• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.15-21
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• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• Journal of Oriental Neuropsychiatry
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• v.16 no.2
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• pp.233-242
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• 2005

'Ul-zeong' comes from obsturction of qi by stress. The mind affect the body. The patient has depressed mood, irritable sign, chest discomfort, costral pain, angry state or some strange feeling on the throat. $'Y{\acute{i}}q{\acute{i}}ngbi{\grave{a}}nq{\grave{i}}'$ is a psychological therapy that a doctor changes the patient ' s psychological condition by using various method. 'yi' means moving, 'qing' means changing. Art therapy means a therapy by using artistic activities and included in $'y{\acute{i}}q{\acute{i}}ngbi{\grave{a}}nq{\grave{i}}'$ In this case, a female patient, 35 years old, who suffered from 'ul-zeong' with depressed mood, anxiety, general body weakness, anorexia, constipation. We used $'y{\acute{i}}q{\acute{i}}ngbi{\grave{a}}nq{\grave{i}}'$ besides herbal medication, acupuncture to her and her condition got improved. Therefore we reported it for the treatment.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.381-392
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• 2007

In 1906, da Rios, a student of Leivi-Civita, wrote a master's thesis modeling the motion of a vortex in a viscous fluid by the motion of a curve propagating in $R^3$, in the direction of its binormal with a speed equal to its curvature. Much later, in 1971 Hasimoto showed the equivalence of this system with the non-linear Schr$\ddot{o}$dinger equation (NLS) $$q_t=i(q_{ss}+\frac{1}{2}{\mid}q{\mid}^2q$$. In this paper, we use the same idea as Terng used in her lecture notes but different technique to extend the above relation to the case of $R^3$, and obtained an analogous equation that $$q_t=i[q_{ss}+(\frac{1}{2}{\mid}q{\mid}^2+1)q]$$.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.3
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• pp.1-6
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• 2008

A dual band I/Q modulator which converts baseband input signals to 2.4GHz or 5GHz RF output has been proposed. The dual band I/Q modulator for 2.4GHz and 5GHz wireless LAN applications consists of $90^{\circ}$ phase shifter and wideband mixer. The I/Q modulator showed 15dB conversion loss at 2.4GHz and 16dB conversion loss at 5GHz. The sideband suppression is about 15dBc at 2.4GHz and 16dBc at 5GHz. Measured data shows 8.5% EVM at 2.4GHz, and 10% EVM at 5GHz for QPSK with symbol rate of 11Mbps. A carrier rejection is about 40dBc at 2.4GHz/5GHz band, and the I/Q modulator satisfied the output wireless LAN spectrum mask with baseband input signal.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.55-107
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.

• Proceedings of the Plant Resources Society of Korea Conference
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• 2002.11b
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• pp.68-68
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• 2002

아열대성 식물 4종 (문주란, Crinum asiaticum var. japonicum; 박달목서, Osmanthus insularis; 죽절초, Chloranthus glaber; 파초일엽, Asplenium antiquum)을 대상으로 자연 환경요인의 변화에 따른 엽록소형광을 분석하여 이들 식물의 활력도를 검토하였다. 여름철 일변화에 있어서 양지에 자라는 문주란과 박달목서는 Fv/Fm이 새벽과 밤에는 0.80~0.83 범위의 높은 값을 보이지만, 낮시간에는 0.65~0.73으로 낮았다. 1-qN과 1-qP도 낮시간에 크게 낮아졌다. 음지에 자라는 죽절초와 파초일엽의 Fv/Fm은 높아서 0.83~0.85 범위를 유지하였으며 일변화적 특성은 관찰되지 않았다. 1-qP의 변화는 거의 관찰되지 않았으나 1-qN이 낮시간에 다소 감소하는 경향을 보여주었다. 죽절초와 파초일엽에서는 광억제가 거의 일어나지 않으나 문주란과 박달목서에서는 낮시간의 고광에 의한 광억제가 나타난다. 하지만 여기에너지의 일부를 열의 형태로 방출하여 광피해를 완화시키고 있는 것으로 보인다. 겨울철에는 Fv/Fm이 모든 종에서 0.8 이하의 값을 나타내었는데, 특히 문주란의 Fv/Fm 값은 다른 3종 보다 더 낮았다. 그리고 모든 종에서 일변화적인 특성은 관찰되지 않았다. 문주란의 1-qN은 낮시간에 다소 감소하였지만, 나머지 3종의 식물은 높은 값을 나타내었다. 그리고 l-qP는 문주란과 박달목서에서는 낮시간에 0.6 범위로 낮아졌다. 이는 종에 따라 차이가 있지만 겨울철 저온의 영향을 받은 결과로 보인다. 한편, 여름철 문주란과 박달목서의 O-J-I-P곡선은 거의 유사하며 낮에 뚜렷하게 낮았고, 죽절초와 파초일엽에서는 일변화적 특성은 두드러지지 않았다. 그리고 P $I_{NO}$ 와 SF $I_{NO}$ 가 죽절초를 제외한 3종에서 여름철 낮시간에 증가하였다. 겨울철의 O-J-I-P곡선은 모든 종에서 낮시간에 다소 낮아지지만 큰 변화는 없었다. 그리고, 문주란, 박달목서, 파초일엽에서 $\psi$o/(1-$\psi$o)가 낮시간에 다소 증가하였다. 이로부터 P $I_{NO}$ , SF $I_{NO}$ , $\psi$o/(1-$\psi$o)등의 변수는 식물의 활력도를 검정하는 지표로 활용될 가능성이 높다고 할 수 있다.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.