• 제목/요약/키워드: Polynomial equation

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Polynomial Equation in Radicals

  • Khan, Muhammad Ali;Aslam, Muhammad
    • Kyungpook Mathematical Journal
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    • 제48권4호
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    • pp.545-551
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    • 2008
  • Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\rho$(R[x]) = ($\rho$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

CONVEX SOLUTIONS OF THE POLYNOMIAL-LIKE ITERATIVE EQUATION ON OPEN SET

  • Gong, Xiaobing
    • 대한수학회보
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    • 제51권3호
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    • pp.641-651
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    • 2014
  • Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

THE NUMBERS OF PERIODIC SOLUTIONS OF THE POLYNOMIAL DIFFERENTIAL EQUATION

  • Zhengxin, Zhou
    • Journal of applied mathematics & informatics
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    • 제16권1_2호
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    • pp.265-277
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    • 2004
  • This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

영구자석의 overhang 길이 및 skew 효과를 고려한 LSM 추력함수 도출 (A Elicitation of Polynomial Equation of Thrust Coefficient for Linear Synchronous Motor by Experimental Design Method)

  • 장기봉;표세호;김규탁
    • 전기학회논문지
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    • 제58권6호
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    • pp.1105-1109
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    • 2009
  • This paper deals with a polynomial thrust equation of a permanent magnet linear synchronous motor that is considered by a skew and overhang effects of permanent magnet. The skew length, the overhang length, the width and height of permanent magnet, the teeth length and air-gap length which effect to the flux density of air-gap are selected as variables of the polynomial thrust equation. Polynomial thrust equation is elicited by the 6 parameters. The results are satisfied that the values by polynomial thrust equation are compared ones by using 3-dimensional finite element analysis and experiment.

부영양상태 호수유역의 강우유출수에 의한 초기세척효과 분석 (An Analysis on the First Flush Phenomenon by Stormwater Runoff in Eutrophic Lake Watershed)

  • 조재현;서형준
    • 환경영향평가
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    • 제16권5호
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    • pp.341-350
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    • 2007
  • Lake Youngrang is a lagoon whose effluent flows into the East Sea. Because two resort towns and two golf courses are situated at the lake basin, many tourists visit this area. Stormwater runoff surveys were carried out for the eight storm events from 2004 to 2005 in the eutrophic lake watershed to give a basic data for the diffuse pollution control of the lake. Dimensionless mass-volume curves indicating the distribution of pollutant mass vs. volume were used to analyze the first flush phenomenon. The mass-volume curves were fitted with a power function and polynomial equation curves. The regression analysis showed that the polynomial equation curves were better than the power function in representing the tendency of the first flush, and second degree polynomial equation curves indicated the strength of the first flush effectively.

전대수 다항식형 확률강우강도식의 최적차수 결정 및 회귀계수에 대한 유의성 검정 (Determination of optimal order for the full-logged I-D-F polynomial equation and significance test of regression coefficients)

  • 박진희;이재준
    • 한국수자원학회논문집
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    • 제55권10호
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    • pp.775-784
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    • 2022
  • 본 연구에서는 임의지속기간의 확률강우량 산정을 위해 실무에서 주로 사용되고 있는 전대수 다항식형 확률강우강도식의 최적차수 결정을 위하여 경상북도 내 9개 지점을 대상으로 확률강우량을 산정하고 전대수 다항식형 강우강도식의 회귀계수를 추정하였다. 추정된 지점별 다항식을 대상으로 단계선택법을 이용하여 각 지점별 다항식의 최적변수를 선정하고 선정된 변수들의 통계적 유의성을 검토하기 위하여 분산분석을 통한 유의성 검정을 실시하였으며, 이들 결과를 이용하여 각 지점별 통계적으로 적절하게 산정된 강우강도식을 제시하였다. 경북 9개 지점의 전대수 다항식형 강우강도식의 변수선정 결과는 6개 지점에서 1~3차식이 최적식으로 나타났고 1개 지점이 불완전 3차식이 최적식으로 나타났다. 그 중 1차는 Sherman 식, 2차는 General 식의 형태와 유사하므로 독립변수의 수를 증가시켜 적합도를 높이고 사용 편의를 위해 통일된 형태의 강우강도식으로 제시한다면 전대수 다항식형 강우강도식은 3차 회귀식까지만 고려하여도 통계학적으로 문제가 없는 것으로 판단된다.

Certain Class of Multidimensional Convolution Integral Equations Involving a Generalized Polynomial Set

  • Shenan, Jamal Mohammed;Salim, Tariq Omar
    • Kyungpook Mathematical Journal
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    • 제51권3호
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    • pp.251-260
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    • 2011
  • The aim of this paper is to obtain a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. A number of results follow as special cases from the main theorem by specifying the parameters of the generalized polynomial set.

FREDHOLM INTEGRAL EQUATION WITH SINGULAR KERNEL

  • M. A. Abdou;S. A. Hassan
    • Journal of applied mathematics & informatics
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    • 제7권1호
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    • pp.223-236
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    • 2000
  • In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

NUMERICAL EXPERIMENTS OF THE LEGENDRE POLYNOMIAL BY GENERALIZED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING THE LAPLACE EQUATION

  • Amoupour, Ebrahim;Toroqi, Elyas Arsanjani;Najafi, Hashem Saberi
    • 대한수학회논문집
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    • 제33권2호
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    • pp.639-650
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    • 2018
  • Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

다항식 형태의 증기압 상관식의 성능 평가 (Performance Evaluation of Vapor Pressure Correlations in a Polynomial Expression)

  • 박경근
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2003년도 춘계학술대회
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    • pp.1401-1406
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    • 2003
  • Performance of two vapor pressure correlation equations in a polynomial expression is compared. These are the Wagner-type equation and the Inverted form equation. The equations are fitted to correlate the data in the ASHRAE tables and from NIST Chemistry WebBook for 17 pure substances. Some observations on the exponents in the two polynomial equations are made, which results in a proposal of a new closed form vapor pressure equation. The new equation yields the accuracy comparable to that of the Wagner-type equation and better than that of the Inverted form equation.

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