• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.29-39
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• 2015

In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.

• 대한수학회논문집
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• 제32권1호
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• pp.29-38
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• 2017

The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.239-244
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• 1978

The object of the present paper is to obtain certain results involving the H function of several complex variables. An integral involving the generalized Whittaker functions and the multiple H function has been evaluated and this result has been further utilized in finding out an expansion formula for the multiple H function in terms of the Laguerre polynomials. Some particular cases of interest have also been indicated.

• 정보보호학회논문지
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• 제19권1호
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• pp.125-133
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• 2009

사용자 인증을 위해 저장된 중요한 바이오정보가 타인에게 유출되어 도용된다면 패스워드나 PIN과 달리 변경이 불가능하므로 심각한 문제를 일으킬 수 있다. 따라서 타인에게 유출되더라도 재사용이 불가능하도록 하기 위하여 사용자의 바이오정보에 역변환이 불가능한 함수를 적용하여 저장하고 변환된 상태에서 인증과정을 수행할 수 있는 방법이 필요하다. 최근 바이오정보를 안전하게 보호하기 위해 암호학적 방법으로 연구되어지고 있는 퍼지볼트 이론을 지문정보에 적용하는 연구가 활발히 진행되고 있다. 그러나 대부분의 연구들이 지문 특징점의 개수를 고려하지 않고 고정된 차수의 다항식을 선택하기 때문에 지문영상에서 특징점의 개수가 다항식의 차수보다 적을 경우 동작하지 못하는 문제점이 발생한다. 본 논문에서는 지문 퍼지볼트의 보안성과 인식성능을 향상시키기 위해서 다항식의 차수를 특징점의 개수에 따라 가변적으로 선택하는 방법을 제안한다. 특히, 낮은 차수의 다항식을 사용할 경우 두 개 이상의 서로 다른 다항식을 사용하여 보안성을 향상시킬 수 있다. 실험을 통하여 제안한 방법은 보안성과 인식성능이 향상되는 것을 확인하였다.

• Asian-Australasian Journal of Animal Sciences
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• 제31권5호
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• pp.636-642
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• 2018

Objective: The objective of this study was to estimate genetic parameters of milk, fat, and protein yields within and across lactations in Tunisian Holsteins using a random regression test-day (TD) model. Methods: A random regression multiple trait multiple lactation TD model was used to estimate genetic parameters in the Tunisian dairy cattle population. Data were TD yields of milk, fat, and protein from the first three lactations. Random regressions were modeled with third-order Legendre polynomials for the additive genetic, and permanent environment effects. Heritabilities, and genetic correlations were estimated by Bayesian techniques using the Gibbs sampler. Results: All variance components tended to be high in the beginning and the end of lactations. Additive genetic variances for milk, fat, and protein yields were the lowest and were the least variable compared to permanent variances. Heritability values tended to increase with parity. Estimates of heritabilities for 305-d yield-traits were low to moderate, 0.14 to 0.2, 0.12 to 0.17, and 0.13 to 0.18 for milk, fat, and protein yields, respectively. Within-parity, genetic correlations among traits were up to 0.74. Genetic correlations among lactations for the yield traits were relatively high and ranged from $0.78{\pm}0.01$ to $0.82{\pm}0.03$, between the first and second parities, from $0.73{\pm}0.03$ to $0.8{\pm}0.04$ between the first and third parities, and from $0.82{\pm}0.02$ to $0.84{\pm}0.04$ between the second and third parities. Conclusion: These results are comparable to previously reported estimates on the same population, indicating that the adoption of a random regression TD model as the official genetic evaluation for production traits in Tunisia, as developed by most Interbull countries, is possible in the Tunisian Holsteins.

• 대한수학회보
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• 제60권3호
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

• 한국수학사학회지
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• 제33권6호
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• pp.303-314
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• 2020

Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation p(x) = 0 are determined by the linear factorization of p(x). The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.

• 대한수학회논문집
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• 제35권2호
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• 전자공학회논문지B
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• 제31B권3호
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• pp.60-68
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• 1994

In this paper, the multiplicative algorithm of two polynomials over finite field GF(($p^{m}$) is presented. Using the presented algorithm, the multiple-valued multiplier of the serial input-output modular structure by CCD is constructed. This multiple-valued multiplier on CCD is consisted of three operation units: the multiplicative operation unit, the modular operation unit, and the primitive irreducible polynomial operation unit. The multiplicative operation unit and the primitive irreducible operation unit are composed of the overflow gate, the inhibit gate and mod(p) adder on CCD. The modular operation unit is constructed by two mod(p) adders which are composed of the addition gate, overflow gate and the inhibit gate on CCD. The multiple-valued multiplier on CCD presented here, is simple and regular for wire routing and possesses the property of modularity. Also. it is expansible for the multiplication of two elements on finite field increasing the degree mand suitable for VLSI implementation.

• 전기학회논문지
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• 제63권7호
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• pp.875-882
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• 2014

In this paper, we propose a new parameter estimation method that can deal with the data of multiple time intervals simultaneously. If there are common modes in the multiple time intervals, it is possible to create a new polynomial by summing the coefficients of the prediction error polynomials of each time interval. By calculating the roots of the new polynomial, it is possible to estimate the common modes that exist in each time interval. The accuracy of the proposed parameter estimation method has been proven by using appropriate test signals.