• 제목/요약/키워드: quadratic form

검색결과 273건 처리시간 0.034초

INTEGRABILITY AS VALUES OF CUSP FORMS IN IMAGINARY QUADRATIC

  • Kim, Dae-Yeoul;Koo, Ja-Kyung
    • 대한수학회논문집
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    • 제16권4호
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    • pp.585-594
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    • 2001
  • Let η be the complex upper half plane, let h($\tau$) be a cusp form, and let $\tau$ be an imaginary quadratic in η. If h($\tau$)$\in$$\Omega$( $g_{2}$($\tau$)$^{m}$ $g_{3}$ ($\tau$)$^{ι}$with $\Omega$the field of algebraic numbers and m. l positive integers, then we show that h($\tau$) is integral over the ring Q[h/$\tau$/n/)…h($\tau$+n-1/n)] (No Abstract.see full/text)

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The Convolution Sum $\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(1, 14),(2, 7),(1, 7)

  • Alaca, Ayse;Alaca, Saban;Ntienjem, Ebenezer
    • Kyungpook Mathematical Journal
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    • 제59권3호
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    • pp.377-389
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    • 2019
  • We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

FORM CLASS GROUPS ISOMORPHIC TO THE GALOIS GROUPS OVER RING CLASS FIELDS

  • Yoon, Dong Sung
    • East Asian mathematical journal
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    • 제38권5호
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    • pp.583-591
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    • 2022
  • Let K be an imaginary quadratic field and 𝒪 be an order in K. Let H𝒪 be the ring class field of 𝒪. Furthermore, for a positive integer N, let K𝒪,N be the ray class field modulo N𝒪 of 𝒪. When the discriminant of 𝒪 is different from -3 and -4, we construct an extended form class group which is isomorphic to the Galois group Gal(K𝒪,N/H𝒪) and describe its Galois action on K𝒪,N in a concrete way.

최소조파 저항성능을 갖는 최적 선수형상에 관한 연구 (A Study on the Optimal Forebody Forms for Minimum Wave Resistance)

  • 김성은
    • 대한조선학회논문집
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    • 제28권2호
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    • pp.28-39
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    • 1991
  • 조파저항과 마찰저항이 최소가 되는 선수형상을 구하기 위한 최적화문제에 관한 연구를 수행하였다. 선미부는 기존선형으로 고정하며 선수부만의 offsets을 설계변수로 하였다. 구하고자 하는 최적선형을 기존선형과 이에 대한 미소변화량으로 나누어 조파저항계산시 기존선형에는 Neumann-Kelvin 이론을 적용하고 미소변화량에는 thin ship 이론을 적용하였으며 마찰저항은 ITTC 1957 모형선-실선 상관곡선을 이용하였다. 선체표면을 모양함수(shape function)를 이용하여 근사시켰고, 이로부터 목적함수인 조파저항과 마찰저항은 offsets에 대한 2차식 형태로 표현되므로 선형구속조건을 적용하면 2차계획(quadratic programing)문제를 세울 수 있으며 complementary pivot method를 이용하여 해를 구하였다. 대상선형은 Series 60 $C_{B}$=0.6이고 Fn=0.289에서 최적화하였으며, 적절한 구속조건을 주어서 현실적인 최적선수형상을 구하고자 하였다. 본 방법으로 구한 최적선형은 thin ship 이론만을 이용하여 구한 선형과 비교할 때 설계속도 Fn=0.289에서 약간의 조파저항성능 개선(1.92%)를 가져왔다.

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A study on log-density ratio in logistic regression model for binary data

  • Kahng, Myung-Wook
    • Journal of the Korean Data and Information Science Society
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    • 제22권1호
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    • pp.107-113
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    • 2011
  • We present methods for studying the log-density ratio, which allow us to select which predictors are needed, and how they should be included in the logistic regression model. Under multivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of many predictors. The linear, quadratic and crossproduct terms are required in general. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms.

GENERALIZED HYERES{ULAM STABILITY OF A QUADRATIC FUNCTIONAL EQUATION WITH INVOLUTION IN QUASI-${\beta}$-NORMED SPACES

  • Janfada, Mohammad;Sadeghi, Ghadir
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1421-1433
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    • 2011
  • In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

On the numerical assessment of the separation zones in semirigid column base plate connections

  • Baniotopoulos, C.C.
    • Structural Engineering and Mechanics
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    • 제2권3호
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    • pp.295-309
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    • 1994
  • The present paper concerns the mathematical study and the numerical treatment of the problem of semirigid connections in bolted steel column base plates by taking into account the possibility of appearance of separation phenomena on the contact surface under certain loading conditions. In order to obtain a convenient discrete form to simulate the structural behaviour of a steel column base plate, the continuous contact problem is first formulated as a variational inequality problem or, equivalently, as a quadratic programming problem. By applying an appropriate finite element scheme, the discrete problem is formulated as a quadratic optimization problem which expresses, from the standpoint of Mechanics, the principle of minimum potential energy of the semirigid connection at the state of equilibrium. For the numerical treatment of this problem, two effective and easy-to-use solution strategies based on quadratic optimization algorithms are proposed. This technique is illustrated by means of a numerical application.

Robust $L_2$Optimization for Uncertain Systems

  • Kim, Kyung-Soo;Park, Youngjin
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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    • pp.348-351
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    • 1995
  • This note proposes a robust LQR method for systems with structured real parameter uncertainty based on Riccati equation approach. Emphasis is on the reduction of design conservatism in the sense of quadratic performance by utilizing the uncertainty structure. The class of uncertainty treated includes all the form of additive real parameter uncertainty, which has the multiple rank structure. To handle the structure of uncertainty, the scaling matrix with block diagonal structure is introduced. By changing the scaling matrix, all the possible set of uncertainty structures can be represented. Modified algebraic Riccati equation (MARE) is newly proposed to obtain a robust feedback control law, which makes the quadratic cost finite for an arbitrary scaling matrix. The remaining design freedom, that is, the scaling matrix is used for minimizing the upper bound of the quadratic cost for all possible set of uncertainties within the given bounds. A design example is shown to demonstrate the simplicity and the effectiveness of proposed method.

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A control allocation sterategy based on multi-parametric quadratic programming algorithm

  • Jeong, Tae-Yeong;Ji, Sang-Won;Kim, Young-Bok
    • 수산해양기술연구
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    • 제49권2호
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    • pp.153-160
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    • 2013
  • Control allocation is an important part of a system. It implements the function that map the desired command forces from the controller into the commands of the different actuators. In this paper, the authors present an approach for solving constrained control allocation problem in vessel system by using multi-parametric quadratic programming (mp-QP) algorithm. The goal of mp-QP algorithm applied in this study is to compute a solution to minimize a quadratic performance index subject to linear equality and inequality constraints. The solution can be pre-computed off-line in the explicit form of a piecewise linear (PWL) function of the generalized forces and constrains. The efficiency of mp-QP approach is evaluated through a dynamic positioning simulation for a vessel by using four tugboats with constraints about limited pushing forces and found to work well.