Search results for: Sphere coordinates
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 208

Search results for: Sphere coordinates

178 Static Single Point Positioning Using The Extended Kalman Filter

Authors: I. Sarras, G. Gerakios, A. Diamantis, A. I. Dounis, G. P. Syrcos

Abstract:

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.

Keywords: Extended Kalman filter, GPS, Pseudorange

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177 Alternative Approach in Ground Vehicle Wake Analysis

Authors: L. Sterken, S. Sebben, L. Löfdahl

Abstract:

In this paper an alternative visualisation approach of the wake behind different vehicle body shapes with simplified and fully-detailed underbody has been proposed and analysed. This allows for a more clear distinction among the different wake regions. This visualisation is based on a transformation of the cartesian coordinates of a chosen wake plane to polar coordinates, using as filter velocities lower than the freestream. This transformation produces a polar wake plot that enables the division and quantification of the wake in a number of sections. In this paper, local drag has been used to visualise the drag contribution of the flow by the different sections. Visually, a balanced wake can be observed by the concentric behaviour of the polar plots. Alternatively, integration of the local drag of each degree section as a ratio of the total local drag yields a quantifiable approach of the wake uniformity, where different sections contribute equally to the local drag, with the exception of the wheels.

Keywords: Coordinate transformation, ground vehicle, local drag, wake.

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176 Design and Implementation of a Neural Network for Real-Time Object Tracking

Authors: Javed Ahmed, M. N. Jafri, J. Ahmad, Muhammad I. Khan

Abstract:

Real-time object tracking is a problem which involves extraction of critical information from complex and uncertain imagedata. In this paper, we present a comprehensive methodology to design an artificial neural network (ANN) for a real-time object tracking application. The object, which is tracked for the purpose of demonstration, is a specific airplane. However, the proposed ANN can be trained to track any other object of interest. The ANN has been simulated and tested on the training and testing datasets, as well as on a real-time streaming video. The tracking error is analyzed with post-regression analysis tool, which finds the correlation among the calculated coordinates and the correct coordinates of the object in the image. The encouraging results from the computer simulation and analysis show that the proposed ANN architecture is a good candidate solution to a real-time object tracking problem.

Keywords: Image processing, machine vision, neural networks, real-time object tracking.

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175 An Approach for Transient Response Calculation of large Nonproportionally Damped Structures using Component Mode Synthesis

Authors: Alexander A. Muravyov

Abstract:

A minimal complexity version of component mode synthesis is presented that requires simplified computer programming, but still provides adequate accuracy for modeling lower eigenproperties of large structures and their transient responses. The novelty is that a structural separation into components is done along a plane/surface that exhibits rigid-like behavior, thus only normal modes of each component is sufficient to use, without computing any constraint, attachment, or residual-attachment modes. The approach requires only such input information as a few (lower) natural frequencies and corresponding undamped normal modes of each component. A novel technique is shown for formulation of equations of motion, where a double transformation to generalized coordinates is employed and formulation of nonproportional damping matrix in generalized coordinates is shown.

Keywords: component mode synthesis, finite element models, transient response, nonproportional damping

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174 Comparisons of Surveying with Terrestrial Laser Scanner and Total Station for Volume Determination of Overburden and Coal Excavations in Large Open-Pit Mine

Authors: B. Keawaram, P. Dumrongchai

Abstract:

The volume of overburden and coal excavations in open-pit mine is generally determined by conventional survey such as total station. This study aimed to evaluate the accuracy of terrestrial laser scanner (TLS) used to measure overburden and coal excavations, and to compare TLS survey data sets with the data of the total station. Results revealed that, the reference points measured with the total station showed 0.2 mm precision for both horizontal and vertical coordinates. When using TLS on the same points, the standard deviations of 4.93 cm and 0.53 cm for horizontal and vertical coordinates, respectively, were achieved. For volume measurements covering the mining areas of 79,844 m2, TLS yielded the mean difference of about 1% and the surface error margin of 6 cm at the 95% confidence level when compared to the volume obtained by total station.

