**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**363

# Search results for: curves

##### 363 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.

##### 362 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.

##### 361 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.

##### 360 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.

##### 359 New DES based on Elliptic Curves

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

**Abstract:**

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

##### 358 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.

##### 357 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.

##### 356 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

##### 355 Centrifuge Modeling of Monopiles Subjected to Lateral Monotonic Loading

**Authors:**
H. R. Khodaei,
M. Moradi,
A. H. Tajik

**Abstract:**

The type of foundation commonly used today for berthing dolphins is a set of tubular steel piles with large diameters, which are known as monopiles. The design of these monopiles is based on the theories related with laterally loaded piles. One of the most common methods to analyze and design the piles subjected to lateral loads is the p-y curves. In the present study, centrifuge tests are conducted in order to obtain the p-y curves. Series of tests were designed in order to investigate the scaling laws in the centrifuge for monotonic loading. Also, two important parameters, the embedded depth L of the pile in the soil and free length e of the pile, as well as their ratios were studied via five experimental tests. Finally, the p-y curves of API are presented to be compared with the curves obtained from the tests so that the differences could be demonstrated. The results show that the p-y curves proposed by API highly overestimate the lateral load bearing capacity. It suggests that these curves need correction and modification for each site as the soil conditions change.

**Keywords:**
Centrifuge modeling,
monopile,
lateral loading,
p-y curves.

##### 354 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.

##### 353 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.

##### 352 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.

##### 351 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.

##### 350 Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves

**Authors:**
Taweechai Nuntawisuttiwong,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Newton interpolation,
Lagrange interpolation,
linear
complexity.

##### 349 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.

##### 348 Single Feed Circularly Polarized Poly Fractal Antenna for Wireless Applications

**Authors:**
V. V. Reddy,
N. V. S. N. Sarma

**Abstract:**

A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x- axis, yaxis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel polyfractal antenna are demonstrated.

**Keywords:**
Circular polarization,
Fractal,
Koch,
Minkowski.

##### 347 An Approach to Polynomial Curve Comparison in Geometric Object Database

**Authors:**
Chanon Aphirukmatakun,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Bezier curve,
Said-Ball curve,
Wang-Ball curve,
DP curve,
CAGD,
comparison,
geometric object database.

##### 346 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.

##### 345 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.

##### 344 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.

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

**Authors:**
Ahmet Tekcan

**Abstract:**

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

##### 342 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.

##### 341 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.

##### 340 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

##### 339 Flow Duration Curves and Recession Curves Connection through a Mathematical Link

**Authors:**
Elena Carcano,
Mirzi Betasolo

**Abstract:**

This study helps Public Water Bureaus in giving reliable answers to water concession requests. Rapidly increasing water requests can be supported provided that further uses of a river course are not totally compromised, and environmental features are protected as well. Strictly speaking, a water concession can be considered a continuous drawing from the source and causes a mean annual streamflow reduction. Therefore, deciding if a water concession is appropriate or inappropriate seems to be easily solved by comparing the generic demand to the mean annual streamflow value at disposal. Still, the immediate shortcoming for such a comparison is that streamflow data are information available only for few catchments and, most often, limited to specific sites. Subsequently, comparing the generic water demand to mean daily discharge is indeed far from being completely satisfactory since the mean daily streamflow is greater than the water withdrawal for a long period of a year. Consequently, such a comparison appears to be of little significance in order to preserve the quality and the quantity of the river. In order to overcome such a limit, this study aims to complete the information provided by flow duration curves introducing a link between Flow Duration Curves (FDCs) and recession curves and aims to show the chronological sequence of flows with a particular focus on low flow data. The analysis is carried out on 25 catchments located in North-Eastern Italy for which daily data are provided. The results identify groups of catchments as hydrologically homogeneous, having the lower part of the FDCs (corresponding streamflow interval is streamflow Q between 300 and 335, namely: Q(300), Q(335)) smoothly reproduced by a common recession curve. In conclusion, the results are useful to provide more reliable answers to water request, especially for those catchments which show similar hydrological response and can be used for a focused regionalization approach on low flow data. A mathematical link between streamflow duration curves and recession curves is herein provided, thus furnishing streamflow duration curves information upon a temporal sequence of data. In such a way, by introducing assumptions on recession curves, the chronological sequence upon low flow data can also be attributed to FDCs, which are known to lack this information by nature.

**Keywords:**
Chronological sequence of discharges,
recession curves,
streamflow duration curves,
water concession.

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

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 337 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.

##### 336 An Implicit Representation of Spherical Product for Increasing the Shape Variety of Super-quadrics in Implicit Surface Modeling

**Authors:**
Pi-Chung Hsu

**Abstract:**

**Keywords:**
Implicit surfaces,
Soft objects,
Super-quadrics.

##### 335 A Study of General Attacks on Elliptic Curve Discrete Logarithm Problem over Prime Field and Binary Field

**Authors:**
Tun Myat Aung,
Ni Ni Hla

**Abstract:**

**Keywords:**
Discrete logarithm problem,
general attacks,
elliptic curves,
strong curves,
prime field,
binary field,
attack experiments.

##### 334 Seismic Fragility Curves for Shallow Circular Tunnels under Different Soil Conditions

**Authors:**
Siti Khadijah Che Osmi,
Syed Mohd Ahmad

**Abstract:**

This paper presents a methodology to develop fragility curves for shallow tunnels so as to describe a relationship between seismic hazard and tunnel vulnerability. Emphasis is given to the influence of surrounding soil material properties because the dynamic behaviour of the tunnel mostly depends on it. Four ground properties of soils ranging from stiff to soft soils are selected. A 3D nonlinear time history analysis is used to evaluate the seismic response of the tunnel when subjected to five real earthquake ground intensities. The derived curves show the future probabilistic performance of the tunnels based on the predicted level of damage states corresponding to the peak ground acceleration. A comparison of the obtained results with the previous literature is provided to validate the reliability of the proposed fragility curves. Results show the significant role of soil properties and input motions in evaluating the seismic performance and response of shallow tunnels.

**Keywords:**
Fragility analysis,
seismic performance,
tunnel lining,
vulnerability.