Search results for: Center manifold theorem.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 707

Search results for: Center manifold theorem.

617 An Experimental Study on the Effect of Premixed and Equivalence Ratios on CO and HC Emissions of Dual Fuel HCCI Engine

Authors: M. Ghazikhani, M. R. Kalateh, Y. K. Toroghi, M. Dehnavi

Abstract:

In this study, effects of premixed and equivalence ratios on CO and HC emissions of a dual fuel HCCI engine are investigated. Tests were conducted on a single-cylinder engine with compression ratio of 17.5. Premixed gasoline is provided by a carburetor connected to intake manifold and equipped with a screw to adjust premixed air-fuel ratio, and diesel fuel is injected directly into the cylinder through an injector at pressure of 250 bars. A heater placed at inlet manifold is used to control the intake charge temperature. Optimal intake charge temperature results in better HCCI combustion due to formation of a homogeneous mixture, therefore, all tests were carried out over the optimum intake temperature of 110-115 ºC. Timing of diesel fuel injection has a great effect on stratification of in-cylinder charge and plays an important role in HCCI combustion phasing. Experiments indicated 35 BTDC as the optimum injection timing. Varying the coolant temperature in a range of 40 to 70 ºC, better HCCI combustion was achieved at 50 ºC. Therefore, coolant temperature was maintained 50 ºC during all tests. Simultaneous investigation of effective parameters on HCCI combustion was conducted to determine optimum parameters resulting in fast transition to HCCI combustion. One of the advantages of the method studied in this study is feasibility of easy and fast transition of typical diesel engine to a dual fuel HCCI engine. Results show that increasing premixed ratio, while keeping EGR rate constant, increases unburned hydrocarbon (UHC) emissions due to quenching phenomena and trapping of premixed fuel in crevices, but CO emission decreases due to increase in CO to CO2 reactions.

Keywords: Dual fuel HCCI engine, premixed ratio, equivalenceratio, CO and UHC emissions.

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616 Object Detection based Weighted-Center Surround Difference

Authors: Seung-Hun Kim, Kye-Hoon Jeon, Byoung-Doo Kang, I1-Kyun Jung

Abstract:

Intelligent traffic surveillance technology is an issue in the field of traffic data analysis. Therefore, we need the technology to detect moving objects in real-time while there are variations in background and natural light. In this paper, we proposed a Weighted-Center Surround Difference method for object detection in outdoor environments. The proposed system detects objects using the saliency map that is obtained by analyzing the weight of each layers of Gaussian pyramid. In order to validate the effectiveness of our system, we implemented the proposed method using a digital signal processor, TMS320DM6437. Experimental results show that blurred noisy around objects was effectively eliminated and the object detection accuracy is improved.

Keywords: Saliency Map, Center Surround Difference, Object Detection, Surveillance System

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615 Privacy Protection Principles of Omnichannel Approach

Authors: Renata Mekovec, Dijana Peras, Ruben Picek

Abstract:

The advent of the Internet, mobile devices and social media is revolutionizing the experience of retail customers by linking multiple sources through various channels. Omnichannel retailing is a retailing that combines multiple channels to allow customers to seamlessly leverage all the distribution information online and offline while shopping. Therefore, today data are an asset more critical than ever for all organizations. Nonetheless, because of its heterogeneity through platforms, developers are currently facing difficulties in dealing with personal data. Considering the possibilities of omnichannel communication, this paper presents channel categorization that could enhance the customer experience of omnichannel center called hyper center. The purpose of this paper is fundamentally to describe the connection between the omnichannel hyper center and the customer, with particular attention to privacy protection. The first phase was finding the most appropriate channels of communication for hyper center. Consequently, a selection of widely used communication channels has been identified and analyzed with regard to the effect requirements for optimizing user experience. The evaluation criteria are divided into 3 groups: general, user profile and channel options. For each criterion the weight of importance for omnichannel communication was defined. The most important thing was to consider how the hyper center can make user identification while respecting the privacy protection requirements. The study carried out also shows what customer experience across digital networks would look like, based on an omnichannel approach owing to privacy protection principles.

Keywords: Personal data, privacy protection, omnichannel communication, retail.

