• Title, Summary, Keyword: polynomial functions

Search Result 404, Processing Time 0.034 seconds

The Use of Generalized Gamma-Polynomial Approximation for Hazard Functions

  • Ha, Hyung-Tae
    • The Korean Journal of Applied Statistics
    • /
    • v.22 no.6
    • /
    • pp.1345-1353
    • /
    • 2009
  • We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

Maximal Algebraic Degree of the Inverse of Linearized Polynomial (선형 다항식의 역원의 maximal 대수적 차수)

  • Lee, Dong-Hoon
    • Journal of the Korea Institute of Information Security & Cryptology
    • /
    • v.15 no.6
    • /
    • pp.105-110
    • /
    • 2005
  • The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

A Study about the Properties of Quadratic Functions and Classroom Implications from a Polynomial Perspective (다항식 관점에 의한 이차함수의 성질 탐구와 지도방안 탐색)

  • Cho, Cheong-Soo
    • Journal of the Korean School Mathematics Society
    • /
    • v.9 no.2
    • /
    • pp.121-139
    • /
    • 2006
  • This study identified the problems of teaching quadratic functions using a translation and a vertex form by completing squares of which method make teaching contents not to be interconnected and tend to interfere students' conceptual understanding. This seems to generated from which the current mathematics curriculum is not organized to deliver the related contents of quadratic functions from polynomial expressions students have already known. To resolve it this study investigates the properties of quadratic functions from a polynomial perspective and discusses classroom implications with a couple of concrete applications.

  • PDF

APPROXIMATION IN LIPSCHITZ ALGEBRAS OF INFINITELY DIFFERENTIABLE FUNCTIONS

  • Honary, T.G.;Mahyar, H.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.36 no.4
    • /
    • pp.629-636
    • /
    • 1999
  • We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

  • PDF

Optimal Basis Function Selection for Polynomial Response Surface Model Using Genetic Algorithm (유전 알고리즘을 이용한 다항식 반응면 모델의 최적 기저함수 선정)

  • Kim, Sang-Jin;You, Heung-Cheol;Bae, Seung-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.41 no.1
    • /
    • pp.48-53
    • /
    • 2013
  • Polynomial response surface model has been widely used as approximation model which replace physical or numerical experiments in various engineering fields. Generally, low-order model is used to reduce experimental points required to construct the response surfaces, but this approach has limit to represent the highly non-linear phenomena. In this paper, we developed the method to expand modeling capabilities of polynomial response surfaces by increasing order of polynomial and selecting optimum polynomial basis functions. Genetic algorithm is used to choose optimal polynomial basis functions. Developed method was applied to analytic functions with 1 or 2 variables and wind tunnel test data modeling. The results show that this method is applicable to building response surface models for highly non-linear phenomena.

PATCHWISE REPRODUCING POLYNOMIAL PARTICLE METHOD FOR THICK PLATES: BENDING, FREE VIBRATION, AND BUCKLING

  • Kim, Hyunju;Jang, Bongsoo
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.17 no.2
    • /
    • pp.67-85
    • /
    • 2013
  • Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. Also, we demonstrate that our method is highly effective than other existing results for various aspect ratios and boundary conditions.

SAMPLING EXPANSION OF BANDLIMITED FUNCTIONS OF POLYNOMIAL GROWTH ON THE REAL LINE

  • Shin, Chang Eon
    • Communications of the Korean Mathematical Society
    • /
    • v.29 no.2
    • /
    • pp.379-385
    • /
    • 2014
  • For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

SOME GROWTH ASPECTS OF SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE AND MEROMORPHIC FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH ORDERS

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.27 no.4
    • /
    • pp.899-927
    • /
    • 2019
  • In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.