**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1295

# Search results for: polynomial equation

##### 1295 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

**Authors:**
Tsun-Hui Huang,
Shyue-Cheng Yang,
Chiou-Fen Shieh

**Abstract:**

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

**Keywords:**
Polynomial constitutive equation,
solitary.

##### 1294 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner.

##### 1293 On CR-Structure and F-Structure Satisfying Polynomial Equation

**Authors:**
Manisha Kankarej

**Abstract:**

**Keywords:**
CR-submainfolds,
CR-structure,
Integrability condition & Nijenhuis tensor.

##### 1292 Method of Finding Aerodynamic Characteristic Equations of Missile for Trajectory Simulation

**Authors:**
Attapon Charoenpon,
Ekkarach Pankeaw

**Abstract:**

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

**Keywords:**
Aerodynamic,
Characteristic Equation,
Angle ofAttack,
Polynomial interpolation,
Trajectories

##### 1291 Blow up in Polynomial Differential Equations

**Authors:**
Rudolf Csikja,
Janos Toth

**Abstract:**

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

**Keywords:**
blow up,
finite escape time,
polynomial ODE,
singularity,
Lotka–Volterra equation,
Painleve analysis,
Ψ-series,
global existence

##### 1290 The Adsorption of SDS on Ferro-Precipitates

**Authors:**
R.Marsalek

**Abstract:**

**Keywords:**
ferro-precipitate,
adsorption,
SDS,
zeta potential

##### 1289 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 1288 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

**Authors:**
Reza Mohammadi,
Mahdieh Sahebi

**Abstract:**

**Keywords:**
Fourth-order parabolic equation,
variable coefficient,
polynomial quintic spline,
off-step points,
stability analysis.

##### 1287 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.

##### 1286 A New Approach to Polynomial Neural Networks based on Genetic Algorithm

**Authors:**
S. Farzi

**Abstract:**

**Keywords:**
GMDH,
GPNN,
GA,
PNN.

##### 1285 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

**Authors:**
Oleksandr Poliakov,
Yevgen Pashkov,
Marina Kolesova,
Olena Chepenyuk,
Mykhaylo Kalinin,
Vadym Kramar

**Abstract:**

**Keywords:**
Iterative method,
Laguerre's method,
Newton's
method,
polynomial equation,
system of equations

##### 1284 A Novel Deinterlacing Algorithm Based on Adaptive Polynomial Interpolation

**Authors:**
Seung-Won Jung,
Hye-Soo Kim,
Le Thanh Ha,
Seung-Jin Baek,
Sung-Jea Ko

**Abstract:**

**Keywords:**
Deinterlacing,
polynomial interpolation.

##### 1283 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method

**Authors:**
Said Laachir,
Aziz Laaribi

**Abstract:**

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

**Keywords:**
Helmholtz equation,
Nikiforov-Uvarov method,
exact solutions,
eigenfunctions.

##### 1282 Factoring a Polynomial with Multiple-Roots

**Authors:**
Feng Cheng Chang

**Abstract:**

**Keywords:**
Polynomial roots,
greatest common divisor,
Longhand polynomial division,
Euclidean GCD Algorithm.

##### 1281 Designing FIR Filters with Polynomial Approach

**Authors:**
Sunil Bhooshan,
Vinay Kumar

**Abstract:**

**Keywords:**
FIR filter,
Polynomial.

##### 1280 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers

**Authors:**
Nurhakimah Ab. Rahman,
Lazim Abdullah

**Abstract:**

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

**Keywords:**
Dual fuzzy polynomial equations,
Interval type-2,
Ranking method,
Value.

##### 1279 Matrix Valued Difference Equations with Spectral Singularities

**Authors:**
Serifenur Cebesoy,
Yelda Aygar,
Elgiz Bairamov

**Abstract:**

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

**Keywords:**
Difference Equations,
Jost Functions,
Asymptotics,
Eigenvalues,
Continuous Spectrum,
Spectral Singularities.

##### 1278 Empirical Statistical Modeling of Rainfall Prediction over Myanmar

**Authors:**
Wint Thida Zaw,
Thinn Thu Naing

**Abstract:**

**Keywords:**
Polynomial Regression,
Rainfall Forecasting,
Statistical forecasting.

##### 1277 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 1276 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

**Authors:**
Watcharakorn Thongchuay,
Puntip Toghaw,
Montri Maleewong

**Abstract:**

**Keywords:**
Galerkin finite element method,
Heat equation ,
Lagrange basis function,
Wavelet basis function.

##### 1275 Evolutionary Design of Polynomial Controller

**Authors:**
R. Matousek,
S. Lang,
P. Minar,
P. Pivonka

**Abstract:**

**Keywords:**
Evolutionary design,
Genetic algorithms,
PID controller,
Pole placement,
Polynomial controller

##### 1274 Discrete Polynomial Moments and Savitzky-Golay Smoothing

**Authors:**
Paul O'Leary,
Matthew Harker

**Abstract:**

**Keywords:**
Gram polynomials,
Savitzky-Golay Smoothing,
Discrete Polynomial Moments

##### 1273 Mathematical Modelling of Transport Phenomena in Radioactive Waste-Cement-Bentonite Matrix

**Authors:**
Ilija Plecas,
Uranija Kozmidis-Luburic,
Radojica Pesic

**Abstract:**

The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

**Keywords:**
bentonite,
cement ,
radioactive waste,
composite,
disposal,
diffusion

##### 1272 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

**Authors:**
Suparman

**Abstract:**

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

**Keywords:**
Piecewise,
Bayesian,
reversible jump MCMC,
segmentation.

##### 1271 Fuzzy Fingerprint Vault using Multiple Polynomials

**Authors:**
Daesung Moon,
Woo-Yong Choi,
Kiyoung Moon

**Abstract:**

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

**Keywords:**
Fuzzy vault,
fingerprint recognition multiple polynomials.

##### 1270 Computable Function Representations Using Effective Chebyshev Polynomial

**Authors:**
Mohammed A. Abutheraa,
David Lester

**Abstract:**

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

**Keywords:**
Approximation Theory,
Chebyshev Polynomial,
Computable Functions,
Computable Real Arithmetic,
Integration,
Numerical Analysis.

##### 1269 Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB

**Authors:**
Yong-Je Choi,
Moo-Seop Kim,
Hang-Rok Lee,
Ho-Won Kim

**Abstract:**

**Keywords:**
Elliptic Curve Cryptosystem,
Crypto Algorithm,
Polynomial Basis,
Optimal Normal Basis,
Security.

##### 1268 Improved Neutron Leakage Treatment on Nodal Expansion Method for PWR Reactors

**Authors:**
Antonio Carlos Marques Alvim,
Fernando Carvalho da Silva,
Aquilino Senra Martinez

**Abstract:**

**Keywords:**
Transverse leakage,
nodal expansion method,
power
density,
PWR reactors

##### 1267 A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes

**Authors:**
Zohreh O. Akbari

**Abstract:**

**Keywords:**
Clique problem,
Deterministic Polynomial-time
Algorithm,
Equality of P and NP Complexity Classes.

##### 1266 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

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

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

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