• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• 대한수학회논문집
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• 제38권4호
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• 한국환경복원기술학회지
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• 제4권2호
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• pp.74-83
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• 2001

The purpose of this study was investigate to the influence of forest roads characteristics and environment factors on the soil erosion, stability and vegetation survival of cut slope in forest roads. The results obtained could be summarized as follows; 1. The correlated factors between slope erosion and variables in cut slope were altitude, convex, degree of slope, length of slope and soil depth. In the stepwise regression analysis, length of slope and soil hardness was a high significant and its regression equation was given by -89.6136 + 15.0667X14 + 16.6713X15($R^2$ = 0.6712). 2. The main factors influencing the stability of cut slope were significant in order of coverage, middle, convex, length of slope and north, and its discriminant equation was given by -1.019 + 0.064X22 - 0.808X8 - 0.622X24 + 0.742X11 - 0.172X14 - 0.545X6 ($R^2$ = 0.793). 3. The centroids value of discriminant function in the stability and unstability estimated to 1.244 and -1.348, respectively. The boundary value between two groups related to slope stability was -0.1038. The prediction rate of discriminant function for stability evaluation of was as high as 91.3%. 4. The dominant species of invasion vegetation on the cut slope consist with Carex humilis, Agropyron tsukushiense var. transiens, Calamagrostis arundinacea, Miscanthus sinensis var. purpurascens, and Ixeris dentata in survey area. The rate of vegetation invasion more increased by time passed. 5. The life form of invasion vegetation in cut slop showed to $H-D_1-R_{2,3}-e$ type of the hemicryptophyte of dormancy form, dissem inated widely by wind and water of dissminule type, moderate extent and narrowest extent of radicoid type, erect form of growth form. 6. The correlated factors between forest enviroment and coverage appeared north, passage years and middle position of slope at 5% level. The forest environment factors influencing the invasion plants in survey area were shown in order to altitude, passage years, rock(none), forest type(mixed) and stone amount. The regression equation was given by 17.5228 - 0.0911X3 + 3.6189X28 15.8493X22 19.8544X25 + 0.3558X26 ($R^2$ = 0.4026).

• Journal of the Korean Data and Information Science Society
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• 제28권6호
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• pp.1229-1244
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• 2017

최근 여러 분야에서 데이터에 근거한 분석방법론에 대한 수요가 증대됨에 따라 이를 처리할 수 있는 최적화 방법이 발전되고 있다. 특히 통계학과 기계학습 분야의 문제들에서 요구되는 다양한 제약 조건은 볼록 최적화 (convex optimization) 방법으로 해결할 수 있다. 본 논문에서 리뷰하는 alternating direction method of multipliers (ADMM) 알고리즘은 선형 제약 조건을 효과적으로 처리할 수 있으며, 합의 방식을 통해 병렬연산을 수행할 수 있어서 범용적인 표준 최적화 툴로 자리매김 되고 있다. ADMM은 원래의 문제보다 최적화가 쉬운 부분문제로 분할하고 이를 취합함으로써 복잡한 원 문제를 해결하는 방식의 근사알고리즘이다. 부드럽지 않거나 복합적인 (composite) 목적 함수를 최적화할 때 유용하며, 쌍대이론과 proximal 작용소 이론을 토대로 체계적으로 알고리즘을 구성할 수 있기 때문에 통계 및 기계학습 분야에서 폭 넓게 활용되고 있다. 본 논문에서는 최근 통계와 관련된 여러 분야에서 ADMM알고리즘의 활용도를 살펴보고자 하며 주요한 두 가지 주제에 중점을 두고자 한다. (1) 목적식의 분할 전략과 증강 라그랑지안 방법 및 쌍대문제의 설명과 (2) proximal 작용소의 역할이다. 알고리즘이 적용된 사례로, 별점화 함수 추정 등의 조정화 (regularization)를 활용한 방법론들을 소개한다. 모의 자료를 활용하여 lasso 문제의 최적화에 대한 실증결과를 제시한다.

• 한국광학회지
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• 제24권5호
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• pp.217-223
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• 2013

10 diopter에서 20 diopter까지의 양볼록 검안렌즈에 대한 백색광 MTF(Modulation Transter Function)를 각주파수와 시력으로 나타낸 후, 이들을 각각 AIM(Aerial Image Modulation) curve와 비교하였다. 축상시야에서 평가된 양볼록 검안렌즈 모두 시력 2.0까지는 란돌트 링을 분해할 수 있는 MTF를 가지고 있었다. 하지만 반시야각 $5.0^{\circ}$인 비축시야에서는 10 diopter의 검안렌즈는 시력 0.9, 20 diopter의 검안렌즈는 0.8까지 란돌트 링을 분해할 수 있는 것으로 평가되어 시력을 1.0까지 측정하기에는 충분한 해상력을 가지지 못한 것으로 평가되었다.

• Smart Structures and Systems
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• 제31권3호
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• pp.247-257
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• 2023

In structural health monitoring of large-scale structures, optimal sensor placement plays an important role because of the high cost of sensors and their supporting instruments, as well as the burden of data transmission and storage. In this study, a vibration sensor placement algorithm based on deep reinforcement learning (DRL) is proposed, which can effectively solve non-convex, high-dimensional, and discrete combinatorial sensor placement optimization problems. An objective function is constructed to estimate the quality of a specific vibration sensor placement scheme according to the modal assurance criterion (MAC). Using this objective function, a DRL-based algorithm is presented to determine the optimal vibration sensor placement scheme. Subsequently, we transform the sensor optimal placement process into a Markov decision process and employ a DRL-based optimization algorithm to maximize the objective function for optimal sensor placement. To illustrate the applicability of the proposed method, two examples are presented: a 10-story braced frame and a sea-crossing bridge model. A comparison study is also performed with a genetic algorithm and particle swarm algorithm. The proposed DRL-based algorithm can effectively solve the discrete combinatorial optimization problem for vibration sensor placements and can produce superior performance compared with the other two existing methods.