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614 Gender Differences in Biology Academic Performances among Foundation Students of PERMATApintar® National Gifted Center

Authors: N. Nor Azman, M. F. Kamarudin, S. I. Ong, N. Maaulot

Abstract:

PERMATApintar® National Gifted Center is, to the author’s best of knowledge, the first center in Malaysia that provides a platform for Malaysian talented students with high ability in thinking. This center has built a teaching and learning biology curriculum that suits the ability of these gifted students. The level of PERMATApintar® biology curriculum is basically higher than the national biology curriculum. Here, the foundation students are exposed to the PERMATApintar® biology curriculum at the age of as early as 11 years old. This center practices a 4-time-a-year examination system to monitor the academic performances of the students. Generally, most of the time, male students show no or low interest towards biology subject compared to female students. This study is to investigate the association of students’ gender and their academic performances in biology examination. A total of 39 students’ scores in twelve sets of biology examinations in 3 years have been collected and analyzed by using the statistical analysis. Based on the analysis, there are no significant differences between male and female students against the biology academic performances with a significant level of p = 0.05. This indicates that gender is not associated with the scores of biology examinations among the students. Another result showed that the average score for male studenta was higher than the female students. Future research can be done by comparing the biology academic achievement in Malaysian National Examination (Sijil Pelajaran Malaysia, SPM) between the Foundation 3 students (Grade 9) and Level 2 students (Grade 11) with similar PERMATApintar® biology curriculum.

Keywords: Academic performances, biology, gender differences, gifted students.

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613 The Effect of Shear Wall Positions on the Seismic Response of Frame-Wall Structures

Authors: Anas M. Fares

Abstract:

The configuration of shear walls in plan of building will affect the seismic design of structure. The position of these walls will change the stiffness of each floor in the structure, the diaphragm center of mass displacement, and the drift of floor. Structural engineers preferred to distribute the walls in buildings to make the center of mass almost close enough to the center of rigidity, but to make this condition satisfied, they have many choices: construct the walls on the perimeter, or use intermediate walls, or use walls as core. In this paper and by using ETABS, each case is studied and compared to other cases according to three parameters: lateral stiffness, diaphragm displacement, and drift. It is found that the core walls are the best choice for the position of the walls in the buildings to resist earthquake loads.

Keywords: Lateral loads, lateral displacement, reinforced concrete, shear wall, seismic, ASCE7-16 code, ACI code, stiffness, drift.

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612 The Balanced Hamiltonian Cycle on the Toroidal Mesh Graphs

Authors: Wen-Fang Peng, Justie Su-Tzu Juan

Abstract:

The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).

Keywords: Hamiltonian cycle, balanced, Cartesian product.

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611 A Review on Development of Historical City Center and Revitalization Process in Isfahan/Iran

Authors: Reihaneh Rafiemanzelat, Maryam Imani Emadi

Abstract:

The need to protect our cultural heritage was stressed on revitalization of historical city centers in communities. The main aim of this research is to attract finance and activities to the historical city centers through the citizens and municipalities participation while cities expanded their boundaries toward suburban areas. Today the main problems which facing to the most historical city centers, is loss of their centrality through effect of urbanization on any point of the cities which is the most important issue on neglect and abandonment of the historical central area by decentralizing living, commerce and public areas. This article evaluate the ways in which city center revitalization can be effect on vitality and viability of the central area in case of Naghshe Jahan square which situated at the center of Isfahan city, Iran. Constructed between 1598 and 1629, it is now an important historical site, and one of UNESCO's World Heritage Sites.

Keywords: City centers, revitalization, urban development, vitality and viability.

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610 Curvature of Almost Split Quaternion Kaehler Manifolds

Authors: Erhan Ata, H. Hilmi Hacisalihoğlu, Yusuf Yayli

Abstract:

In this work some characterizations of semi Riemannian curvature tensor on almost split quaternion Kaehler manifolds and some characterizations of Ricci tensor on almost split quaternion Kaehler manifolds are given.

Keywords: Almost split quaternion Kaehler manifold, Riemann curvature, Ricci curvature.

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609 Intelligent BRT in Tehran

Authors: P. Parvizi, S. Mohammadi

Abstract:

an intelligent BRT system is necessary when communities looking for new ways to use high capacity rapid transit at a reduced cost.This paper will describe the intelligent control system that works with Datacenter. With the help of GPS system, the data center can monitor the situation of each bus and bus station. Through RFID technology, bus station and traffic light can transfer data with bus and by Wimax communication technology all of parts can talk together; data center learns all information about the location of bus, the arrival of bus in each station and the number of passengers in station and bus.Finally, the paper presents the case study of those theories in Tehran BRT.

