• 대한수학회지
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• 제43권6호
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.133-140
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• 1995

The D-optimal design criterion for precise parameter estimation in nonlinear regression analysis is called the determinant criterion because the determinant of a matrix is to be maximized. In this thesis, we derive the gradient and the Hessian of the determinant criterion, and apply a QR decomposition for their efficient computations. We also propose an approximate form of the Hessian matrix which can be calculated from the first derivative of a model function with respect to the design variables. These equations can be used in a Gauss-Newton type iteration procedure.

• 대한수학회보
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• 제59권6호
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• pp.1423-1438
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• 2022

In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

• 전기전자학회논문지
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• 제23권4호
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• pp.1302-1308
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• 2019

본 논문은 CNN (Convolutional Neural Network)와 2D Lidar 센서에서 획득한 위치 데이터를 이용하여 이미지를 분류하는 방법을 제시한다. Lidar 센서는 데이터 정확도, 형상 왜곡 및 광 변화에 대한 강인성 측면에서의 이점으로 인해 무인 장치에 널리 사용되어 왔다. CNN 알고리즘은 하나 이상의 컨볼루션 및 풀링 레이어로 구성되며 이미지 분류에 만족스러운 성능을 보여 왔다. 본 논문에서는 학습 방법에 따라 다른 유형의 CNN 아키텍처들인 Gradient Descent (GD) 및 Levenberg-arquardt (LM)를 구현하였다. LM 방법에는 학습 파라메터를 업데이트하는 요소 중 하나인 Hessian 행렬 근사 빈도에 따라 두 가지 유형이 있다. LM 알고리즘의 시뮬레이션 결과는 GD 알고리즘보다 이미지 데이터의 분류 성능이 우수하였다. 또한 Hessian 행렬 근사가 더 빈번한 LM 알고리즘은 다른 유형의 LM 알고리즘보다 작은 오류를 보여주었다.

• 한국해안·해양공학회논문집
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• 제22권1호
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• pp.47-57
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• 2010

Woo and Liu (2004)의 확장형 Boussinesq FEM 수치모형에서 한계점으로 지적되었던 수치진동현상과 계산 효율성이 크게 개선되었다. 수치진동을 해결하기 위해 subgrid scale stabilization method를 사용하였고, 계산효율성을 높이기 위해서 Hessian 연산자를 도입하였으며, 유속벡터에 대한 행렬 구성을 하나의 행렬로 구성하였다. 또한 추가변수에 대한 행렬은 mass lumping technique을 사용하여 대각행렬로 구성하였다. Vincent and Briggs(1989)의 파랑 굴절 및 회절에 대한 수치실험 결과 수치진동현상이 확연히 줄어 들은 것을 관찰할 수 있었으며, 수리실험 결과와도 상당히 일치하는 결과를 보였다. 이전 모형에 비해 약 10배의 계산소요시간이 줄어 향후 항만부진동이나 퇴적물 이동과 같은 현실적인 문제에 적용이 가능할 것으로 기대된다.

• 한국수학교육학회지시리즈A:수학교육
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• 제32권2호
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• pp.173-177
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• 1993

• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 추계학술대회 논문집 학회본부
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• pp.35-38
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• 1991

Recent, problems on the voltage-instability have been paid attention in power system and methods to find the limit of voltage-stability, concerned with these problems, were developed. However, these methods are short of precision on the limit of voltage-instability. Here, using the second-order load flow, constraint equation(d Pi/d Vi=0) and its patial differentiations are precisely formulated. Also, since the taylor series expansion of power flow equations terminates at the second-order terms, partial differentiations of constraint equation, that is Hessian, are constant. Then, Hessian matrix are calculated once during iteration process.

• 응용통계연구
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• 제8권2호
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• pp.65-75
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• 1995

설명변수 축소방법들인 Sliced Inverse Regression과 Principal Hessian Directions에서는 효과적 차원축소공간의 차원을 결정하기 위하여 설명변수의 정규성과 충분한 수의 자료가 요구되는 점근적검정(asymptotic test)을 제시하고 있다. 본 연구에서는 Cook과 Weisberg(1991)가 제안하였던 순열검정통계량(permutation test statistic)을 개발하여 SIR과 PHD에서 제시된 점근적 검정 통계량과 검정력을 비교하기로 한다.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.129-140
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• 2020

In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.

• 한국작물학회지
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• 제44권3호
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• pp.302-307
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• 1999

Hamlet (PI549276) possessing 2RL was obtained by cross between a wheat cultivar ND7532 (Froid/Centurk) and a rye cultivar Chaupon. Chaupon was known to have resistant gene to biotype L of Hessian fly [Mayetiola destructor (Say)] larvae. The wheat-rye translocation line (Coker797*4/Hamlet) was also known to be resistant to biotype L of Hessian fly larvae. We analysed a set of 96 ESTs from the wheat-rye translocation line (2BS/2RL). ESTs were classified by various physiological processings, such as primary metabolism, secondary metabolism, transcription, translation, transport, signal transduction, defense, transposable element, and others. Three sequences encoding thioredoxin peroxidase, 26S rRNA, and rubisco small subunits were homologous to registered genes in rye. Although limited number of clones were used to develop ESTs, these clones and their sequence information may be useful for researchers studying general physiology and molecular biology on the translocation line.