**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2895

# Search results for: Recurrences relation and Generalization of the new class matrix polynomial set.

##### 2895 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.

##### 2894 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.

##### 2893 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.

##### 2892 A Generalization of Planar Pascal’s Triangle to Polynomial Expansion and Connection with Sierpinski Patterns

**Authors:**
Wajdi Mohamed Ratemi

**Abstract:**

**Keywords:**
Generalized Pascal’s triangle,
Pascal’s triangle,
polynomial expansion,
Sierpinski’s triangle,
staircase horizontal
vertical method.

##### 2891 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.

##### 2890 Dimensionality Reduction of PSSM Matrix and its Influence on Secondary Structure and Relative Solvent Accessibility Predictions

**Authors:**
Rafał Adamczak

**Abstract:**

State-of-the-art methods for secondary structure (Porter, Psi-PRED, SAM-T99sec, Sable) and solvent accessibility (Sable, ACCpro) predictions use evolutionary profiles represented by the position specific scoring matrix (PSSM). It has been demonstrated that evolutionary profiles are the most important features in the feature space for these predictions. Unfortunately applying PSSM matrix leads to high dimensional feature spaces that may create problems with parameter optimization and generalization. Several recently published suggested that applying feature extraction for the PSSM matrix may result in improvements in secondary structure predictions. However, none of the top performing methods considered here utilizes dimensionality reduction to improve generalization. In the present study, we used simple and fast methods for features selection (t-statistics, information gain) that allow us to decrease the dimensionality of PSSM matrix by 75% and improve generalization in the case of secondary structure prediction compared to the Sable server.

**Keywords:**
Secondary structure prediction,
feature selection,
position specific scoring matrix.

##### 2889 A Class of Formal Operators for Combinatorial Identities and its Application

**Authors:**
Ruigang Zhang,
Wuyungaowa,
Xingchen Ma

**Abstract:**

In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

**Keywords:**
Generating functions,
operators sequence group,
Riordan arrays,
R. G operator group,
combinatorial identities.

##### 2888 Discrete Polynomial Moments and Savitzky-Golay Smoothing

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

**Abstract:**

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

##### 2887 Sign Pattern Matrices that Admit P0 Matrices

**Authors:**
Ling Zhang,
Ting-Zhu Huang

**Abstract:**

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

**Keywords:**
Sign pattern matrices,
P0 matrices,
graph,
digraph.

##### 2886 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.

##### 2885 On CR-Structure and F-Structure Satisfying Polynomial Equation

**Authors:**
Manisha Kankarej

**Abstract:**

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

##### 2884 A New Weighted LDA Method in Comparison to Some Versions of LDA

**Authors:**
Delaram Jarchi,
Reza Boostani

**Abstract:**

**Keywords:**
Discriminant vectors,
weighted LDA,
uncorrelation,
principle components,
Fisher-face method,
Bootstarp method.

##### 2883 Factoring a Polynomial with Multiple-Roots

**Authors:**
Feng Cheng Chang

**Abstract:**

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

##### 2882 Several Spectrally Non-Arbitrary Ray Patterns of Order 4

**Authors:**
Ling Zhang,
Feng Liu

**Abstract:**

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern *A *of order *n *is called spectrally arbitrary if the complex matrices in the ray pattern class of *A* give rise to all possible *n*th degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern*.* We call that a spectrally arbitrary ray pattern *A *of order *n *is minimally spectrally arbitrary if any nonzero entry of *A* is replaced, then *A *is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