Keywords: TehranBRT, RFID, Intelligent Transportation

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608 Curriculum Based Measurement and Precision Teaching in Writing Empowerment Enhancement: Results from an Italian Learning Center

Authors: I. Pelizzoni, C. Cavallini, I. Salvaderi, F. Cavallini

Abstract:

We present the improvement in writing skills obtained by 94 participants (aged between six and 10 years) with special educational needs through a writing enhancement program based on fluency principles. The study was planned and conducted with a single-subject experimental plan for each of the participants, in order to confirm the results in the literature. These results were obtained using precision teaching (PT) methodology to increase the number of written graphemes per minute in the pre- and post-test, by curriculum based measurement (CBM). Results indicated an increase in the number of written graphemes for all participants. The average overall duration of the intervention is 144 minutes in five months of treatment. These considerations have been analyzed taking account of the complexity of the implementation of measurement systems in real operational contexts (an Italian learning center) and important aspects of replicability and cost-effectiveness of such interventions.

Keywords: Precision teaching, writing skills, CBM, Italian Learning Center.

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607 A New Implementation of Miura-Arita Algorithm for Miura Curves

Authors: A. Basiri, S. Rahmany, D. Khatibi

Abstract:

The aim of this paper is to review some of standard fact on Miura curves. We give some easy theorem in number theory to define Miura curves, then we present a new implementation of Arita algorithm for Miura curves.

Keywords: Miura curve, discrete logarithm problem, algebraic curve cryptography, Jacobian group.

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606 Existence of Solution for Boundary Value Problems of Differential Equations with Delay

Authors: Xiguang Li

Abstract:

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

Keywords: Banach space, boundary value problem, differential equation, delay.

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605 Basic Research for Electroretinogram Moving the Center of the Multifocal Hexagonal Stimulus Array

Authors: Naoto Suzuki

Abstract:

Many ophthalmologists can examine declines in visual sensitivity at arbitrary points on the retina using a precise perimetry device with a fundus camera function. However, the retinal layer causing the decline in visual sensitivity cannot be identified by this method. We studied an electroretinogram (ERG) function that can move the center of the multifocal hexagonal stimulus array in order to investigate cryptogenic diseases, such as macular dystrophy, acute zonal occult outer retinopathy, and multiple evanescent white dot syndrome. An electroretinographic optical system, specifically a perimetric optical system, was added to an experimental device carrying the same optical system as a fundus camera. We also added an infrared camera, a cold mirror, a halogen lamp, and a monitor. The software was generated to show the multifocal hexagonal stimulus array on the monitor using C++Builder XE8 and to move the center of the array up and down as well as back and forth. We used a multifunction I/O device and its design platform LabVIEW for data retrieval. The plate electrodes were used to measure electrodermal activities around the eyes. We used a multifocal hexagonal stimulus array with 37 elements in the software. The center of the multifocal hexagonal stimulus array could be adjusted to the same position as the examination target of the precise perimetry. We successfully added the moving ERG function to the experimental ophthalmologic device.

Keywords: Moving ERG, precise perimetry, retinal layers, visual sensitivity.

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604 Marketing Management and Cultural Learning Center: The Case Study of Arts and Cultural Office, Suansunandha Rajabhat University

Authors: Pirada Techaratpong

Abstract:

This qualitative research has 2 objectives: to study marketing management of the cultural learning center in Suansunandha Rajabhat University and to suggest guidelines to improve its marketing management. This research is based on a case study of the Arts and Culture Office in Suansunandha Rajabhat University, Bangkok. This research found the Art and Culture Office has no formal marketing management. However, the marketing management is partly covered in the overall business plan, strategic plan, and action plan. The process can be divided into 5 stages. The marketing concept has long been introduced to its policy but not apparently put into action due to inflexible system. Some gaps are found in the process. The research suggests the Art and Culture Office implement the concept of marketing orientation, meeting the needs and wants of its target customers and adapt to the changing situation. Minor guidelines for improvement are provided.

Keywords: Marketing, management, museum, cultural learning center.

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603 The Technological Problem of Simulation of the Logistics Center

Authors: Juraj Camaj, Anna Dolinayova, Jana Lalinska, Miroslav Bariak

Abstract:

Planning of infrastructure and processes in logistic center within the frame of various kinds of logistic hubs and technological activities in them represent quite complex problem. The main goal is to design appropriate layout, which enables to realize expected operation on the desired levels. The simulation software represents progressive contemporary experimental technique, which can support complex processes of infrastructure planning and all of activities on it. It means that simulation experiments, reflecting various planned infrastructure variants, investigate and verify their eligibilities in relation with corresponding expected operation. The inducted approach enables to make qualified decisions about infrastructure investments or measures, which derive benefit from simulation-based verifications. The paper represents simulation software for simulation infrastructural layout and technological activities in marshalling yard, intermodal terminal, warehouse and combination between them as the parts of logistic center.

Keywords: Marshalling yard, intermodal terminal, warehouse, transport technology, simulation.

