• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Korean Journal of Materials Research
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• v.32 no.3
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• pp.168-179
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• 2022

Microbiologically Influenced Corrosion (MIC) occurring in underground buried pipes of API 5L X65 steel was investigated. MIC is a corrosion phenomenon caused by microorganisms in soil; it affects steel materials in wet atmosphere. The microstructure and mechanical properties resulting from MIC were analyzed by OM, SEM/EDS, and mapping. Corrosion of pipe cross section was composed of ① surface film, ② iron oxide, and ③ surface/internal microbial corrosive by-product similar to surface corrosion pattern. The surface film is an area where concentrations of C/O components are on average 65 %/16 %; the main components of Fe Oxide were measured and found to be 48Fe-42O. The MIC area is divided into surface and inner areas, where high concentrations of N of 6 %/5 % are detected, respectively, in addition to the C/O component. The high concentration of C/O components observed on pipe surfaces and cross sections is considered to be MIC due to the various bacteria present. It is assumed that this is related to the heat-shrinkable sheet, which is a corrosion-resistant coating layer that becomes the MIC by-product component. The MIC generated on the pipe surface and cross section is inferred to have a high concentration of N components. High concentrations of N components occur frequently on surface and inner regions; these regions were investigated and Na/Mg/Ca basic substances were found to have accumulated as well. Therefore, it is presumed that the corrosion of buried pipes is due to the MIC of the NRB (nitrate reducing bacteria) reaction in the soil.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) which consists of functionals F of the form : $$F(x)={\int}_H\;{\exp}\{i(h,x)^{\sim}\}df(h),\;x{\in}B$$ where $({\cdot}{\cdot})^{\sim}$ is a stochastic inner product between H and B, and $f$ is in $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.223-233
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• 1998

This paper is concerned with the problem of existence of solutions to the initial value problem u'(t) = A(t, u(t)), u(a) = z in a probabilistic normed space where $A : [a,b)\;{\times}\;D->E$ is continuous, D is a closed subset of a probabilistic normed space E, and $z\;{\in}\;D$. With a dissipative type condition on A, we estabilish sufficient conditions for this initial value problem to have a solution.

• Korean Institute of Interior Design Journal
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• v.16 no.2 s.61
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• pp.87-96
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• 2007

This study analyzes the place of modem architecture based on the place theory of C. N, Schultz. For applying Schultz's theory to the modern architecture, It is required to examine the modern cityscape, features of inner space of architecture and features of program. By analyzing the avant-garde architecture of Rem Koolhaas on such basis, the potentiality of placeness of modern architecture could be verified and the alternatives would be searched. It is inferred that the placeness features of Rem Koolhaas' public architecture is under the influence of the interpretation of program based on the humane background rather than the physical aspects of surroundings. The inner space shows the non-linear features, the metaphor of city. The obscurity of physical boundary illustrates the flexible features with ambiguous boundary. Consequently, the inner space expresses the surreal atmosphere that doesn't match the purposes of usage of architecture, the traditional concept. The outer shape is recognized as the by-product from the interpretation of internal program rather than it considered the surrounding context. The outer shape has the relatively simple formative shape and contrasts against the complicated inner space by using the non-physical materials. It is found that Koolhaas' architecture doesn't pursue the features of placeness of traditional concept. However, It is inferred that his architecture has the possibility of placeness by attaching the meaning through the social roles of each architecture. It gives the substantial suggestion to the modern architecture that can't easily acquire the placeness of traditional concept due to the environment of modern city.

• East Asian mathematical journal
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• v.34 no.5
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1705-1723
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• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.23-25
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• 1998

Many of the currently used PN code acquisition algorithms detect the phase of the incoming PN signal on the basis of ML estimation principle and utilize statistics grounded in taking inner products. By showing that any set of 2n-1 PN sequences arising in SSRG or MSRG (those typically used in IS'95 implementations) configuration constitutes a linearly independent set and that the number of candidate PN sequences has to equal the dimension of the span of the candidate PN sequences, we prove that the lowerbounding computational complexity involved in any PN code acquistion, utilizing (only) inner product computations at each stage of acquisition, corresponds precisely to those, such as double dwell acquistion circuitries, currently used.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.1-16
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• 1997

In this paper we study efficient parallel implementation for hybrid iterative methods BICGSTAB and BICGSTAB $(\ell)$ with ${Well}=2$ on the CRAY C90 and the efficiency of their parallel performance is evaluated. numerical experiments suggest that on the CRAY C90 a parallel inner product algorithm called PDOTB be used for the par-allelization of hybrid iterative methods containing sensitive values of inner products. Lastly it is shown that the number of iterations in which parallel hybrid iterative methods satisfy a certain convergence criterion depends on the number of processors to be used.

• Journal of Powder Materials
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• v.11 no.4
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• pp.294-300
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• 2004

This study for preparation of aluminum nitride (AlN) with high purity was carried out by self-propagating high-temperature synthesis method in two different systems, $Al-N_{2}$ and $Al-N_{2}$-AlN, with the change of nitrogen gas pressure and dilution factor. On the occasion of $Al-N_{2}$ system, unreacted aluminum was detected in the product in spite of high nitrogen pressure, 10 MPa, This may be caused by obstructing nitrogen gas flow to inner part of molten and agglomerate of aluminum, formed in pre-heating zone. In $Al-N_{2}$-AlN system, AlN with a purity of 95% or ever can be prepared in the condition of $f_{Dil}\geq0.5$, $P_{N_{2}}\geq$ 1 MPa, and the purity can be elevated to 98% over in the condition of $f_{Dil}$ = 0.7 and $P_{N_{2}}$ = 10 MPa.