• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.413-424
• /
• 2003

L. H Encinas, A. J. Menezes and J. M. Masque in [3] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [2] obtained the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_{2-}$ using direct counting method. We have obtained isomorphism classes of hyperelliptic curves of genus 2 over $F_{2n}$ for odd n, represented by an equation of the form $y^2$ + $a_{5}$ y = $x^{5}$ + $a_{8}$ x + $a_{10}$ ( $a_{5}$ $\neq$0) [1]. In this paper we characterize hyperelliptic curves of genus 2 over $F_{2n}$ for even n, represented by an equation of the form $y^2$ + $a_{5}$ y = $x^{5}$ + $a_{5}$ x + $a_{10}$ ( $a_{5}$ $\neq$0).>0).

• Journal of applied mathematics & informatics
• /
• 제32권1_2호
• /
• pp.17-26
• /
• 2014

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of genus 3 hyperelliptic curves of type $y^2=x^7+ax$ over finite prime fields. The problem of determining the group order of the Jacobian varieties of algebraic curves defined over finite fields is important not only arithmetic geometry but also curve-based cryptosystems in order to find a secure curve. Based on this, we provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety of hyperelliptic curve $y^2=x^7+ax$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ modulo 12. Moreover, we also introduce some implementation results by using our algorithm.

• Restorative Dentistry and Endodontics
• /
• 제47권2호
• /
• pp.16.1-16.9
• /
• 2022

Objectives: This study compared the cyclic fatigue resistance of One Curve (C wire) and F6 Skytaper (conventional austenite nickel-titanium [NiTi]), and 2 instruments with thermos-mechanically treated NiTi: Protaper Next X2 (M wire) and Hyflex CM (CM wire). Materials and Methods: Ten new instruments of each group (size: 0.25 mm, 6% taper in the 3 mm tip region) were tested using a rotary bending machine with a 60° curvature angle and a 5 mm curvature radius, at room temperature. The number of cycles until fracture was recorded. The length of the fractured instruments was measured. The fracture surface of each fragment was examined with a scanning electron microscope (SEM). The data were analyzed using one-way analysis of variance and the post hoc Tukey test. The significance level was set at 0.05. Results: At 60°, One Curve, F6 Skytaper and Hyflex CM had significantly longer fatigue lives than Protaper Next X2 (p < 0.05). No statistically significant differences were found in the cyclic fatigue lives of One Curve, F6 Skytaper, and Hyflex CM (p > 0.05). SEM images of the fracture surfaces of the different instruments showed typical features of fatigue failure. Conclusions: Within the conditions of this study, at 60° and with a 5 mm curvature radius, the cyclic fatigue life of One Curve was not significantly different from those of F6 Skytaper and Hyflex CM. The cyclic fatigue lives of these 3 instruments were statistically significantly longer than that of Protaper Next.

• 한국안광학회지
• /
• 제14권1호
• /
• pp.47-56
• /
• 2009

목적: 시감도가 최적화된 투과필터의 칼라위치를 추정한다. 방법: 시감도 최적화를 위한 칼라를 Y(Yellow), G(green)과 P(Red)를 이용하여 CR-39에 담그기 법으로 $Y_{1-x}G_{x}$, $Y_{1-x}P_{x}$를 제작하였다. 투과광에서 최종 비시감도의 추정방법 모델은 파장에 따른 눈의 시감도와 렌즈의 투과율 세기의 곱($P_f$ ($P_f({\lambda}=T({\lambda}){\cdot}P({\lambda}).)$.)으로 나타낸다. 400~700 nm 영역에서 투과광의 평가는 비시감도 곡선의 면적, Peak, 폭, 최고높이 값으로 평가한다. 결과: $Y_{1-x}G_{x}$에서 x=0.04, x=0.08, x=0.10, x=0.12, x=0.14, x=0.5에서 ${\beta}=S_1/S_0{\cdot}100$ 값은 각각 76.1, 77.9, 80.7, 81.6, 80.2, 18.6을 갖는다. $Y_{1-x}P_{x}$에서 x=1.00, x=0.2, x=0.6, x=0.8에서 ${\beta}=S_1/S_0{\cdot}100$ 값은 각각 74.3, 74.0, 70.5, 33.0을 갖는다. 투과광의 면적과 최고높이를 평가한 결과는 $Y_{1-x}P_{x}$보다 $Y_{1-x}G_{x}$가 더 큰 값을 갖게 되어 비시감도 최적화에 접근하였다. 결론: 비시감도 최적화는 $Y_{1-x}G_{x}$에서 X=0.12~0.14의 값을 갖는다.

