered region with high quality.

Keywords: thresholding technique, tamper proofing, tamper recovery

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1396 On the Positive Definite Solutions of Nonlinear Matrix Equation

Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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1395 On Symmetry Analysis and Exact Wave Solutions of New Modified Novikov Equation

Authors: Anupma Bansal, R. K. Gupta

Abstract:

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.

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