• 충청수학회지
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• 제24권4호
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• pp.919-920
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• 2011

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that ${\theta}_A(\tau)/{\theta}_B(\tau)$ is a rational function of J, satisfying a certain condition. Where ${\theta}_A(\tau)$ and ${\theta}_B(\tau)$ are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

• 해양환경안전학회지
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• 제21권2호
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• pp.179-187
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• 2015

본 연구의 목적은 통항분포함수 계산 시 적용하는 기준선의 방향과 기준점의 수평위치 및 수직위치에 따라서 통항분포함수가 변하는 양상을 식별하기 위한 것이다. 목포항 입구에 있는 항로를 대상으로 2013년 1월달의 AIS 실측자료를 이용하여 기준선의 방향(${\theta}$), 수평위치($\mathfrak{L}_H$) 및 수직위치($\mathfrak{L}_V$) 등의 3가지 변수가 통항분포함수의 평균($\bar{x}$)과 표준편차(${\delta}$)에 미치는 영향을 실험하였다. 실험결과, ${\theta}$에 따라 추출되는 샘플 데이터가 달라지기 때문에 ${\theta}$의 변화에 따라서 $\bar{x}$와 ${\delta}$가 변화됨을 나타냈고, ${\theta}$에 따른 $\bar{x}$와 ${\delta}$의 변화는 사인(sine)함수 합의 관계로 도출되었다. 또한 항로가 복잡한 해역에서 최적의 통항분포함수를 결정하기 위해서는 ${\delta}$의 변화 값이 최소가 되는 ${\theta}$을 기준선의 방향으로 설정하는 것이 타당함을 알았다. 본 연구의 결과는 정규분포가 보다 더 정량화된 수치로 표현되어 해상교통흐름을 파악하고 해상교통안전관리 의사결정을 위한 기초자료로 활용될 것으로 판단된다.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.153-165
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• 2007

This paper deals with the empirical Bayes two-action problem of testing $H_0\;:\;{\theta}{\leq}{\theta}_0$: versus $H_1\;:\;{\theta}>{\theta}_0$ using a linear error loss for some discrete nonexponential families having probability function either $$f_1(x{\mid}{\theta})=(x{\alpha}+1-{\theta}){\theta}^x\prod\limits_{j=0}^x\;(j{\alpha}+1)$$ or $$f_2(x{\mid}{\theta})=[{\theta}\prod\limits_{j=0}^{x-1}(j{\alpha}+1-{\theta})]/[\prod\limits_{j=0}^x\;(j{\alpha}+1)]$$. Two empirical Bayes tests ${\delta}_n^*\;and\;{\delta}_n^{**}$ are constructed. We have shown that both ${\delta}_n^*\;and\;{\delta}_n^{**}$ are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp(-cn)) for some c>0, where n is the number of historical data available when the present decision problem is considered.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.182-185
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• 1990

Let a p-component vector y have a p-variate normal distribution $N(b\theta, \Sigma), \Sigma$ unknown, b specified, then for testing $\theta = 0$ against general $\theta$, Khatri and Rao (1987) derive a certain t test and obtain its power function. This paper presents a direct derivation of this power function in terms of the original variates unlike Khatri and Rao (1987) who resort to the canonical transformations of the original variates and the conditional distributions.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• 대한예방한의학회지
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• 제4권2호
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• pp.214-234
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• 2000

This study was carried to identify whether acupuncture of several acupuncture points can affect the brain and to observe which aspects appear in EEG mapping, using electroencephalography. Those results are as follows ; 1. The pattern of resting computerized EEG map in intact human is appered normal 2. Each Acupuncture in Kwan Weon or Jog Sam Ri meridian points bring about the increase in $\theta,\;\alpha-wave$ activity and at various area of the cerebrium and the decrease in $\delta,\;\beta-wave$ activity. It strands to reason that brain function is elevated On the other hand , synchronous acupuncture bring about the decrease of brain function in view of the decrease of $\delta,\;\theta-wave$ activity at frontal area, and the unstable brain state in view of the increase of $\beta-wave$ activity. 3. Acupuncture in Hyeon Jong meridian point bring about the increase of $\delta,\;\theta-wave$ activity at frontal area and $\beta-wave$ activity at temporal area. From these we deduce that brain function is declined and brain is unstable. Synchronous acupuncture with other meridian points reversly showed that brain function is elevated. 4. Synchronous acupuncture in Kwan Weon , Jog Sam Ri, Hyeon Jong bring about the decrease of the brain function and the unstable brain state, showing the pattern of increased $\delta,\;\theta-wave$ activity at frontal, parietal area, and increased $\beta-wave$ activity at temporal area.

• 천문학논총
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• 제23권2호
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• pp.25-29
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• 2008

Scattering of incident light by the interstellar dust is usually approximated by Henyey-Greenstein scattering phase function. Recently, Draine (2003) proposed a new analytic phase function with two parameters. We describe an algorithm to generate random numbers distributed according to the Draine’s function, and compare two phase functions. It is also derived exact solutions of two parameters for given values ${\langle}cos{\theta}{\rangle}$ and ${\langle}cos^2{\theta}{\rangle}$. It is found that Henyey-Greenstein function with g = ${\langle}cos{\theta}{\rangle}$ provides a good approximation for ${\lambda}\;>\;2000{\AA}$. At shorter wavelengths, more realistic phase function may be needed for radiative transfer models.

• East Asian mathematical journal
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• 제33권1호
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• 한국해양학회지
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• 제5권1호
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• pp.6-13
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• 1970

Ten days and monthly mean temperatures were analysed daily data observed during July, 1916 to March, 1970 statistically. Periodic characters were calculated by Δn, new method of approximate solution of Schuster Method. According to ten days mean temperatures, annual variation function is F($\theta_d$)=16.29-5.27 cos $\theta_d$+0.75 cos2 $\theta_d$-3.14 sin $\theta_d$+1.16 sin2 $\theta_d$-0.63 sin $\3{theta}_d$, where $\theta_d$=$-\frac{\pi}{18}$(d-3), d is the order of ten days period, 1 to 36. Annual mean water temperature is 16.3$^{\circ}C$, minimum in the last ten days of February 10.9$^{\circ}C$, maximum in the last ten days of August 24.5$^{\circ}C$. Periodic character of secular variation shows 11 year and its curve is F($\theta_y$)=16.29+0.53 cos $\theta_y$ -0.16cos $2{\theta}_y$+0.10 cos$3{\theta}_y$-0.10 sin $\theta_y$, where $\theta_y$=2$-\frac{2\pi}{11}$(y-1920), y is calendar year. And the relation between air temperature x and water temprature y is following. y=9.67 1.035$\^x$