Keywords: Mine, survey, terrestrial laser scanner, total station.

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173 The Studying of The “Бақыт”(“Happiness”) Concept In The Kazakh Language

Authors: Biyazdykova Aliya Alimbekgyzy, Biyazdykova, Kenzhegul Alimbekgyzy

Abstract:

The given article deals with the usage of the concept in many spheres of science, including its place in the Kazakh linguistics One of such concepts is the role of the “бақыт” (“happiness”) concept in the Kazakh outlook. The work tells us about its studying. The data about studying of the “happiness” concept in the sphere of philosophy, psychology, cognitive linguistics, lingo cultural study, logics, psycho-linguistic are given in this work. Particularly dwelling at length on the studying level of the concept in the sphere of cognitive linguistics, analysis have been made pertaining linguist point of views. It was pointed out that the concept of “happiness” hasn’t been studied yet in the Kazakh linguistics and it is necessary to find out the meaning of the language units related to this concept, i.e. blessings, proverbs, sayings and phrasiological units.

Keywords: Concept, cognitive linguistics, the concept of “happiness”, the Kazakh outlook.

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172 Multidimensional Visualization Tools for Analysis of Expression Data

Authors: Urska Cvek, Marjan Trutschl, Randolph Stone II, Zanobia Syed, John L. Clifford, Anita L. Sabichi

Abstract:

Expression data analysis is based mostly on the statistical approaches that are indispensable for the study of biological systems. Large amounts of multidimensional data resulting from the high-throughput technologies are not completely served by biostatistical techniques and are usually complemented with visual, knowledge discovery and other computational tools. In many cases, in biological systems we only speculate on the processes that are causing the changes, and it is the visual explorative analysis of data during which a hypothesis is formed. We would like to show the usability of multidimensional visualization tools and promote their use in life sciences. We survey and show some of the multidimensional visualization tools in the process of data exploration, such as parallel coordinates and radviz and we extend them by combining them with the self-organizing map algorithm. We use a time course data set of transitional cell carcinoma of the bladder in our examples. Analysis of data with these tools has the potential to uncover additional relationships and non-trivial structures.

Keywords: microarrays, visualization, parallel coordinates, radviz, self-organizing maps.

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171 The Pack-Bed Sphere Liquid Porous Burner

Authors: B. Krittacom, P. Amatachaya, W. Srimuang, K. Inla

Abstract:

The combustion of liquid fuel in the porous burner (PB) was experimented to investigate evaporation mechanism and combustion behavior. The diesel oil was used as fuel and the pebbles carefully chosen in the same size like the solid sphere homogeneously was adopted as the porous media. Two structures of the liquid porous burner, i.e. the PB without and with installation of porous emitter (PE), were performed. PE was installed by lower than PB with distance of 20 cm. The pebbles having porosity (φ) of 0.45 and 0.52 were, respectively, used in PB and PE. The fuel was supplied dropwise from the top through the PB and the combustion was occurred between PB and PE. Axial profiles of temperature along the burner length were measured to clarify the evaporation and combustion phenomena. The pollutant emission characteristics were monitored at the burner exit. From the experiment, it was found that the temperature profiles of both structures decreased with the three ways swirling air flows (QA) increasing. On the other hand, the temperature profiles increased with fuel heat input (QF). Obviously, the profile of the porous burner installed with PE was higher than that of the porous burner without PE

Keywords: Liquid fuel, Porous burner, Temperature profile.

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170 Multi-Scale Gabor Feature Based Eye Localization

Authors: Sanghoon Kim, Sun-Tae Chung, Souhwan Jung, Dusik Oh, Jaemin Kim, Seongwon Cho

Abstract:

Eye localization is necessary for face recognition and related application areas. Most of eye localization algorithms reported so far still need to be improved about precision and computational time for successful applications. In this paper, we propose an eye location method based on multi-scale Gabor feature vectors, which is more robust with respect to initial points. The eye localization based on Gabor feature vectors first needs to constructs an Eye Model Bunch for each eye (left or right eye) which consists of n Gabor jets and average eye coordinates of each eyes obtained from n model face images, and then tries to localize eyes in an incoming face image by utilizing the fact that the true eye coordinates is most likely to be very close to the position where the Gabor jet will have the best Gabor jet similarity matching with a Gabor jet in the Eye Model Bunch. Similar ideas have been already proposed in such as EBGM (Elastic Bunch Graph Matching). However, the method used in EBGM is known to be not robust with respect to initial values and may need extensive search range for achieving the required performance, but extensive search ranges will cause much more computational burden. In this paper, we propose a multi-scale approach with a little increased computational burden where one first tries to localize eyes based on Gabor feature vectors in a coarse face image obtained from down sampling of the original face image, and then localize eyes based on Gabor feature vectors in the original resolution face image by using the eye coordinates localized in the coarse scaled image as initial points. Several experiments and comparisons with other eye localization methods reported in the other papers show the efficiency of our proposed method.

Keywords: Eye Localization, Gabor features, Multi-scale, Gabor wavelets.

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169 Ultra Wideband Breast Cancer Detection by Using SAR for Indication the Tumor Location

Authors: Wittawat Wasusathien, Samran Santalunai, Thanaset Thosdeekoraphat, Chanchai Thongsopa

Abstract:

This paper presents breast cancer detection by observing the specific absorption rate (SAR) intensity for identification tumor location, the tumor is identified in coordinates (x,y,z) system. We examined the frequency between 4-8 GHz to look for the most appropriate frequency. Results are simulated in frequency 4-8 GHz, the model overview include normal breast with 50 mm radian, 5 mm diameter of tumor, and ultra wideband (UWB) bowtie antenna. The models are created and simulated in CST Microwave Studio. For this simulation, we changed antenna to 5 location around the breast, the tumor can be detected when an antenna is close to the tumor location, which the coordinate of maximum SAR is approximated the tumor location. For reliable, we experiment by random tumor location to 3 position in the same size of tumor and simulation the result again by varying the antenna position in 5 position again, and it also detectable the tumor position from the antenna that nearby tumor position by maximum value of SAR, which it can be detected the tumor with precision in all frequency between 4-8 GHz.

Keywords: Specific absorption rate (SAR), ultra wideband (UWB), coordinates and cancer detection

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168 Numerical Analysis of Electrical Interaction between two Axisymmetric Spheroids

Authors: Kuan-Liang Liu, Eric Lee, Jung-Jyh Lee, Jyh-Ping Hsu

Abstract:

The electrical interaction between two axisymmetric spheroidal particles in an electrolyte solution is examined numerically. A Galerkin finite element method combined with a Newton-Raphson iteration scheme is proposed to evaluate the spatial variation in the electrical potential, and the result obtained used to estimate the interaction energy between two particles. We show that if the surface charge density is fixed, the potential gradient is larger at a point, which has a larger curvature, and if surface potential is fixed, surface charge density is proportional to the curvature. Also, if the total interaction energy against closest surface-to-surface curve exhibits a primary maximum, the maximum follows the order (oblate-oblate) > (sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve has a secondary minimum, the absolute value of the minimum follows the same order.

Keywords: interaction energy, interaction force, Poisson-Boltzmann equation, spheroid.

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167 Chaotic Oscillations of Diaphragm Supported by Nonlinear Springs with Hysteresis

Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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166 On-line Handwritten Character Recognition: An Implementation of Counterpropagation Neural Net

Authors: Muhammad Faisal Zafar, Dzulkifli Mohamad, Razib M. Othman

Abstract:

On-line handwritten scripts are usually dealt with pen tip traces from pen-down to pen-up positions. Time evaluation of the pen coordinates is also considered along with trajectory information. However, the data obtained needs a lot of preprocessing including filtering, smoothing, slant removing and size normalization before recognition process. Instead of doing such lengthy preprocessing, this paper presents a simple approach to extract the useful character information. This work evaluates the use of the counter- propagation neural network (CPN) and presents feature extraction mechanism in full detail to work with on-line handwriting recognition. The obtained recognition rates were 60% to 94% using the CPN for different sets of character samples. This paper also describes a performance study in which a recognition mechanism with multiple thresholds is evaluated for counter-propagation architecture. The results indicate that the application of multiple thresholds has significant effect on recognition mechanism. The method is applicable for off-line character recognition as well. The technique is tested for upper-case English alphabets for a number of different styles from different peoples.

