Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1012

Search results for: Learning Curves

1012 The Elliptic Curves y2 = x3 - t2x over Fp

Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.

Keywords: Elliptic curves over finite fields, rational points onelliptic curves, rank, trace of Frobenius.

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1011 Some Characterizations of Isotropic Curves In the Euclidean Space

Authors: Süha Yılmaz, Melih Turgut

Abstract:

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.

Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.

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1010 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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1009 New DES based on Elliptic Curves

Authors: Ghada Abdelmouez M., Fathy S. Helail, Abdellatif A. Elkouny

Abstract:

It is known that symmetric encryption algorithms are fast and easy to implement in hardware. Also elliptic curves have proved to be a good choice for building encryption system. Although most of the symmetric systems have been broken, we can create a hybrid system that has the same properties of the symmetric encryption systems and in the same time, it has the strength of elliptic curves in encryption. As DES algorithm is considered the core of all successive symmetric encryption systems, we modified DES using elliptic curves and built a new DES algorithm that is hard to be broken and will be the core for all other symmetric systems.

Keywords: DES, Elliptic Curves, hybrid system, symmetricencryption.

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1008 The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

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

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1007 On the Differential Geometry of the Curves in Minkowski Space-Time II

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut

Abstract:

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.

Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.

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1006 Analytical Development of a Failure Limit and Iso-Uplift Curves for Eccentrically Loaded Shallow Foundations

Authors: N. Abbas, S. Lagomarsino, S. Cattari

Abstract:

Examining existing experimental results for shallow rigid foundations subjected to vertical centric load (N), accompanied or not with a bending moment (M), two main non-linear mechanisms governing the cyclic response of the soil-foundation system can be distinguished: foundation uplift and soil yielding. A soil-foundation failure limit, is defined as a domain of resistance in the two dimensional (2D) load space (N, M) inside of which lie all the admissible combinations of loads; these latter correspond to a pure elastic, non-linear elastic or plastic behavior of the soil-foundation system, while the points lying on the failure limit correspond to a combination of loads leading to a failure of the soil-foundation system. In this study, the proposed resistance domain is constructed analytically based on mechanics. Original elastic limit, uplift initiation limit and iso-uplift limits are constructed inside this domain. These limits give a prediction of the mechanisms activated for each combination of loads applied to the foundation. A comparison of the proposed failure limit with experimental tests existing in the literature shows interesting results. Also, the developed uplift initiation limit and iso-uplift curves are confronted with others already proposed in the literature and widely used due to the absence of other alternatives, and remarkable differences are noted, showing evident errors in the past proposals and relevant accuracy for those given in the present work.

Keywords: Foundation uplift, Iso-uplift curves, Resistance domain, Soil yield.

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1005 The Use of S Curves in Technology Forecasting and its Application On 3D TV Technology

Authors: Gizem Intepe, Tufan Koc

Abstract:

S-Curves are commonly used in technology forecasting. They show the paths of product performance in relation to time or investment in R&D. It is a useful tool to describe the inflection points and the limit of improvement of a technology. Companies use this information to base their innovation strategies. However inadequate use and some limitations of this technique lead to problems in decision making. In this paper first technology forecasting and its importance for company level strategies will be discussed. Secondly the S-Curve and its place among other forecasting techniques will be introduced. Thirdly its use in technology forecasting will be discussed based on its advantages, disadvantages and limitations. Finally an application of S-curve on 3D TV technology using patent data will also be presented and the results will be discussed.

Keywords: Patent analysis, Technological forecasting. S curves, 3D TV

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1004 Finding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems

Authors: Pu Duan, Shi Cui, Choong Wah Chan

Abstract:

Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this paper a new method is presented to find more non-supersingular elliptic curves for pairing-based cryptosystems with general embedding degree k and large values of cofactor h. In addition, some effective parameters of these non-supersingular elliptic curves are provided in this paper.

Keywords: Family of group order, kth root of unity, non-supersingular elliptic curves polynomial field.

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1003 Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime

Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul

Abstract:

In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.

Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.

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1002 Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1

Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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1001 Circular Approximation by Trigonometric Bézier Curves

Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa

Abstract:

We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

Keywords: Control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions.

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1000 Entropy based Expeditive Methodology for Rating Curves Assessment

Authors: D. Mirauda, M. Greco, P. Moscarelli

Abstract:

The river flow forecasting represents a crucial point to employ for improving a management policy addressed to the right use of water resources as well as for conjugating prevention and defense actions against environmental degradation. The difficulties occurring during the field activities encourage the development and implementation of operative computation and measuring methods addressed to time reduction for data acquisition and processing maintaining a good level of accuracy. Therefore, the aim of the present work is to test a new entropy based expeditive methodology for the evaluation of the rating curves on three gauged sections with different geometric and morphological characteristics. The methodology requires the choice of only three verticals along the measure section and the sampling of only the maximum velocity. The results underline how in most conditions the rating curves drawn can replace those built with classic methodologies, simplifying thus the procedures of data monitoring and calculation.