**Keywords:**
Spectrally arbitrary,
Nilpotent matrix,
Ray patterns,
sign patterns.

##### 2881 Designing FIR Filters with Polynomial Approach

**Authors:**
Sunil Bhooshan,
Vinay Kumar

**Abstract:**

**Keywords:**
FIR filter,
Polynomial.

##### 2880 A Contribution to the Polynomial Eigen Problem

**Authors:**
Malika Yaici,
Kamel Hariche,
Tim Clarke

**Abstract:**

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

**Keywords:**
Eigenvalues/Eigenvectors,
Latent values/vectors,
Matrix fraction description,
State space description.

##### 2879 Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

**Keywords:**
Fractional Fourier Transform,
uncertainty principle,
Fractional Fourier Span,
amplitude,
phase.

##### 2878 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

##### 2877 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.

##### 2876 Monomial Form Approach to Rectangular Surface Modeling

**Authors:**
Taweechai Nuntawisuttiwong,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Monomial form,
rectangular surfaces,
CAGD curves,
monomial matrix applications.

##### 2875 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions.

##### 2874 Some Preconditioners for Block Pentadiagonal Linear Systems Based on New Approximate Factorization Methods

**Authors:**
Xian Ming Gu,
Ting Zhu Huang,
Hou Biao Li

**Abstract:**

In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.

**Keywords:**
Parallel algorithm,
Pentadiagonal matrix,
Polynomial
approximate inverse,
Preconditioners,
Stair matrix.

##### 2873 Digital Geomatics Trends for Production and Updating Topographic Map by Using Digital Generalization Procedures

**Authors:**
O. Z. Jasim

**Abstract:**

An accuracy digital map must satisfy the users for two main requirements, first, map must be visually readable and second, all the map elements must be in a good representation. These two requirements hold especially true for map generalization which aims at simplifying the representation of cartographic data. Different scales of maps are very important for any decision in any maps with different scales such as master plan and all the infrastructures maps in civil engineering. Cartographer cannot project the data onto a piece of paper, but he has to worry about its readability. The map layout of any geodatabase is very important, this layout is help to read, analyze or extract information from the map. There are many principles and guidelines of generalization that can be find in the cartographic literature. A manual reduction method for generalization depends on experience of map maker and therefore produces incompatible results. Digital generalization, rooted from conventional cartography, has become an increasing concern in both Geographic Information System (GIS) and mapping fields. This project is intended to review the state of the art of the new technology and help to understand the needs and plans for the implementation of digital generalization capability as well as increase the knowledge of production topographic maps.

**Keywords:**
Cartography,
digital generalization,
mapping,
GIS.

##### 2872 On the Multiplicity of Discriminants of Relative Quadratic Extensions of Quintic Fields

**Authors:**
Schehrazad Selmane

**Abstract:**

According to Hermite there exists only a finite number of number fields having a given degree, and a given value of the discriminant, nevertheless this number is not known generally. The determination of a maximum number of number fields of degree 10 having a given discriminant that contain a subfield of degree 5 having a fixed class number, narrow class number and Galois group is the purpose of this work. The constructed lists of the first coincidences of 52 (resp. 50, 40, 48, 22, 6) nonisomorphic number fields with same discriminant of degree 10 of signature (6,2) (resp. (4,3), (8,1), (2,4), (0,5), (10,0)) containing a quintic field. For each field in the lists, we indicate its discriminant, the discriminant of its subfield, a relative polynomial generating the field over its quintic field and its relative discriminant, the corresponding polynomial over Q and its Galois closure are presented with concluding remarks.

**Keywords:**
Discriminant,
nonisomorphic fields,
quintic fields,
relative quadratic extensions.

##### 2871 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

##### 2870 Some Results on the Generalized Higher Rank Numerical Ranges

**Authors:**
Mohsen Zahraei

**Abstract:**

**Keywords:**
Rank−k numerical range,
isometry,
numerical range,
rectangular matrix polynomials.

##### 2869 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.

##### 2868 Matrix Completion with Heterogeneous Observation Cost Using Sparsity-Number of Column-Space

**Authors:**
Ilqar Ramazanli

**Abstract:**

The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

**Keywords:**
Matrix completion,
adaptive learning,
heterogeneous
cost,
Matroid optimization.

##### 2867 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.

##### 2866 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.