• 대한수학회보
• /
• 제53권1호
• /
• pp.29-38
• /
• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

• 대한수학회보
• /
• 제38권1호
• /
• pp.1-6
• /
• 2001

We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.

• Korean Journal of Mathematics
• /
• 제21권4호
• /
• pp.365-374
• /
• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1235-1243
• /
• 2011

In this paper, we investigate sharing value problems related to a meromorphic function f(z) and f(qz), where q is a non-zero constant. It is shown, for instance, that if f(z) is zero-order and shares two valves CM and one value IM with f(qz), then f(z) = f(qz).

• 대한수학회보
• /
• 제50권4호
• /
• pp.1157-1171
• /
• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• 정보처리학회논문지B
• /
• 제10B권6호
• /
• pp.587-592
• /
• 2003

강화학습을 적용하기에 적합한 많은 실세계의 제어 문제들은 연속적인 상태 또는 행동(continuous states or actions)을 갖는다. 연속 값을 갖는 문제인 경우, 상태공간의 크기가 거대해져서 모든 상태-행동 쌍을 학습하는데 메모리와 시간상의 문제가 있다. 이를 해결하기 위하여 학습된 유사한 상태로부터 새로운 상태에 대한 추측을 하는 함수 근사 방법이 필요하다. 본 논문에서는 1-step Q-learning의 함수 근사를 위하여 퍼지 클러스터링을 기초로 한 Fuzzy Q-Map을 제안한다. Fuzzy Q-Map은 데이터에 대한 각 클러스터의 소속도(membership degree)를 이용하여 유사한 상태들을 군집하고 행동을 선택하고 Q값을 참조했다. 또한 승자(winner)가 되는 퍼지 클러스터의 중심과 Q값은 소속도와 TD(Temporal Difference) 에러를 이용하여 갱신하였다. 본 논문에서 제안한 방법은 마운틴 카 문제에 적용한 결과, 빠른 수렴 결과를 보였다.

• 대한수학회보
• /
• 제50권3호
• /
• pp.731-745
• /
• 2013

In this paper, we investigate uniqueness problems of certain types of $q$-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where $q$-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function $f$ and a non-zero complex constant $q$, $E(S_j,f)=E(S_j,{\Delta}_qf)$ for $j=1,2$ imply $f(z)=t{\Delta}_qf$, where $t^n=1$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $f(z)$ and $t{\Delta}_qf$.

• 대한수학회보
• /
• 제55권6호
• /
• pp.1755-1771
• /
• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• 충청수학회지
• /
• 제27권1호
• /
• pp.9-16
• /
• 2014

Let $\mathbb{A}=\mathbb{F}_q[T]$ be a polynomial ring over $\mathbb{F}_q$. In this paper we determine an asymptotic mean value of quadratic Dirich-let L-functions L(s, ${\chi}_{{\gamma}D}$) at the central point s=$\frac{1}{2}$, where D runs over all monic square-free polynomials of even degree in $\mathbb{A}$ and ${\gamma}$ is a generator of $\mathbb{F}_q^*$.

• 산업경영시스템학회지
• /
• 제14권24호
• /
• pp.23-30
• /
• 1991

This study aimed at the improvement of the conventional methods of VE Function Analysis, the most important phase of VE process, through Quality Function Development. The use of Function Requirement Coefficients in Quality Function Development makes the Function Development more objective, and it was found that VE techniques, when used in combination with QC techniques. Improve the value of product considerably.