**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.

##### 1011 Some Characterizations of Isotropic Curves In the Euclidean Space

**Authors:**
Süha Yılmaz,
Melih Turgut

**Abstract:**

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

##### 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.

##### 1009 New DES based on Elliptic Curves

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

**Abstract:**

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

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

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

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

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

**Authors:**
Süha Yılmaz,
Emin Özyılmaz,
Melih Turgut

**Abstract:**

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

##### 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.

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

**Authors:**
Gizem Intepe,
Tufan Koc

**Abstract:**

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

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

**Authors:**
Pu Duan,
Shi Cui,
Choong Wah Chan

**Abstract:**

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

##### 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:**

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

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

**Authors:**
Kaoutar Lamrini Uahabi,
Mohamed Atounti

**Abstract:**

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

##### 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.

##### 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.

##### 999 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

**Authors:**
Ahmet Tekcan

**Abstract:**

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

##### 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.

##### 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.

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

**Authors:**
Süha Yılmaz,
Melih Turgut

**Abstract:**

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

##### 995 E-Learning Experiences of Hong Kong Students

**Abstract:**

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

##### 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:**

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

##### 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

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

**Authors:**
Melih Turgut,
Süha Yılmaz

**Abstract:**

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

##### 991 Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

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

##### 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.

##### 989 Effects of Human Factors on Workforce Scheduling

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

**Abstract:**

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

##### 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.

##### 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:**

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

##### 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.

##### 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 2^{nd} 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.

##### 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

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

**Authors:**
K. Kumpas

**Abstract:**

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