• Kyungpook Mathematical Journal
• /
• 제54권2호
• /
• pp.203-209
• /
• 2014

We assume that the existence and termination conjecture for flips holds. A complex projective manifold is said to be of almost general type if the intersection number of the canonical divisor with every very general curve is strictly positive. Let f be an algebraic fiber space from X to Y. Then the manifold X is of almost general type if every very general fiber F and the base space Y of f are of almost general type.

• 충청수학회지
• /
• 제15권2호
• /
• pp.1-12
• /
• 2003

L. H. Encinas, A. J. Menezes, and J. M. Masque in [2] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [1] obtained for the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_q$ using direct counting method. In this paper we will classify the isomorphism classes of hyperelliptic curves of genus 2 over $F_{2^n}$ for odd n, represented by an equation of the form $y^2+a_5y=x^5+a_8x+a_{10}(a_5{\neq}0)$.

• 대한수학회보
• /
• 제51권1호
• /
• pp.29-41
• /
• 2014

In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+${\cdots}$+f(nx) = 0, with $n{\geq}2$, which are related to the partial sums of the Riemann zeta function. These curves ${\alpha}$-densify a large class of compact sets of the plane for arbitrary small ${\alpha}$, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the $n^{th}$ power of the density approaches the Jordan content of the compact set which the curve densifies.

• 대한수학회지
• /
• 제57권1호
• /
• pp.145-169
• /
• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• 반도체디스플레이기술학회지
• /
• 제14권1호
• /
• pp.13-17
• /
• 2015

$YAlO_3:Tb{_x}^{3+}$ has been synthesized by a combustion process and the concentration x of Tb was varied from 0.001 and 0.05 mol% per mole of YAlO3. The energy transfer of $^5D_3{\rightarrow}^7F_6$(385nm) and $^5D_4{\rightarrow}^7F_5$(544nm) transitions on the $YAlO_3:Tb{_x}^{3+}$(x =0.001, 0.05) have been investigated by using decay curves. The energy transfer mechanism was explained by Inokuti and Hirayama model. The results of calculation and fitting showed that values of n are 6.11(x=0.01) and 6.13(x=0.005). These indicate that the energy transfer mechanism between $Tb^{3+}$ ions is dipole-dipole interaction.

• 대한수학회지
• /
• 제53권6호
• /
• pp.1431-1443
• /
• 2016

Let k be a global field of characteristic unequal to two. Let $C:y^2=f(x)$ be a nonsingular projective curve over k, where f(x) is a quartic polynomial over k with nonzero discriminant, and K = k(C) be the function field of C. For each prime spot p on k, let ${\hat{k}}_p$ denote the corresponding completion of k and ${\hat{k}}_p(C)$ the function field of $C{\times}_k{\hat{k}}_p$. Consider the map $$h:Br(K){\rightarrow}{\prod\limits_{\mathfrak{p}}}Br({\hat{k}}_p(C))$$, where p ranges over all the prime spots of k. In this paper, we explicitly describe all the constant classes (coming from Br(k)) lying in the kernel of the map h, which is an obstruction to the Hasse principle for the Brauer groups of the curve. The kernel of h can be expressed in terms of quaternion algebras with their prime spots. We also provide specific examples over ${\mathbb{Q}}$, the rationals, for this kernel.