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602 On Musical Information Geometry with Applications to Sonified Image Analysis

Authors: Shannon Steinmetz, Ellen Gethner

Abstract:

In this paper a theoretical foundation is developed to segment, analyze and associate patterns within audio. We explore this on imagery via sonified audio applied to our segmentation framework. The approach involves a geodesic estimator within the statistical manifold, parameterized by musical centricity. We demonstrate viability by processing a database of random imagery to produce statistically significant clusters of similar imagery content.

Keywords: Sonification, musical information geometry, image content extraction, automated quantification, audio segmentation, pattern recognition.

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601 Synchronization of Chaos in a Food Web in Ecological Systems

Authors: Anuraj Singh, Sunita Gakkhar

Abstract:

The three-species food web model proposed and investigated by Gakkhar and Naji is known to have chaotic behaviour for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.

Keywords: Lyapunov Exponent, Bidirectional Coupling, ChaosSynchronization, Synchronization Manifold

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600 Likelihood Estimation for Stochastic Epidemics with Heterogeneous Mixing Populations

Authors: Yilun Shang

Abstract:

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.

Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.

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599 Evaluation of the Power Generation Effect Obtained by Inserting a Piezoelectric Sheet in the Backlash Clearance of a Circular Arc Helical Gear

Authors: Barenten Suciu, Yuya Nakamoto

Abstract:

Power generation effect, obtained by inserting a piezo- electric sheet in the backlash clearance of a circular arc helical gear, is evaluated. Such type of screw gear is preferred since, in comparison with the involute tooth profile, the circular arc profile leads to reduced stress-concentration effects, and improved life of the piezoelectric film. Firstly, geometry of the circular arc helical gear, and properties of the piezoelectric sheet are presented. Then, description of the test-rig, consisted of a right-hand thread gear meshing with a left-hand thread gear, and the voltage measurement procedure are given. After creating the tridimensional (3D) model of the meshing gears in SolidWorks, they are 3D-printed in acrylonitrile butadiene styrene (ABS) resin. Variation of the generated voltage versus time, during a meshing cycle of the circular arc helical gear, is measured for various values of the center distance. Then, the change of the maximal, minimal, and peak-to-peak voltage versus the center distance is illustrated. Optimal center distance of the gear, to achieve voltage maximization, is found and its significance is discussed. Such results prove that the contact pressure of the meshing gears can be measured, and also, the electrical power can be generated by employing the proposed technique.

Keywords: Power generation, circular arc helical gear, piezo- electric sheet, contact problem, optimal center distance.

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598 Analysis of Public-Key Cryptography for Wireless Sensor Networks Security

Authors: F. Amin, A. H. Jahangir, H. Rasifard

Abstract:

With the widespread growth of applications of Wireless Sensor Networks (WSNs), the need for reliable security mechanisms these networks has increased manifold. Many security solutions have been proposed in the domain of WSN so far. These solutions are usually based on well-known cryptographic algorithms. In this paper, we have made an effort to survey well known security issues in WSNs and study the behavior of WSN nodes that perform public key cryptographic operations. We evaluate time and power consumption of public key cryptography algorithm for signature and key management by simulation.

Keywords: Wireless Sensor Networks, Security, Public Key Cryptography, Key Management.

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597 Simulation and Workspace Analysis of a Tripod Parallel Manipulator

Authors: A. Arockia Selvakumar, R. Sivaramakrishnan, Srinivasa Karthik.T.V, Valluri Siva Ramakrishna, B.Vinodh.

Abstract:

Industrial robots play a vital role in automation however only little effort are taken for the application of robots in machining work such as Grinding, Cutting, Milling, Drilling, Polishing etc. Robot parallel manipulators have high stiffness, rigidity and accuracy, which cannot be provided by conventional serial robot manipulators. The aim of this paper is to perform the modeling and the workspace analysis of a 3 DOF Parallel Manipulator (3 DOF PM). The 3 DOF PM was modeled and simulated using 'ADAMS'. The concept involved is based on the transformation of motion from a screw joint to a spherical joint through a connecting link. This paper work has been planned to model the Parallel Manipulator (PM) using screw joints for very accurate positioning. A workspace analysis has been done for the determination of work volume of the 3 DOF PM. The position of the spherical joints connected to the moving platform and the circumferential points of the moving platform were considered for finding the workspace. After the simulation, the position of the joints of the moving platform was noted with respect to simulation time and these points were given as input to the 'MATLAB' for getting the work envelope. Then 'AUTOCAD' is used for determining the work volume. The obtained values were compared with analytical approach by using Pappus-Guldinus Theorem. The analysis had been dealt by considering the parameters, link length and radius of the moving platform. From the results it is found that the radius of moving platform is directly proportional to the work volume for a constant link length and the link length is also directly proportional to the work volume, at a constant radius of the moving platform.

