• Journal for History of Mathematics
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• v.24 no.4
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• pp.33-43
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• 2011

In this paper I discuss if we can regard Hilbert at the time of Hilbert's program as an instrumentalist. For this I first provide some textual evidences for the instrumentalist interpretation, then examine the three recent criticisms in turn. I argue that the reading Hilbert as an instrumentalist is still tenable in spite of these criticisms.

• Korean Journal of Logic
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• v.14 no.2
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• pp.1-38
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• 2011

Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this article tries to distinguish carefully between Hilbert's and Bernays' views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays' estimation of the place of Hilbert's achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays' criticism of Carnap, for Carnap's project of philosophy of science in the late 1950's seems to be a continuation and an extension of Hilbert's faith in the uniformity of the axiomatic method.

• Journal of Advanced Navigation Technology
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• v.16 no.2
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• pp.240-246
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• 2012

The Hilbert transform, which has been hitherto discussed in coherent imaging, is for the first time investigated in the context of incoherent imaging. Because the Hilbert transform of the information is superposed coherently with the original light field. We present a two-pupil optical heterodyne scanning system and analyze mathematically the design of its two pupils such that the optical system can perform the Hilbert transform on incoherent objects. In this paper, we review and formulate the definition of an analytic signal of a function and from which we can obtain the Hilbert transform of the function. and we analyze the design of pupils so as to obtain the Hilbert transform and show some 2-D simulations. Computer simulation results of the idea clarify the theoretical results.

• The KIPS Transactions:PartD
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• v.11D no.1
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• pp.23-30
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• 2004

In order to approximate the spatial query result size we partition the input rectangles into subsets and estimate the query result size based on the partitioned spatial area. In this paper we examine query result size estimation in skewed data. We examine the existing spatial partitioning techniques such as equi-area and equi-count partitioning, which are analogous to the equi-width and equi-height histograms used in relational databases, and examine the other partitioning techniques based on spatial indexing. In this paper we propose a new spatial partitioning technique based on the Hilbert space filling curve. We present a detailed experimental evaluation comparing the proposed technique and the existing techniques using synthetic as well as real-life datasets. The experiments showed that the proposed partitioning technique based on the Hilbert space filling curve achieves better query result size estimation than the existing techniques for space query size, bucket numbers, skewed data, and spatial data size.

• Journal of KIISE:Databases
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• v.37 no.4
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• pp.203-208
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• 2010

This paper deals with an efficient index scheduling technique based on Hilbert curve and MBR for k-NN query in a single wireless broadcast channel environment. Previous works have two major problems. One is that they need a long time to process queries due to the back-tracking problem. The other is that they have to download too many spatial data since they can not reduce search space rapidly. Our proposed method broadcasts spatial data based on Hilbert curve order where a distributed index table is also broadcast with each spatial data. Each entry of index table represents the MBR which groups spatial data. By predicting the unknown location of spatial data, our proposed index scheme allows mobile clients to remove unnecessary data and to reduce search space rapidly. As a result, our method gives the decreased tuning time and access latency.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10b
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• pp.46-48
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• 2003

최근 시공간 데이타에 대한 OLAP연산 효율을 증가시키기 위한 여러 가지 연구들이 행하여지고 있다. 이들 연구의 대부분은 다중트리구조에 기반하고 있다. 다중트리구조는 공간차원을 색인하기 위한 하나의 R-tree와 시간차원을 색인하기 위한 다수의 B-tree로 이루어져 있다. 하지만, 이러한 다중트리구조는 높은 유지비용과 불충분한 질의 처리 효율로 인해 현실적으로 시공간 OLAP연산에 적용하기에는 어려운 점이 있다. 본 논문에서는 이러한 문제를 근본적으로 개선하기 위한 접근 방법으로서 힐버트큐브(Hilbert Cube, H-Cube)를 제안하고 있다. H-Cube는 집계질의(aggregation query) 처리 효율을 높이기 위해 힐버트 곡선을 이용하여 셀들에게 완전순서(total-order)를 부여하고 있으며, 아울러 전통적인 누적합(prefix-sum) 기법을 함께 적용하고 있다. H-Cube는 적응적이며, 완전순서화되어 있으며, 또한 누적합을 이용한 셀 기반의 색인구조이다. 본 논문에서는 H-Cube의 성능 평가를 위해서 다양한 실험을 하였으며, 그 결과로서 유지비용과 질의 처리 효율성면 모두에서 다중트리구조보다 높은 성능 향상이 있음을 보인다.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1994.04a
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• pp.179-184
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• 1994

다입력/단일출력 모형을 이용하여 소음/진동원을 규명할 때 입력들간의 상관관계가 존재하면 이들 사이의 우선순위 결정은 매우 중요한 문제가 된다. 본 실험에서는, 이러한 상관관계를 입력들간에 구성되는 선형계 H$_{xy}$(f)로부터 힐버트 관계와 충격응답함수의 특성을 살핌으로써 우선순위를 결정하였으며, 부분 기여도함수 기법을 적용하여 차량의 실내 소음원과 전달경로에 대한 정보를 얻을 수 있었다. 그러나 충격응답함수와 전달함수의 힐버트 관계를 이용한 우선순위 결정법의 상대적인 차이점, 오차등에 대해서는 앞으로 더 연구 되어야 할 과제이다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1255-1265
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• 1992

Under uniform heat flow, the thermal stress intensity factors for the interfacial crack on a rigid cusp-type inclusion are determined by Hilbert problem expressed with complex variable. The thermal stress intensity factors are expressed in terms of the periodic function of heat flow angle. When the tip of the interfacial crack meets that of the cusp crack, the thermal stress intensity factors have singularities. The thermal stress intensity factors at the interfacial crack tip located in the distance from the cusp crack tip vary with the location of the interfacial crack tip. From the results of the analysis, the complex potential functions and the thermal stress intensity factors for the cusp-type inclusion without the interfacial crack are derived under the cusp surface boundary conditions insulated or fixed to zero relative temperature.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of KIISE:Databases
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• v.30 no.5
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• pp.451-463
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• 2003

Recently, there have been various research efforts to develop strategies for accelerating OLAP operations on huge amounts of spatio-temporal data. Most of the work is based on multi-tree structures which consist of a single R-tree variant for spatial dimension and numerous B-trees for temporal dimension. The multi~tree based frameworks, however, are hardly applicable to spatio-temporal OLAP in practice, due mainly to high management cost and low query efficiency. To overcome the limitations of such multi-tree based frameworks, we propose a new approach called Hilbert Cube(H-Cube), which employs fractals in order to impose a total-order on cells. In addition, the H-Cube takes advantage of the traditional Prefix-sum approach to improve Query efficiency significantly. The H-Cube partitions an embedding space into a set of cells which are clustered on disk by Hilbert ordering, and then composes a cube by arranging the grid cells in a chronological order. The H-Cube refines cells adaptively to handle regional data skew, which may change its locations over time. The H-Cube is an adaptive, total-ordered and prefix-summed cube for spatio-temporal data warehouses. Our approach focuses on indexing dynamic point objects in static spatial dimensions. Through the extensive performance studies, we observed that The H-Cube consumed at most 20% of the space required by multi-tree based frameworks, and achieved higher query performance compared with multi-tree structures.