Keywords: gauged station, entropic approach, expeditive methodology, rating curves.

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999 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

Authors: Ahmet Tekcan

Abstract:

Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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998 Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime

Authors: Gokhan Soydan, Musa Demirci, Nazli Yildiz Ikikardes, Ismail Naci Cangul

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.

Keywords: Elliptic curves over finite fields, rational points.

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997 Improved of Elliptic Curves Cryptography over a Ring

Authors: A. Chillali, A. Tadmori, M. Ziane

Abstract:

In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

Keywords: Elliptic Curves, Finite Ring, Cryptography.

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996 A Method to Calculate Frenet Apparatus of W-Curves in the Euclidean 6-Space

Authors: Süha Yılmaz, Melih Turgut

Abstract:

These In this work, a regular unit speed curve in six dimensional Euclidean space, whose Frenet curvatures are constant, is considered. Thereafter, a method to calculate Frenet apparatus of this curve is presented.

Keywords: Classical Differential Geometry, Euclidean 6-space, Frenet Apparatus of the curves.

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995 E-Learning Experiences of Hong Kong Students

Authors: J. Lam, R. Chan

Abstract:

The adoption of e-learning in Hong Kong has been increasing rapidly in the past decade. To understand the e-learning experiences of the students, the School of Professional and Continuing Education of The University of Hong Kong conducted a survey. The survey aimed to collect students- experiences in using learning management system, their perceived e-learning advantages, barriers in e-learning and preferences in new e-learning development. A questionnaire with 84 questions was distributed in mid 2012 and 608 valid responds were received. The analysis results showed that the students found e-learning helpful to their study. They preferred interactive functions and mobile features. Blended learning mode, both face-to-face learning mode integrated with online learning and face-to-face learning mode supplemented with online resources, were preferred by the students. The results of experiences of Hong Kong students in e-learning provided a contemporary reference to the e-learning practitioners to understand the e-learning situation in Asia.

Keywords: E-learning, blended learning, learning experience, learning management system.

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994 The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields

Authors: Musa Demirci, Nazlı Yıldız İkikardeş, Gökhan Soydan, İsmail Naci Cangül

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.

Keywords: Elliptic curves over finite fields, rational points, quadratic residue.

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993 On Frenet-Serret Invariants of Non-Null Curves in Lorentzian Space L5

Authors: Melih Turgut, José Luis López-Bonilla, Süha Yılmaz

Abstract:

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated.

Keywords: Lorentzian 5-space, Frenet-Serret Invariants, Nonnull Curves

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992 Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space

Authors: Melih Turgut, Süha Yılmaz

Abstract:

In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

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991 Elliptic Divisibility Sequences over Finite Fields

Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.

Keywords: Elliptic divisibility sequences, singular elliptic divisibilitysequences, elliptic curves, singular curves.

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990 Regionalization of IDF Curves with L-Moments for Storm Events

Authors: Noratiqah Mohd Ariff, Abdul Aziz Jemain, Mohd Aftar Abu Bakar

Abstract:

The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station.

Keywords: IDF curves, L-moments, regionalization, storm events.

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989 Effects of Human Factors on Workforce Scheduling

Authors: M. Othman, N. Bhuiyan, G. J. Gouw

Abstract:

In today-s competitive market, most companies develop manufacturing systems that can help in cost reduction and maximum quality. Human issues are an important part of manufacturing systems, yet most companies ignore their effects on production performance. This paper aims to developing an integrated workforce planning system that incorporates the human being. Therefore, a multi-objective mixed integer nonlinear programming model is developed to determine the amount of hiring, firing, training, overtime for each worker type. This paper considers a workforce planning model including human aspects such as skills, training, workers- personalities, capacity, motivation, and learning rates. This model helps to minimize the hiring, firing, training and overtime costs, and maximize the workers- performance. The results indicate that the workers- differences should be considered in workforce scheduling to generate realistic plans with minimum costs. This paper also investigates the effects of human learning rates on the performance of the production systems.

Keywords: Human Factors, Learning Curves, Workers' Differences, Workforce Scheduling

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988 The Design and Analysis of Learning Effects for a Game-based Learning System

Authors: Wernhuar Tarng, Weichian Tsai

Abstract:

The major purpose of this study is to use network and multimedia technologies to build a game-based learning system for junior high school students to apply in learning “World Geography" through the “role-playing" game approaches. This study first investigated the motivation and habits of junior high school students to use the Internet and online games, and then designed a game-based learning system according to situated and game-based learning theories. A teaching experiment was conducted to analyze the learning effectiveness of students on the game-based learning system and the major factors affecting their learning. A questionnaire survey was used to understand the students- attitudes towards game-based learning. The results showed that the game-based learning system can enhance students- learning, but the gender of students and their habits in using the Internet have no significant impact on learning. Game experience has a significant impact on students- learning, and the higher the experience value the better the effectiveness of their learning. The results of questionnaire survey also revealed that the system can increase students- motivation and interest in learning "World Geography".

Keywords: Game-based learning, situated learning, role playing, learning effectiveness, learning motivation.

