• Wind and Structures
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• v.18 no.6
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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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• v.25 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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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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• v.63 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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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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• v.20 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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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).

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.4B
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• pp.361-367
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• 2011

The channel-forming discharge, which is a standard and single flow for the river maintenance and restoration project, should be estimated necessarily in the stable channel design. It is difficult to produce the specific pattern for the channel-forming discharge in the domestic rivers due to the insufficient researches and case studies. Also, it is improper to adopt the foreign cases for the domestic rivers and streams which have the high coefficients of river regime. Therefore, the channel-forming discharge possible to use for rivers with high coefficients of river regime is suggested in this study through analyzing the bankfull, specified recurrence interval, and effective discharges of Mangyeong River, Cheongmi Stream, and Hampyeong Stream for the abandoned channel restoration project. The bankfull discharge was calculated with geometric data using the HEC-RAS modeling and the flow, bed materials, and sediment data for the study reaches were used to estimate the specified recurrence interval and effective discharges. As a result for calculating the channel-forming discharge, the effective discharge was greater than the bankfull discharge in the river with high coefficient of river regime and the effective discharge was greater than the bankfull and there was no correlation between the coefficient of river regime and the characteristics of the specified recurrence interval discharges.

• Journal of the Optical Society of Korea
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• v.18 no.2
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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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• v.1 no.3
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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.