• 방송공학회논문지
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• 제17권1호
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• pp.195-198
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• 2012

일반적으로 표면반사율과 분광반사율을 N차원의 칼라 코드로부터 정확히 복원하기 위해서는 N개의 기저함수가 필요하다. 전형적인 렌더링 응용에서 벡터의 덧셈, 스칼라 곱셈 및 성분별 곱셈에 대한 벡터 연산이 이질동형이라고 가정하고 광원의 중첩, 광원-표면간 상호간섭 및 상호반사와 같은 물리적인 연산을 모델링하지만 벡터 연산이 물리적인 현상을 그대로 반영하는 것은 아니다. 그러나 만약 기저함수가 특성함수로써 제한된다면 표면반사율과 분광반사율의 사상 결과 및 벡터들은 렌더링에서 물리적인 연산인 이질이형을 유지하게 된다. 본 논문은 새로운 N차원의 특성함수를 제안하고 N차원의 기저함수로 근사화된 먼셀 칼라 칩에 대하여 제안한 알고리즘의 정확성을 평가할 것이다.

• 호남수학학술지
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• 제36권3호
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• pp.531-542
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• 2014

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function ${\gamma}_D^{(n)}$ and ${\Gamma}_D^{(n)}$ of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

• 대한수학회보
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• 제47권6호
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• pp.1181-1188
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• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• 충청수학회지
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• 제29권4호
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• pp.573-584
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• 2016

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on ${\mathbb{Z}}_{2^n}$ which generates an n-bit word sequence without consecutive elements of period $2^n$.

• 호남수학학술지
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• 제37권2호
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• pp.149-185
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• 2015

Let ${\sigma}_s(N)={\sum}_{d{\mid}N}d^s$ denote the sum of sth powers of the positive divisors of N. In this article, we consider the convolution sums of four divisor functions.

• 대한수학회지
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• 제8권1호
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.77-85
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• 2011

In this paper, we introduce the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) analytic functions with positive real part. The radius of convexity of this integral operator when ${\beta}$ = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators $\int\limits_0^z(f(t)/t)^{\alpha}$dt and $\int\limits_0^z(f'(t))^{\alpha}dt$.

• 융합신호처리학회논문지
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• 제11권1호
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• pp.47-52
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• 2010

암호화 시스템에서 대부분의 선형시스템은 쉽게 해석될 수 있기 때문에 비선형성은 매우 중요하다. 비선형 함수인 bent함수와 유사한 특성을 갖고 C.Bracken, Z.Zha 등에 의하여 제안된 APN(Almost Perfect Nonlinear) 함수를 이용하여 두 종류의 새로운 부호계열 발생 알고리즘을 제안하였다. 이를 이용하여 GF(2)상에서 발생된 부호계열의 자기상관함수 $R_{ii}(\tau)$, ${\tau}\;{\neq}\;0$와 상호상관함수 $R_{ik}(\tau)$의 값은 {-1, $-1-2^{n/2}$, $-1+2^{n/2}$}을 가진다. 이 개념을 확장한 GF(p), $p\;{\geq}\;3$상에서 발생된 비 이원부호계열의 자기상관함수 $R_{p,ii}(\tau}$, ${\tau}\;{\neq}\;0$와 상호상관함수 $R_{p,ik}(\tau)$의 값은 {$-1+p^{n-1}$, $-1-p^{(n-1)/2}+p^{n-1}$, $-1+p^{(n-1)/2}+p^{n-1}$} 로 역시 3종류 값을 가짐을 보였다. 이 분석결과로부터 발생된 부호계열의 상관함수가 Gold 부호계열과 유사한 특성을 가짐을 확인하였다.

• 비교문화연구
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• 제37권
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• pp.361-382
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• 2014

This study aims to investigate the change of functions of duibuqi and analysis other fuctions of duibuqi apart from apology from pragmatics and conversation analysis perspectives. Duibuqi consists of dui(face) and buqi(be not capable of performing), and means 'be not capable of facing'. After that, it is assumed to have changed to 'ashamed' and finally 'sorry'. In terms of functions, duibuqi is generally regarded as meaning 'sorry' typically, so mei guanxi is considered to consist adjacency pair with it, but in this investigation, mei guanxi is very little adjacent to duibuqi contrary to expectation(n=2/28, per.=7.1/100). About half of duibuqi(n=15/28, per.=53.6/100) functions in apology action sequence, and in the sequence, duibuqi functions much more for take the lead in apology(n=11/15) but not for a reaction against scolding(n=4/15). And the other half of duibuqi(n=13/28, per.=46.4/100) functions for softening the impact of reject or direct action, or for switching situations, e.g. from favorable situation to unfavorable situation, or for expressing speaker's emotion to the other's repair etc. Consequently, duibuqi has being changed its meanings and its functions is being changed accordingly.

• East Asian mathematical journal
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• 제19권2호
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• pp.165-171
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• 2003

We show that any F-harmonic map from a compact manifold M to N is necessarily constant if N possesses a strictly-convex function, and prove 'Liouville type theorems' for F-harmonic maps. Finally, when the target manifold is the real line, we get a result for F-subharmonic functions.