• Wind and Structures
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• 제18권6호
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• pp.633-650
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• 2014

The uncertainty of extreme wind speeds is one key contributor to the uncertainty of wind loads and their effects on structures. The probability distribution of annual extreme wind speeds may be characterized using a classical Gumbel Type distribution. The expression that establishes the relationship between the extreme wind speeds at different recurrence periods and the corresponding coefficients of variation is formulated, and its efficacy is validated. The coefficients of variation are calibrated to be about 0.125 and 0.184 according to defined Chinese and US design specifications, respectively. Based on the wind data of 54 cities in China, 49 meteorological stations in the US, 3 stations in Singapore, the coefficients span intervals of (0.1, 0.35), (0.08, 0.20) and (0.06, 0.14), respectively. For hurricanes in the US, the coefficients range approximately from 0.3 to 0.4. This convenient technique is recommended as one alternative tool for coefficient of variation analyses in the future revisions of related codes. The sensitivities of coefficients of variation for 49 meteorological stations in the US are quantified and demonstrated. Some contradictions and incompatibilities can be clearly detected and illustrated by comparing the coefficients of variation obtained with different combinations of recurrence period wind data.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• 대한수학회보
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• 제44권4호
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• pp.841-849
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• 2007

In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.463-484
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• 2023

An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The 𝓡(p, q)-deformed multinomial probability distribution and the negative 𝓡(p, q)-deformed multinomial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature.

• 대한수학회지
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• 제50권5호
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.623-635
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• 2006

In this paper, we derive an elementary formula for the linearization coefficients of the product of two Legendre polynomials. Our main purpose is to study the method which can be used to derive the formula, which is straightforward from the integration and their orthogonality.

• 대한수학회보
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• 제59권5호
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• pp.1269-1277
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• 2022

In this paper we consider a sequence of polynomials defined by some recurrence relation. They include, for instance, Poupard polynomials and Kreweras polynomials whose coefficients have some combinatorial interpretation and have been investigated before. Extending a recent result of Chapoton and Han we show that each polynomial of this sequence is a self-reciprocal polynomial with positive coefficients whose all roots are unimodular. Moreover, we prove that their arguments are uniformly distributed in the interval [0, 2𝜋).

• 대한토목학회논문집
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• 제31권4B호
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• pp.361-367
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• 2011

하천 정비 및 하천 복업사업의 기준유량이 되는 하도형성유량 산정은 안정하도 설계시 반드시 선행되어야 하는 것이다. 국내의 경우 하도형성유량 산정방법에 대한 연구가 많이 수행되지 않아 특정패턴을 도출하기가 어려운 실정이다. 국내하천의 경우 외국의 주요하천과 비교하여 하상계수가 크게 나타나는 특성으로 인해 외국사례를 국내에 적용하기에 어려움이 있다. 따라서 현재 구하도 복원이 진행 되고 있거나 계획되어 있는 만경강, 청미천, 함평천을 대상으로 하도형성유량 산정을 위해 만제유량, 특정 재현기간별 유량, 유효유량을 산정해보고 각각의 상호관계를 분석하여 하상계수가 큰 국내하천에 적용 가능한 하도형성유량을 제안하고자 한다. 만제유량은 대상유역의 지형자료를 이용한 HEC-RAS 모의를 통해 산정하였으며 특정 재현기간별 유량과 유효유량은 대상구간의 유량, 하상토, 유사 자료를 이용하여 산정하였다. 산정결과 하상계수가 큰 하천에서는 유효유량이 만제유량보다 크게 나타났으며 하상계수와 관련하여 특정 재현기간별 유량은 일관성 있는 특징이 없는 것으로 나타났다.

• Journal of the Optical Society of Korea
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• 제18권2호
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• pp.188-193
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• 2014

A general theory of scalar wave scattering by two separated particles is developed to give the coefficients of scattering and transmission in the form of recurrence formulae. Iterative applications of the formulae yield the coefficients in the form of power series of the coefficients obtained from single-particle scattering theories, and each term of the of power series can be interpreted as multiple scattering of the wave between the two particles in increasingly higher order.

• Journal of Advanced Research in Ocean Engineering
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• 제1권3호
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.