• 호남수학학술지
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• 제27권3호
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• 대한수학회지
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• 제45권6호
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.507-513
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• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• 충청수학회지
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• 제9권1호
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• pp.115-121
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• 1996

Let $\{X(t);\;t{\in}R^n\}$ be a measurable, separable and H-sssis random fields. Here, we suppose that the increments are invariant under all Euclidean rigid body motions. We investigate some properties of H-sssis random fields and monotonicity of projection process $\{X_e(t);\;t{\in}R^1\}$ in any direction $e{\in}R^n$.

• Journal of Chest Surgery
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• 제14권3호
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• pp.235-240
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• 1981

A total of 102 patients who had an Open Heart Surgery from April 1976 to July 1981 were reviewed. 55 paeitnts were congenital heart disease and 47 patients were acquired heart disease. Among SS patients of congenital heart disease, 18 T 0 F, 18 V S D, 8 A S D, and each one case of l\ulcorner 0 R V, Truncus arteriosus, Ebstein anomaly, Single ventricle, P D A, P 5, A S D + P 5, E C D, V 5 D + P D A, A - P window, D C R V were noted respectively. In 47 patients of acquired heart disease and one Ebstein patient, 46 prosthetic values were implanted: 17 had M V R, 4 had A V R, 2 had M V R + A V R, and 4 had M V R + T V R and one T V R. The operative mortality was 8.S% in acquired heart disease and 17% in congenital heart disease. The follow up period was between 6 months and 6 years. There were 3 cases of late mortality in acquired heart disease and one case in congenital heart disease.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.91-101
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• 2008

Let H be a Hilbert space. Assume that $0{\leq}{\alpha}$, ${\beta}{\leq}1$ and r(t) > 0 in I = [0, T]. By means of the fixed point theorem of Leray-Schauder type the existence principles of solutions for two point boundary value problems of the form $\array{(r(t)x^{\prime}(t))^{\prime}+f(t,x(t),r(t)x^{\prime}(t))=0,\;t{\in}I\\x(0)=x(T)=0}$ are established where f satisfies for positive constants a, b and c ${\mid}{f(t,x,y){\mid}{\leq}a{\mid}x{\mid}^{\alpha}+b{\mid}y{\mid}^{\beta}+c\;\;for\;all(t,x,y){\in}I{\times}H{\times}H$.

• 대한수학회지
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• 제50권5호
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• 한국식품과학회지
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• 제30권5호
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• pp.1085-1091
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• 1998

본 실험에서는 변형력 완화시험을 통하여 고기풀을 주원료로 하는 시중 게맛살과 어묵의 물성학적 성질을 조사하였다. 또한 변형력완화시험과 T.P.A.값과의 상관관계를 조사하였다. 시료의 내부구조적 변화에 의한 영향을 가능한 한 피하기 위하여 인장율 20%에서, 또한 변형속도는 2.4 mm/sec의 조건에서 실험을 실시하였다. 어묵과 맛살의 변형력완화시험결과 초기변형력의 경우 2종류의 어묵(370.4 g)과 5종류의 맛살의 평균값(436.4 g)은 유사한 값을 나타내었으나, 변형력완화시간과 점성성분은 2종류 어묵의 평균값(17256.1 sec, $1.357{\times}10^{10}$ poise)이 5종류의 맛살의 평균값(6110 sec,$0.519^{\ast}10^{10}$ poise)보다 월등히 높은 값을 나타내었다. 변형력완화시험 결과와 T.P.A.결과를 비교시 지수항의 직선식에 대한 절편값은 T.P.A.실험에서의 경도 및 껌성, 씹힘성과 높은 상관관계(r=0.93, 0.93, 0.95, p

• 한국생물공학회:학술대회논문집
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• 한국생물공학회 2005년도 생물공학의 동향(XVI)
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• pp.35-35
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• 2005

Recombinant human $interferon-{\beta}-1a(rIFN-{\beta})$ is a single glycosylated protein (at N80, 1N) with anti-viral activity. However, present drugs have a relatively short serum half-life of $rIFN-{\beta}$, thus patients suffer from frequent $infections.^{1)}$ To improve its half-life, eight glycosylation analogs were prepared, which have additional N-linked glycosylation consensus sequences (N-X-T/S) within the $IFN-{\beta}$ molecule and/or at C-terminal. Each $rIFN-{\beta}$ analog was examined for the presence of additional N-linked glycosylation and the maintenance of anti-viral activity in CHO cells. The molecular weights of five analogs were not changed. However, two analogs, R27T within $rIFN-{\beta}$ (27 kDa, 2N) and GNITVNITV at C-terminal (29kDa, 2N), showed a clear increase in molecular weights, compared to native $rIFN-{\beta}$ (23 kDa, 1N). And another combined analog of R27T+GNITVNITV showed increased molecular weight (33 kDa, 3N). It was confimed that the molecular weight increment of analogs was caued by the N-linked glycosylation with the treatment of N-glycansae. In the case of anti-viral activity, the analog GNITVNITV showed a reduction in activity compared to native $IFN-{\beta}$, whereas the analogs R27T and R27T+GNITVNITV were found to have distinctly increased activities. Pharmacokinetic study in rats also disclosed that the analogs R27T and R27T+GNITVNITV had 2 3 fold increased serum half-life, respectively. In conclusion, the addition of N-linked glycosylation in $rIFN-{\beta}$ increased serum half-life, thereby its less frequent administration will be expected.

• 대한수학회지
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• 제49권3호
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.