• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.169-190
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• 2008

Second-order parabolic equations with variable coefficients are considered on $\mathbb{R}^d$ and $C^1$ domains. Existence and uniqueness results are given in $L_q(L_p)$-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• English Language & Literature Teaching
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• v.10 no.2
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• pp.1-23
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• 2004

This article reports a bi-directional interlanguage study designed to investigate the initial state of L2 acquisition with regard to English and Korean wh-questions. Based on the UG system in line with the minimalist theory, it was hypothesized that the L2 initial state is characterized by the most economical form of syntax in which no overt wh-movement to Spec-CP is assumed. Results of the early interlanguage study showed that 1) L1 Korean learners of L2 English predominantly produced wh-questions with the fronted wh-word, but without productive wh-movement to the Spec-CP position; and 2) L1 English learners of L2 Korean overwhelmingly produced wh-questions with the wh-word remaining in-situ. These results were interpreted as supporting the minimalist account of the L2 initial grammar in that no overt syntactic wh-movement were adopted in early interlanguages of both English and Korean regardless of the learner's L1.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.359-369
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• 2000

Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.479-483
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• 2006

For any fixed $\lambda\leq-\frac{1}{2}$, there exists $f(\eta){\in}C^1[0,+\infty)$ which satisfies the following nonlinear boundary value problem f'+ff'+$\lambda(l-f'^2)=0$ a.e.in $(0,+\infty)$, f(0)=0, f'(0) = 0, $f'(+\infty)=1$, which arises in boundary layer theory in fluid mechanics.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Water for future
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• v.19 no.2
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• pp.131-138
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• 1986

Both hydraulic and dynamic characteristics of a single perforated wall are studied theoretically and experimentally. Theoretically, the effect of evanescent modes on wave force acting on a single perated wall is studied by use of the Horiguchi theory. The wave force on the perforated wall is presented to be insensitive to evanescent modes. According to experimental study, The larger perforation ratio(${\gamma}$) grows, the weaker the wave force on the wall becomes sensitively. And in the small value of l/D (ratio of wall thickness(l) to hole diameter(D)) where the holes on the wall are regarded as orifice, the wave force on the wall is insensitive to the variation of l/D. Energy loss coefficient f is estimated at 1.0 in this small value of l/D by use of Horiguchi theory. But in the large value of l/D where the holes are regarded as pipe, the wave force on the wall is relatively sensitive to the variation of l/D and f is estimated at 1.5 by use of Horiguchi theory.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.171-181
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• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.620-620
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• 2013

When $MoS_2$ is thinned to single layer (1L), photoluminescence (PL) quantum yield drastically increases due to emergence of direct band gap. A recent theory predicts that the electronic structure of 1L $MoS_2$ is very sensitive to its lattice constants. We investigated the response of 1L $MoS_2$ to biaxial tensile strain using spatially resolved PL and Raman spectroscopy. Changes in the lattice constants were monitored by the Raman frequency of the in-plane ($E^1{_2g}$) mode. Systematic correlations between PL and Ramanspectral features, revealed in the preliminary results, will be further tested with samples on other substrates and against thermal stress. The results will also be discussed in regard to the theory which predicts that 1L $MoS_2$ becomes an indirect semiconductor at small tensile strain and turns metallic when further extended.

• Educational Technology International
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• v.13 no.1
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• pp.1-25
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• 2012

Despite the relatively short history of Social Network Sites or Services (SNS), it has quickly gained popularity with more than seven hundred million users all over the globe. The SNS emerged as one of the strongest cultural influences for the contemporary society. The SNS would provide both chances and challenges for Education. The main purpose of the article was to explore the way education react and adapt to the emergence of social network and SNS. It tried to provide major theoretical grounds that bridge education and social network. In the due process, the researchers have examined the curriculum and instructional design process of education from the perspective of disruptive and sustainable aspect of SNS technology. Consequently, four major theoretical grounds were identified and reviewed: Gibson's theory of affordance, Vygotsky's social constructivism, Rha's human visual intelligence theory, and the network theory. By investigating these theories, the educational potentials of social network and SNS were emerged. The SNS was viewed as a new medium with abundant potentials of expanding the learning space, empowering the affective aspects of learning, and facilitating the formation of group intelligence. Finally, some future implications and challenges of SNS were suggested.