• Title, Summary, Keyword: quadratic function

Search Result 736, Processing Time 0.04 seconds

ON CONTINUED FRACTIONS, FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FUNCTION FIELDS

  • Kang, Pyung-Lyun
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.27 no.2
    • /
    • pp.183-203
    • /
    • 2014
  • We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.

REAL QUADRATIC FUNCTION FIELDS OF MINIMAL TYPE

  • Byeon, Dongho;Keem, Jiae;Lee, Sangyoon
    • Communications of the Korean Mathematical Society
    • /
    • v.28 no.4
    • /
    • pp.735-740
    • /
    • 2013
  • In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.

HILBERT 2-CLASS FIELD TOWERS OF IMAGINARY QUADRATIC FUNCTION FIELDS

  • Ahn, Jaehyun;Jung, Hwanyup
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.23 no.4
    • /
    • pp.699-704
    • /
    • 2010
  • In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.

Robust Stable Conditions Based on the Quadratic Form Lyapunov Function (2차 형식 Lyapunov 함수에 기초한 강인한 안정조건)

  • Lee, Dong-Cheol;Bae, Jong-Il;Jo, Bong-Kwan;Bae, Chul-Min
    • Proceedings of the KIEE Conference
    • /
    • /
    • pp.2212-2214
    • /
    • 2004
  • Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

  • PDF

Function Approximation Using an Enhanced Two-Point Diagonal Quadratic Approximation (개선된 이점 대각 이차 근사화를 이용한 함수 근사화)

  • Kim, Jong-Rip;Kang, Woo-Jin;Choi, Dong-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.28 no.4
    • /
    • pp.475-480
    • /
    • 2004
  • Function approximation is one of the most important and active research fields in design optimization. Accurate function approximations can reduce the repetitive computational effort fur system analysis. So this study presents an enhanced two-point diagonal quadratic approximation method. The proposed method is based on the Two-point Diagonal Quadratic Approximation method. But unlike TDQA, the suggested method has two quadratic terms, the diagonal term and the correction term. Therefore this method overcomes the disadvantage of TDQA when the derivatives of two design points are same signed values. And in the proposed method, both the approximate function and derivative values at two design points are equal to the exact counterparts whether the signs of derivatives at two design points are the same or not. Several numerical examples are presented to show the merits of the proposed method compared to the other forms used in the literature.

ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS

  • Jung, Hwanyup
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.23 no.3
    • /
    • pp.547-553
    • /
    • 2010
  • In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.