Keywords: On-line character recognition, character digitization, counter-propagation neural networks, extreme coordinates.

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165 Localising Gauss's Law and the Electric Charge Induction on a Conducting Sphere

Authors: Sirapat Lookrak, Anol Paisal

Abstract:

Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: Near-field approximation, far-field approximation, localized Gauss’s law, electric charge density.

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164 Development of 3D Coordinates and Damaged Point Detection System for Ducts using IMU

Authors: Ki-Tae Park, Young-Joon Yu, Chin-Hyung Lee, Woosang Lee

Abstract:

Recently, as the scale of construction projects has increases, more ground excavation for foundations is carried out than ever before. Consequently, damage to underground ducts (gas, water/sewage or oil pipelines, communication cables or power cable ducts) or superannuated pipelines frequently cause serious accidents resulting in damage to life and property. (In Korea, the total length of city water pipelines was approximately 2,000 km as of the end of 2009.) In addition, large amounts of damage caused by fractures, water and gas leakage caused by superannuation or damage to underground ducts in construction has been reported. Therefore, a system is required to precisely detect defects and deterioration in underground pipelines and the locations of such defects, for timely and accurate maintenance or replacement of the ducts. In this study, a system was developed which can locate underground structures (gas and water pipelines, power cable ducts, etc.) in 3D-coordinates and monitor the degree and position of defects using an Inertial Measurement Unit (IMU) sensing technique. The system can prevent damage to underground ducts and superannuated pipelines during construction, and provide reliable data for maintenance. The utility of the IMU sensing technique used in aircraft and ships in civil applications was verified.

Keywords: IMU, Pipelines, 3D-Coordinate, monitor.

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163 Using Electrical Impedance Tomography to Control a Robot

Authors: Shayan Rezvanigilkolaei, Shayesteh Vefaghnematollahi

Abstract:

Electrical impedance tomography is a non-invasive medical imaging technique suitable for medical applications. This paper describes an electrical impedance tomography device with the ability to navigate a robotic arm to manipulate a target object. The design of the device includes various hardware and software sections to perform medical imaging and control the robotic arm. In its hardware section an image is formed by 16 electrodes which are located around a container. This image is used to navigate a 3DOF robotic arm to reach the exact location of the target object. The data set to form the impedance imaging is obtained by having repeated current injections and voltage measurements between all electrode pairs. After performing the necessary calculations to obtain the impedance, information is transmitted to the computer. This data is fed and then executed in MATLAB which is interfaced with EIDORS (Electrical Impedance Tomography Reconstruction Software) to reconstruct the image based on the acquired data. In the next step, the coordinates of the center of the target object are calculated by image processing toolbox of MATLAB (IPT). Finally, these coordinates are used to calculate the angles of each joint of the robotic arm. The robotic arm moves to the desired tissue with the user command.

Keywords: Electrical impedance tomography, EIT, Surgeon robot, image processing of Electrical impedance tomography.

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162 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

Abstract:

In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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161 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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160 Transformations between Bivariate Polynomial Bases

Authors: Dimitris Varsamis, Nicholas Karampetakis

Abstract:

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: Bivariate interpolation polynomial, Polynomial basis, Transformations.

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159 A Strategy for Address Coding from HouseHold Registry Database

Authors: Yungchien Cheng, Chienmin Chu

Abstract:

Address Matching is an important application of Geographic Information System (GIS). Prior to Address Matching working, obtaining X,Y coordinates is necessary, which process is calling Address Geocoding. This study will illustrate the effective address geocoding process of using household registry database, and the check system for geocoded address.