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987 Analyzing the Perception of Key Terms in E-Learning in Academia: Case Study of Princess Nourah Bint Abdulrahman University

Authors: M. Almohaimeed, Y. Alhaidari, H. Alhamdan, A. Alfaries, A. Ater Kranov

Abstract:

A university-wide survey to obtain baseline data regarding the perceptions of key terms related to e-learning and distance learning among students, faculty and staff was conducted to help achieve the goals of Princess Nourah bint Abdulrahman University’s and the Kingdom of Saudi Arabia’s National Center for e-learning and Distance Learning. This paper comprises a relevant literature review, the survey methodology, preliminary data analysis, discussion, and recommendations for further research. The major findings indicate a deep and wide differentiation of understanding among users of critical key terms.

Keywords: E-learning, distance learning, on-line learning, perceptions of learning environments.

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986 Educators’ Adherence to Learning Theories and Their Perceptions on the Advantages and Disadvantages of e-Learning

Authors: Samson T. Obafemi, Seraphin D. Eyono Obono

Abstract:

Information and Communication Technologies (ICTs) are pervasive nowadays, including in education where they are expected to improve the performance of learners. However, the hope placed in ICTs to find viable solutions to the problem of poor academic performance in schools in the developing world has not yet yielded the expected benefits. This problem serves as a motivation to this study whose aim is to examine the perceptions of educators on the advantages and disadvantages of e-learning. This aim will be subdivided into two types of research objectives. Objectives on the identification and design of theories and models will be achieved using content analysis and literature review. However, the objective on the empirical testing of such theories and models will be achieved through the survey of educators from different schools in the Pinetown District of the South African Kwazulu-Natal province. SPSS is used to quantitatively analyse the data collected by the questionnaire of this survey using descriptive statistics and Pearson correlations after assessing the validity and the reliability of the data. The main hypothesis driving this study is that there is a relationship between the demographics of educators’ and their adherence to learning theories on one side, and their perceptions on the advantages and disadvantages of e-learning on the other side, as argued by existing research; but this research views these learning theories under three perspectives: educators’ adherence to self-regulated learning, to constructivism, and to progressivism. This hypothesis was fully confirmed by the empirical study except for the demographic factor where teachers’ level of education was found to be the only demographic factor affecting the perceptions of educators on the advantages and disadvantages of e-learning.

Keywords: Academic performance, e-learning, Learning theories, Teaching and Learning.

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985 Arabic Character Recognition Using Regression Curves with the Expectation Maximization Algorithm

Authors: Abdullah A. AlShaher

Abstract:

In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: Shape recognition, Arabic handwritten characters, regression curves, expectation maximization algorithm.

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984 Analysis and Categorization of e-Learning Activities Based On Meaningful Learning Characteristics

Authors: Arda Yunianta, Norazah Yusof, Mohd Shahizan Othman, Dewi Octaviani

Abstract:

Learning is the acquisition of new mental schemata, knowledge, abilities and skills which can be used to solve problems potentially more successfully. The learning process is optimum when it is assisted and personalized. Learning is not a single activity, but should involve many possible activities to make learning become meaningful. Many e-learning applications provide facilities to support teaching and learning activities. One way to identify whether the e-learning system is being used by the learners is through the number of hits that can be obtained from the e-learning system's log data. However, we cannot rely solely to the number of hits in order to determine whether learning had occurred meaningfully. This is due to the fact that meaningful learning should engage five characteristics namely active, constructive, intentional, authentic and cooperative. This paper aims to analyze the e-learning activities that is meaningful to learning. By focusing on the meaningful learning characteristics, we match it to the corresponding Moodle e-learning activities. This analysis discovers the activities that have high impact to meaningful learning, as well as activities that are less meaningful. The high impact activities is given high weights since it become important to meaningful learning, while the low impact has less weight and said to be supportive e-learning activities. The result of this analysis helps us categorize which e-learning activities that are meaningful to learning and guide us to measure the effectiveness of e-learning usage.

Keywords: e-learning system, e-learning activity, meaningful learning characteristics, Moodle

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983 Enhancing Learning Experiences in Outcomebased Higher Education: A Step towards Student Centered Learning

Authors: K. Kumpas

Abstract:

Bologna process has influenced enhancing studentcentered learning in Estonian higher education since 2009, but there is no information about what helps or hinders students to achieve learning outcomes and how quality of student-centered learning might be improved. The purpose of this study is to analyze two questions from outcome-based course evaluation questionnaire which is used in Estonian Entrepreneurship University of Applied Sciences. In this qualitative research, 384 students from 22 different courses described what helped and hindered them to achieve learning outcomes. The analysis showed that the aspects that hinder students to achieve learning outcomes are mostly personal: time management, family and personal matters, motivation and non-academic activities. The results indicate that students- learning is commonly supported by school, where teacher, teaching and characteristics of teaching methods help mostly to achieve learning outcomes, also learning material, practical assignments and independent study was brought up as one of the key elements.

Keywords: Learning outcomes, learning quality, student-centered learning

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