• 한국실내디자인학회논문집
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• 제24권1호
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• pp.178-188
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• 2015

This study has the main objective of being of help as a reference data for the application of the finishing materials when designing the interior of the chapel of the church space through analysis of the finishing materials against the chapels of church space which has complex function. As precedent studies for this, the composition of the function and concept of the church space was surveyed and the complex function of the church space was surveyed. The theoretical surveyed was performed according to the casual composition, behavior of the community and role and location of the duties of the church members. The case objects were 10 chapels constructed by 5 professional interior design companies. The content of the analysis was the finishing materials in the chapels and their application characteristics. The detailed considerations to be referred to when designing the interior of the chapels of church space in the future were proposed. The analysis result of the application of the finishing materials according to the locational function of the chapels of church space can be explained as follows. First, the platform area was the characteristic of applying finishing materials which induce visual immersion. As for the floor materials in the platform, in order to minimize the floor sound and vibration phenomenon occurring during movements, noise insulation and dust protection rubber sheet was place and on top of it the floor or the carpet was placed. Second, the Choir area had the difficult problem of having to consider the appropriate sound absorption occurring due to the proliferation of sound and performance of classical instruments at the same time. However, in the case, this problem was solved through the sculptures of convex shape. Third, since the scheelite is a space where many people move around, the finishing material which absorbs sound was mainly used. Fourth, the entrance area was composed of thick wall materials compared to other walls, and the sound absorption character was most significantly considered when applying the finishing material. Fifth, the broadcasting room was composed either in independent type or an open type and performed its function and the main finishing materials was transparent glass which was highest use frequency.

• 헤리티지:역사와 과학
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• 제39권
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• pp.59-93
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• 2006

경주 월성은 파사니 사금(婆裟尼師今)때 축조된 신라의 왕성으로서 정치적 군사적으로 매우 중요한 역할을 했던 유적이다. 그러한 월성을 에워싸고 있는 월성해자는 전시(戰時)에는 적으로부터 성을 보호하는 방어적 역할과 함께 통일신라시대에 이르러서는 조경의 역할을 담당한 시설물이다. 월성해자 유적의 발굴은 1985년부터 시작되어 현재 까지 이어지고 있으며, 수많은 유물들이 출토되고 있다. 그 중 다량 다종의 수막새들은 신라 초기부터 통일기를 거쳐 그 이후 시기까지 신라시대 막새의 변화 양상을 보여주는 중요한 자료로서 그 가치는 매우 높다 할 수 있다. 기와는 왕궁(王宮), 사찰(寺刹), 산성(山城) 등 국가적인 사업으로 이루어진 건물에서부터 일반적인 기타 건물지까지 가장 널리 사용되었으며, 수량에서도 다른 유물들에 비해 절대적인 우위를 차지하고 있다. 그럼에도 지금까지의 연구 성과는 가장 취약한 분야로 남아있으며, 앞으로 연구되어야 할 과제들이 무궁하게 남아있는 분야라 할 수 있다. 최근 수많은 발굴을 통한 기와 수량의 급격한 증가와 함께 활발한 연구가 이루어지고 있으나, 일반적인 문양의 계보와 제작과정 등에 한정되어 진행되어 온 것이 사실이다. 이에 여기서는 월성해자 출토 단판연화문 수막새를 대상으로 동범와에 관한 판별을 하고자한다. 그 동안 유사와(類似瓦), 동형와(同形瓦)등으로만 판단되었던 막새들의 세부적 특징을 비교해 "동범와"임을 정확히 확인하고자 한다. 동범와에 관한 정확한 판단방법, 동범와로 묶인 형식의 시간적 순서 배열과 동범와가 출토되는 위치 등을 파악함으로써 동범와 판별에 대한 중요성을 강조하고자 한다. 그 결과 다종의 수막새에서 하나의 범(范)으로 찍어낸 막새, 즉 동범와를 판별할 수 있었으며 이러한 동범와들은 출토위치에서 다시 하나로 묶이는 공통점이 확인된다. 동범와의 출토위치를 통해 월성해자의 시기적인 변천이 어떻게 이루어 졌는지와 주변유적인 안압지와의 연관성도 살펴볼 수 있다. 현재 와범이 확인되지 않아 역으로 막새들의 세부적 특징을 비교해 동범와를 파악할 수 밖에 없는 실정이 다. 하지만 여기서는 동범와라는 용어사용에 있어 동범요소의 정확한 확인 후에 사용되어져야 함을 강조하고, 월성해자 동범와를 통해 월성해자의 지역별 시기를 알아보았다.

• Water Engineering Research
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• 제1권1호
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• pp.63-74
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• 2000

This paper presents a two- phase search scheme for optimal pipe expansion of expansion of existing water distribution systems. In pipe network problems, link flows affect the total cost of the system because the link flows are not uniquely determined for various pipe diameters. The two-phase search scheme based on stochastic optimization scheme is suggested to determine the optimal link flows which make the optimal design of existing pipe network. A sample pipe network is employed to test the proposed method. Once the best tree network is obtained, the link flows are perturbed to find a near global optimum over the whole feasible region. It should be noted that in the perturbation stage the loop flows obtained form the sample existing network are employed as the initial loop flows of the proposed method. It has been also found that the relationship of cost-hydraulic gradient for pipe expansion of existing network affects the total cost of the sample network. The results show that the proposed method can yield a lower cost design than the conventional design method and that the proposed method can be efficiently used to design the pipe expansion of existing water distribution systems.

• 대한수학회지
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• 제52권4호
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.