• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.347-365
• /
• 1996

Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

• Journal of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1269-1289
• /
• 2014

We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when $K_{(2p)}$ denotes the ray class field of $K=\mathbb{Q}(e^{2{\pi}i/5})$ modulo 2p for an odd prime p, we describe a subfield of $K_{(2p)}$ generated by the special value of a certain theta constant by using Shimura's reciprocity law.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.553-564
• /
• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.531-543
• /
• 2014

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

• 한국방재학회:학술대회논문집
• /
• 2010.02a
• /
• pp.108.1-108.1
• /
• 2010

본 연구에서는 수리모형실험을 통하여 규칙파를 적용한 수중방파제의 반사특성을 조사하였다. 수중방파제의 형상을 직사각형(${\theta}=90^{\circ}$), 사다리꼴(I)(${\theta}=75^{\circ}$), 사다리꼴(II)(${\theta}=60^{\circ}$), 삼각형(${\theta}=30.96^{\circ}$)으로 설정하여, 각각의 형상들에 대하여 주기, 입사파고, 배열을 변화시켜 얻은 실험결과를 토대로 투과율을 계산하였다.

• Proceedings of the KSMRM Conference
• /
• 2002.11a
• /
• pp.95-95
• /
• 2002

목적： 기존의 척추용 코일은 phased array 코일을 주로 많이 사용하여 왔다. Phased array 코일은 여러개의 표면 코일로 구성되어 있어 RE 자기장의 영역이 표면코일과 비슷하다. 그래서, 척추 영상을 얻기 위해서는 다른 부위의 핵 스핀을 포화시키는 불편함이 있다. 기존의 표면 코일보다 RF penetration depth가 적은 theta coil을 이용하여, 척추에 적합한 코일을 개발했다. 대상 및 방법： theta coil을 길게 제작하여 척추에 적합하게 하였다. 코일의 길이는 약 35cm, 폭은 16cm이다. 수신 전용으로 하기 위해서, 다이오드를 이용하여 detune 회로를 포함하였다. 기존의 코일과 비교하기 위해 theta coil과 GE사의 척추용 코일로부터 각각 영상을 획득하였다.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.173-184
• /
• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• The Pure and Applied Mathematics
• /
• v.28 no.4
• /
• pp.377-386
• /
• 2021

In this paper, we use theta-function identities involving parameters 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.

• The Pure and Applied Mathematics
• /
• v.29 no.3
• /
• pp.245-254
• /
• 2022

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

• The Korean Journal of Nuclear Medicine Technology
• /
• v.20 no.1
• /
• pp.13-19
• /
• 2016

Purpose In order to calculate the left ventricular ejection fraction (LVEF) accurately, it is important to acquire the best septal view of left ventricle in the multi-gated cardiac blood pool scan (GBP). This study aims to acquire the best septal view by measuring angle of ventricular septal wall (${\theta}$) using enhanced CT scan and compare with conventional method using left anterior oblique (LAO) 45 view. Materials and Methods From March to July in 2015, we analyzed the 253 patients who underwent both enhanced chest CT and GBP scan in the department of nuclear medicine at National Cancer Center. Angle (${\theta}$) between ventricular septum and imaginary midline was measured in transverse image of enhanced chest CT scan, and the patients whose difference between the angle of ${\theta}$ and 45 degree was more than 10 degrees were included. GBP scan was acquired using both LAO 45 and LAO ${\theta}$ views, and LVEFs measured by automated and manual region of interest (Auto-ROI and Manual-ROI) modes respectively were analyzed. Results $Mean{\pm}SD$ of ${\theta}$ on total 253 patients was $37.0{\pm}8.5^{\circ}$. Among them, the patients whose difference between 45 and ${\theta}$ degrees were more than ${\pm}10$ degrees were 88 patients ($29.3{\pm}6.1^{\circ}$). In Auto-ROI mode, there was statistically significant difference between LAO 45 and LAO ${\theta}$ (LVEF $45=62.0{\pm}6.6%$ vs. LVEF ${\theta}=64.0{\pm}5.6%$; P = 0.001). In Manual-ROI mode, there was also statistically significant difference between LAO 45 and LAO ${\theta}$ (LVEF $45=66.7{\pm}7.2%$ vs. LVEF ${\theta}=69.0{\pm}6.4%$; P < 0.001). Intraclass correlation coefficients of both methods were more than 95%. In case of comparison between Auto-ROI and Manual ROI of each LAO 45 and LAO ${\theta}$, there was no significant difference statistically. Conclusion We could measure the angle of ventricular septal wall accurately by using transverse image of enhanced chest CT and applied to LAO acquisition in the GBP scan. It might be the alternative method to acquire the best septal view of LAO effectively. We could notify significant difference between conventional LAO 45 and LAO ${\theta}$ view.