• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1323-1330
• /
• 2017

For a nondegenerate projective irreducible variety $X{\subset}{\mathbb{P}}^r$, it is a natural problem to find an upper bound for the value of $${\ell}_{\beta}(X)=max\{length(X{\cap}L){\mid}L={\mathbb{P}}^{\beta}{\subset}{\mathbb{P}}^r,\;{\dim}(X{\cap}L)=0\}$$ for each $1{\leq}{\beta}{\leq}e$. When X is locally Cohen-Macaulay, A. Noma in [10] proves that ${\ell}_{\beta}(X)$ is at most $d-e+{\beta}$ where d and e are respectively the degree and the codimension of X. In this paper, we construct some surfaces $S{\subset}{\mathbb{P}}^5$ of degree $d{\in}\{7,{\ldots},12\}$ which satisfies the inequality $${\ell}_2(S){\geq}d-3+{\lfloor}{\frac{d}{2}}{\rfloor}$$. This shows that Noma's bound is no more valid for locally non-Cohen-Macaulay varieties.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.293-300
• /
• 1995

Let $R = k[y_1,\cdots,y_n] \otimes E[x_1, \cdots, x_n]$ with characteristic $k = p > 2$ (odd prime), where $$\mid$y_i$\mid$ = 2, $\mid$x_i$\mid$ = 1$ and $y_i = \betax_i, \beta$ is the Bockstein homomorphism. Topologically, $R = H^*(B(Z/p)^n,k)$. For a symmetric group $\sum_n, R^{\sum_n} = k[\sigma_1,\cdots,\sigma_n] \otimes E[d\sigma_1, \cdots, d\sigma_n]$ where d is the derivation satisfying $d(y_i) = x_i$ and $d(x_iy_i) = x_iy_i + x_jy_i, 1 \leq i, j \leq n$. We give a direct proof of this theorem by using induction.

• Journal of Korea Game Society
• /
• v.1 no.1
• /
• pp.68-72
• /
• 2001

DirectX Graphics plays the role of hardware independent 3 dimensional drawing interface for 3 dimensional video display. However the APIs in DirectX Graphics provide not only small improvement in velocity in the lowest level but also unstable performance of velocity according to their usages. In this paper, we present the structure of 3D game engine of efficient performance and describe functions and implementational features of game engines for an efficient 3D rendering in the environment of DirecX Graphics.

• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.319-323
• /
• 2013

Let D be a principal ideal domain, X be an indeterminate over D, D[X] be the polynomial ring over D, and $R_n=D[X]/(X^n)$ for an integer $n{\geq}1$. Clearly, $R_n$ is a commutative Noetherian ring with identity, and hence each nonzero nonunit of $R_n$ can be written as a finite product of irreducible elements. In this paper, we show that every irreducible element of $R_n$ is a primary element, and thus every nonunit element of $R_n$ can be written as a finite product of primary elements.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.73-83
• /
• 2018

Let R be an associative ring with involution * and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an $({\alpha},{\beta})^*$-derivation of R if $d(xy)=d(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $F:R{\rightarrow}R$ is called a generalized $({\alpha},{\beta})^*$-derivation of R associated with an $({\alpha},{\beta})^*$-derivation d if $F(xy)=F(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [12], and a theorem of Daif and El-Sayiad [6], moreover, we generalize a theorem of Ali et al. [4] and a theorem of Huang and Koc [9] related to generalized Jordan triple $({\alpha},{\beta})^*$-derivations.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2003.05a
• /
• pp.67-70
• /
• 2003

웹 브라우저로 쉽게 접근 할 수 있는, VRML과 XML을 이용한 X3D(Extensible 3D)구조를 통해 가상공간에서 인간의 움직임에 대한 체험을 하도록 하는 Humanoid를 생성해 사용자와 상호 작용할 수 있는 방법을 제안한다. 즉 X3D의 특징, X3D를 이용하여 컴퓨터 그래픽스의 화려한 영상이 사실처럼 보이는 기술인 반사효과(Reflection), 실시간 디스플레이(Compression & Reduce), 대화식의 상호작용(Interaction)통의 Web3D 기반 3D 그래픽 표현에 대한 알고리즘을 제안하고 검증할 것이다.

• Journal of the Korean Chemical Society
• /
• v.41 no.4
• /
• pp.175-179
• /
• 1997

Luminescence of $Eu^{3+}$ has been studied in $Sr_{2-2x}Eu_xK_xSnO_4$ with two-dimensional $K_2NiF_4$ structure. The $^5D_o$ → $^7F_o$$Eu^{3+}$ ion represents the J=0 → J=0 transition which is forbidden by a Judd-Ofelt selection rule for electric dipole transition in 4f shell of $Eu^{3+}$ ions. However, the emission line of $^5D_o$ → $^7F_o$$Eu^{3+}$ emission spectra of Sr2-2xEuxKxSnO4$Sr_{2-2x}Eu_xK_xSnO_4$structure around $Eu^{3+}$ ions.

• Proceedings of the Korea Multimedia Society Conference
• /
• 2003.11b
• /
• pp.593-596
• /
• 2003

웹상의 3차원 세계를 구현할 수 있는 국제표준 언어인 VRML/X3D를 이용한 Web3D콘텐츠의 요구가 증대되고 있다. 본 논문은 VRMI/X3D에서 지원하는 안개(Fog)효과의 한계를 고찰하고 효과적인 안개효과를 개선할 수 있는 방법을 제안한다 거리계수를 파라미터로 사용함으로서 지역적인 안개의 표현과 다양한 안계밀도를 생성하는 방법을 실험하였다.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.455-462
• /
• 2013

Let D be an integral domain, S be a saturated multi-plicative subset of D such that $D_S$ is a factorial domain, $\{X_{\alpha}\}$ be a nonempty set of indeterminates, and $D[\{X_{\alpha}\}]$ be the polynomial ring over D. We show that S is a splitting (resp., almost splitting, t-splitting) set in D if and only if every nonzero prime t-ideal of D disjoint from S is principal (resp., contains a primary element, is t-invertible). We use this result to show that $D{\backslash}\{0\}$ is a splitting (resp., almost splitting, t-splitting) set in $D[\{X_{\alpha}\}]$ if and only if D is a GCD-domain (resp., UMT-domain with $Cl(D[\{X_{\alpha}\}]$ torsion UMT-domain).

• Journal of the Korean Magnetics Society
• /
• v.6 no.6
• /
• pp.405-410
• /
• 1996

Valence band photoemission spectroscopy (PES) measurements have been performed for $Co_{x}Pd_{100-x}$ alloy films using synchrotron radiation (x = 0, 25, 40, 65). Then the partial spectral weight distributions (PSW's) of Co 3d and Pd 4d electrons have been determined. The Co 3d PSW's exhibit some structures which are quite different from those of the Co film for x < 25 %, whereas they become very similar to those of the Co film for x > 40 %. For x < 25 %, the peak near the Fermi level ($E_F$) and a shoulder around 2 eV binding energy in the Co 3d PSW reflect large hybridization between Pd 4d and Co 3d electrons, suggesting that the hybridization might play an inportant role in determining perpendicualr magnetic anisotropy. The Pd 4d PSW's in Co-Pd alloy films are found to have larger FWHM's (full widths at half maximum), larger binding energies of the main peaks, and larger spectral intensities at $E_F$ than the PES spectrum of the Pd film. The FWHM of the Pd 4d PSW increases with decreasing Pd concentration, which are considered to reflect the disordering effect in the alloy formation or the change in the Pd 4d electronic structure due to hybridization between Co 3d and Pd 4d electrons.