Keywords: Three Degrees of freedom Parallel Manipulator (3DOF PM), ADAMS, Work volume, MATLAB, AUTOCAD, Pappus- Guldinus Theorem.

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596 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements

Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

Abstract:

In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: Complement, degree sum, Hamiltonian, tough.

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595 Integrated Reasoning Approach for Car Faulty Diagnosis

Authors: Diana M.L. Wong

Abstract:

This paper presents an integrated case based and rule based reasoning method for car faulty diagnosis. The reasoning method is done through extracting the past cases from the Proton Service Center while comparing with the preset rules to deduce a diagnosis/solution to a car service case. New cases will be stored to the knowledge base. The test cases examples illustrate the effectiveness of the proposed integrated reasoning. It has proven accuracy of similar reasoning if carried out by a service advisor from the service center.

Keywords: component; case based reasoning (CBR), rule basedreasoning (RBR), decision support systems, diagnosis tool.

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594 Stability and Bifurcation Analysis of a Discrete Gompertz Model with Time Delay

Authors: Yingguo Li

Abstract:

In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark- Sacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis.

Keywords: Gompertz system, Neimark-Sacker bifurcation, stability, time delay.

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593 Stabilization and Observation of Attitude Control Systems for Micro Satellites

Authors: A. Elakkary, A. Echchatbi, N. Elalami

Abstract:

In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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592 Pontrjagin Duality and Codes over Finite Commutative Rings

Authors: Khalid Abdelmoumen, Mustapha Najmeddine, Hussain Ben-Azza

Abstract:

We present linear codes over finite commutative rings which are not necessarily Frobenius. We treat the notion of syndrome decoding by using Pontrjagin duality. We also give a version of Delsarte-s theorem over rings relating trace codes and subring subcodes.

Keywords: Codes, Finite Rings, Pontrjagin Duality, Trace Codes.

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591 Stability and Bifurcation Analysis in a Model of Hes1 Selfregulation with Time Delay

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.

Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop

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590 Automatic Camera Calibration for Images of Soccer Match

Authors: Qihe Li, Yupin Luo

Abstract:

Camera calibration plays an important role in the domain of the analysis of sports video. Considering soccer video, in most cases, the cross-points can be used for calibration at the center of the soccer field are not sufficient, so this paper introduces a new automatic camera calibration algorithm focus on solving this problem by using the properties of images of the center circle, halfway line and a touch line. After the theoretical analysis, a practicable automatic algorithm is proposed. Very little information used though, results of experiments with both synthetic data and real data show that the algorithm is applicable.

Keywords: Absolute conic, camera calibration, circular points, line at infinity.

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589 A New Method in Detection of Ceramic Tiles Color Defects Using Genetic C-Means Algorithm

Authors: Mahkameh S. Mostafavi

Abstract:

In this paper an algorithm is used to detect the color defects of ceramic tiles. First the image of a normal tile is clustered using GCMA; Genetic C-means Clustering Algorithm; those results in best cluster centers. C-means is a common clustering algorithm which optimizes an objective function, based on a measure between data points and the cluster centers in the data space. Here the objective function describes the mean square error. After finding the best centers, each pixel of the image is assigned to the cluster with closest cluster center. Then, the maximum errors of clusters are computed. For each cluster, max error is the maximum distance between its center and all the pixels which belong to it. After computing errors all the pixels of defected tile image are clustered based on the centers obtained from normal tile image in previous stage. Pixels which their distance from their cluster center is more than the maximum error of that cluster are considered as defected pixels.

Keywords: C-Means algorithm, color spaces, Genetic Algorithm, image clustering.

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588 PIL Theory

Authors: A. Peveri

Abstract:

The curvature space-time by the presence of material, this deformation must present a pattern of deformation, not random. Space is uniform, elastic and any modification that occurs in one part, causes a change in another.

This deformation exists, must be a constant value and is independent of the observer, and relates the amount of matter, the force caused by the curvature of space and surface space. This unit of space is defined in this study as PIL and represents a constant area of space, deformable in the direction and sense of the center of mass of the body. The PIL is curved and connected to the center of mass of the Earth, to get to that point, through all matter, thus forming part of any place between particles at atomic and subatomic levels. At these levels the space between each particle is flat, unlike the macro where the space curves.

Keywords: Space flat, Space curved, Unit of space, Deformation.

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