• Communications for Statistical Applications and Methods
• /
• 제19권5호
• /
• pp.655-662
• /
• 2012

Classification is an important research field in pattern recognition with high-dimensional predictors. The support vector machine(SVM) is a penalized feature selector and classifier. It is based on the hinge loss function, the non-convex penalty function, and the smoothly clipped absolute deviation(SCAD) suggested by Fan and Li (2001). We developed the algorithm for the multiclass SVM with the SCAD penalty function using the local quadratic approximation. For multiclass problems we compared the performance of the SVM with the $L_1$, $L_2$ penalty functions and the developed method.

• 대한수학회보
• /
• 제38권1호
• /
• pp.17-27
• /
• 2001

We discuss a finite difference preconditioner for the$C^1$ Lagrance quadratic spline collocation method for a uniformly elliptic operator with homogeneous Dirichlet boundary conditions. Using the generalized field of values argument, we analyzed eigenvalues of the matrix preconditioned by the matrix corresponding to a finite difference operator with zero boundary condition.

• 대한수학회지
• /
• 제50권4호
• /
• pp.847-864
• /
• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.53-59
• /
• 2016

Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.

• 대한수학회논문집
• /
• 제24권1호
• /
• pp.1-4
• /
• 2009

In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic ${\mathbb{Z}}_3$-extension of an imaginary quadratic field is unramified everywhere.

• 대한수학회지
• /
• 제35권4호
• /
• pp.903-931
• /
• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• 대한수학회보
• /
• 제49권4호
• /
• pp.767-774
• /
• 2012

For a positive square-free integer $d$, let $t_d$ and $u_d$ be positive integers such that ${\epsilon}_d=\frac{t_d+u_d{\sqrt{d}}}{\sigma}$ is the fundamental unit of the real quadratic field $\mathbb{Q}(\sqrt{d})$, where ${\sigma}=2$ if $d{\equiv}1$ (mod 4) and ${\sigma}=1$ otherwise For a given positive integer $l$ and a palindromic sequence of positive integers $a_1$, ${\ldots}$, $a_{l-1}$, we define the set $S(l;a_1,{\ldots},a_{l-1})$ := {$d{\in}\mathbb{Z}|d$ > 0, $\sqrt{d}=[a_0,\overline{a_1,{\ldots},2a_0}]$}. We prove that $u_d$ < $d$ for all square-free integer $d{\in}S(l;a_1,{\ldots},a_{l-1})$ with one possible exception and apply it to Ankeny-Artin-Chowla conjecture and Mordell conjecture.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
• /
• pp.87-90
• /
• 1988

This paper reports a simple posteriori error estimate method for adaptive finite element mesh generation using quadratic shape function especially for the magnetic field problems. The elements of quadratic shape function have more precise solution than those of linear shape function. Therefore, the difference of two solutions gives error quantity. The method uses the magnetic flux density error as a basis for refinement. This estimator is tested on two dimensional problem which has singular points. The estimated error is always under estimated but in same order as exact error, and this method is much simpler and more convenient than other methods. The result shows that the adaptive mesh gives even better rate of convergence in global error than the uniform mesh.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1993년도 하계학술대회 논문집 B
• /
• pp.1110-1112
• /
• 1993

Optical and quadratic electrooptic properties were studied for some compositions(BLN/PZ/PT=9.0/70/30,9.0/65/35,8.5/70/30,8.5/65/35) of the two-stage sintered BLN-PZT ceramics. Effective birefringences(${\Delta}n$), quadratic electrooptic coefficients(R) and half-wave voltages($V_{\pi}$) were measured with electric field and temperature. Also, switching times and contrast ratios were measured.

• 한국광학회:학술대회논문집
• /
• 한국광학회 2002년도 제13회 정기총회 및 2002년도 동계학술발표회
• /
• pp.192-193
• /
• 2002

In this paper we investigate the phase modulation efficiency in the electrooptic phase modulator using PPpinNN GaAs/AlGaAs W-type waveguide. The phase change is affected by the refractive index change taking place inside the depletion region. The behavior of the modulator can be understood in terms of two electric field-related and two carrier-related effects linear electrooptic, quadratic electrooptic, plasma, and bandgap shift. As a result, the phase modulation efficiency was measured about 34.6($^{\circ}$/V$.$mm) for the TE polarized light. The quadratic electrooptic coefficient R 5.82${\times}$10$\^$-15/($\textrm{cm}^2$/V$^2$) is Obtained ant the Phase efficiency Caused by the quadratic electrooptic effect is about 10 times larger than that from the conventional linear electrooptic effect.