**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**510

# Search results for: rational approximation.

##### 510 Arc Length of Rational Bezier Curves and Use for CAD Reparametrization

**Authors:**
Maharavo Randrianarivony

**Abstract:**

**Keywords:**
Adaptivity,
Length,
Parametrization,
Rational Bezier

##### 509 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

**Authors:**
J. Kavikumar,
N. S. Manian,
M.B.K. Moorthy

**Abstract:**

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

**Keywords:**
Fuzzy best co-approximation,
fuzzy quotient spaces,
proximinality,
Chebyshevity,
best simultaneous co-approximation.

##### 508 Definable Subsets in Covering Approximation Spaces

**Authors:**
Xun Ge,
Zhaowen Li

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 507 Robust Numerical Scheme for Pricing American Options under Jump Diffusion Models

**Authors:**
Salah Alrabeei,
Mohammad Yousuf

**Abstract:**

**Keywords:**
Integral differential equations,
American options,
jump–diffusion model,
rational approximation.

##### 506 On an Open Problem for Definable Subsets of Covering Approximation Spaces

**Authors:**
Mei He,
Ying Ge,
Jingyu Qian

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 505 Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2DFunctions Approximation

**Authors:**
Wajdi Bellil,
Chokri Ben Amar,
Adel M. Alimi

**Abstract:**

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate Ôêºf as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.

**Keywords:**
Beta wavelets networks,
RBF neural network,
training algorithms,
MSE,
1-D,
2D function approximation.

##### 504 Some Separations in Covering Approximation Spaces

**Authors:**
Xun Ge,
Jinjin Li,
Ying Ge

**Abstract:**

**Keywords:**
Rough set,
covering approximation space,
granularitywise separation.

##### 503 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator

**Authors:**
A. A. Penin

**Abstract:**

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

**Keywords:**
a solar cell generator,
I − V characteristic,
p − n junction,
approximation

##### 502 Rational Chebyshev Tau Method for Solving Natural Convection of Darcian Fluid About a Vertical Full Cone Embedded in Porous Media Whit a Prescribed Wall Temperature

**Authors:**
Kourosh Parand,
Zahra Delafkar,
Fatemeh Baharifard

**Abstract:**

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

**Keywords:**
Tau method,
semi-infinite,
nonlinear ODE,
rational Chebyshev,
porous media.

##### 501 The Conceptual and Procedural Knowledge of Rational Numbers in Primary School Teachers

**Authors:**
R. M. Kashim

**Abstract:**

The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

**Keywords:**
Conceptual knowledge,
primary school teachers,
procedural knowledge,
rational numbers.

##### 500 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.

##### 499 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 498 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

**Authors:**
M. R. Yadav,
A. K. Sharma,
B. S. Thakur

**Abstract:**

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

**Keywords:**
Cyclic contraction,
rational cyclic contraction,
best proximity point and complete metric space.

##### 497 Primary School Teachers’ Conceptual and Procedural Knowledge of Rational Number and Its Effects on Pupils’ Achievement in Rational Numbers

**Authors:**
R. M. Kashim

**Abstract:**

**Keywords:**
Achievement,
conceptual knowledge,
procedural knowledge,
rational numbers.

##### 496 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.

##### 495 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.

##### 494 Analysis of Statistical Data on Social Resources Dimension of Occupational Status Attainment: A Rational Choice Approach

**Authors:**
Oleg Demchenko

**Abstract:**

**Keywords:**
Social resources,
status attainment,
rational choice,
weak ties,
work-related ties.

##### 493 Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types

**Authors:**
Chaghoub Soraya,
Zhang Xiaoyan

**Abstract:**

**Keywords:**
Approximation algorithms,
buy-at-bulk,
combinatorial
optimization,
network design,
p-median.

##### 492 Monotone Rational Trigonometric Interpolation

**Authors:**
Uzma Bashir,
Jamaludin Md. Ali

**Abstract:**

This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.

**Keywords:**
Trigonometric splines,
Monotone data,
Shape preserving,
C1 monotone interpolant.

##### 491 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.

##### 490 Approximation to the Hardy Operator on Topological Measure Spaces

**Authors:**
Kairat T. Mynbaev,
Elena N. Lomakina

**Abstract:**

We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.

**Keywords:**
Approximation numbers,
boundedness and
compactness,
multidimensional Hardy operator,
Hausdorff
topological space.

##### 489 Generating Arabic Fonts Using Rational Cubic Ball Functions

**Authors:**
Fakharuddin Ibrahim,
Jamaludin Md. Ali,
Ahmad Ramli

**Abstract:**

^{1}continuity. The conditions considered are known as the G

^{1}Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

**Keywords:**
Continuity,
data interpolation,
Hermite condition,
rational Ball curve.

##### 488 Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients

**Authors:**
Mario Mastriani

**Abstract:**

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

**Keywords:**
Compression,
denoising,
projections,
wavelets.

##### 487 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.

##### 486 A Note on Negative Hypergeometric Distribution and Its Approximation

**Authors:**
S. B. Mansuri

**Abstract:**

**Keywords:**
Negative hypergeometric distribution,
Poisson distribution,
Poisson approximation,
Stein-Chen identity,
w-function.

##### 485 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation

**Authors:**
Yongxin Yuan,
Hao Liu

**Abstract:**

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

**Keywords:**
Inverse problem,
Least-squares solution,
model updating,
Singular value decomposition (SVD),
Optimal approximation.

##### 484 Approximation Algorithm for the Shortest Approximate Common Superstring Problem

**Authors:**
A.S. Rebaï,
M. Elloumi

**Abstract:**

**Keywords:**
Shortest approximate common superstring,
approximation algorithms,
strings overlaps,
complexities.

##### 483 Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model

**Authors:**
Properties,
Approximation Distribution Reductions in Multigranulation Rough Set Model

**Abstract:**

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

**Keywords:**
Incomplete information system,
maximal compatible class,
multi-granulation rough set model,
reduction.

##### 482 On Diffusion Approximation of Discrete Markov Dynamical Systems

**Authors:**
Jevgenijs Carkovs

**Abstract:**

**Keywords:**
Markov dynamical system,
diffusion approximation,
equilibrium stochastic stability.

##### 481 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.