Keywords: GIS, Address Geocoding, HouseHold Registry Database

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158 GPS Signal Correction to Improve Vehicle Location during Experimental Campaign

Authors: L. Della Ragione, G. Meccariello

Abstract:

In recent years in Italy the progress of the automobile industry, in the field of reduction of emissions values, is very remarkable. Nevertheless their evaluation and reduction is a key problem, especially in the cities, that account for more than 50% of world population. In this paper we dealt with the problem of describing a quantitatively approach for the reconstruction of GPS coordinates and altitude, in the context of correlation study between driving cycles / emission / geographical location, during an experimental campaign realized with some instrumented cars.

Keywords: Air pollution, Driving cycles, GPS signal.

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157 Deriving Generic Transformation Matrices for Multi-Axis Milling Machine

Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

Abstract:

This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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156 An Approximation Method for Three Quark Systems in the Hyper-Spherical Approach

Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

Abstract:

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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155 Numerical Simulation of a Conventional Heat Pipe

Authors: Shoeib Mahjoub, Ali Mahtabroshan

Abstract:

The steady incompressible flow has been solved in cylindrical coordinates in both vapour region and wick structure. The governing equations in vapour region are continuity, Navier-Stokes and energy equations. These equations have been solved using SIMPLE algorithm. For study of parameters variation on heat pipe operation, a benchmark has been chosen and the effect of changing one parameter has been analyzed when the others have been fixed.

Keywords: Vapour region, conventional heat pipe, numerical simulation.

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154 Child Care Policy in Kazakhstan: A New Model

Authors: Dina Maratovna Aikenova

Abstract:

Child care policy must be a priority area of public authorities in any country. This study investigates child care policy in Kazakhstan in accordance with the current position of children and laws. The results show that Kazakhstan policy in this sphere needs more systematic model including state economic and social measures, parental involvement and role of non-government organizations.

Keywords: Children, Kazakhstan, policy, vulnerability.

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153 Learning and Relationships in the Cyberspace

Authors: Gioacchino Lavanco, Viviana Catania, Anna Milio, Floriana Romano

Abstract:

The cyberspace is an instrument through which internet users could get new experiences. It could contribute to foster one-s own growth, widening cognitive, creative and communicative abilities and promoting relationships. In the cyberspace, in fact, it is possible to create virtual learning communities where internet users improve their interpersonal sphere, knowledge and skills. The main element of e-learning is the establishment of online relationships, that are often collaborative.

Keywords: Internet addiction, learner support, virtual relationships.

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152 An Implementation of Stipple Operations

Authors: Nakhoon Baek

Abstract:

Stipples are desired for pattern fillings and transparency effects. In contrast, some graphics standards, including OpenGL ES 1.1 and 2.0, omitted this feature. We represent details of providing line stipples and polygon stipples, through combining texture mapping and alpha blending functions. We start from the OpenGL-specified stipple-related API functions. The details of mathematical transformations are explained to get the correct texture coordinates. Then, the overall algorithm is represented, and its implementation results are followed. We accomplished both of line and polygon stipples, and verified its result with conformance test routines.

Keywords: Stipple operation, OpenGL ES, Implementation.

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151 Investigation of Self-Similarity Solution for Wake Flow of a Cylinder

Authors: A. B. Khoshnevis, F. Zeydabadi, F. Sokhanvar

Abstract:

The data measurement of mean velocity has been taken for the wake of single circular cylinder with three different diameters for two different velocities. The effects of change in diameter and in velocity are studied in self-similar coordinate system. The spatial variations of velocity defect and that of the half-width have been investigated. The results are compared with those published by H.Schlichting. In the normalized coordinates, it is also observed that all cases except for the first station are self-similar. By attention to self-similarity profiles of mean velocity, it is observed for all the cases at the each station curves tend to zero at a same point.

Keywords: Self-similarity, wake of single circular cylinder

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150 The Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields

Authors: Betül Gezer, Hacer Özden, Ahmet Tekcan, Osman Bizim

Abstract:

Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves.

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149 Dominant Correlation Effects in Atomic Spectra

Authors: Hubert Klar

Abstract:

High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: Correlation, resonances, threshold ionization, Cooper pair.

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