• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.763-780
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• 2020

Let R be a commutative ring. An R-module M is said to be w-flat if Tor ^R₁ (M, N) is GV -torsion for any R-module N. It is known that every flat module is w-flat, but the converse is not true in general. The w-flat dimension of a module is defined in terms of w-flat resolutions. In this paper, we study the w-flat dimension of an injective w-module. To do so, we introduce and study the so-called w-copure (resp., strongly w-copure) flat modules and the w-copure flat dimensions for modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. We also study change of rings theorems for the w-copure flat dimension in various contexts. Finally some illustrative examples regarding the introduced concepts are given.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.66.1-66.1
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• 2011

천체망원경을 이용한 측광관측은 주로 CCD를 이용하여 이루어지고 있으며, CCD를 이용한 측광관측은 CCD를 구성하는 픽셀마다 양자효율이 일정하지 않기 때문에 Flat 관측을 이용하여 보정을 하고 있다. 한편, Flat 관측은 주로 빈 하늘을 찍는 Sky Flat 방법을 이용하고 있으나, Sky Flat을 관측하는 방법은 계절에 따라 시작 시간이 다르고, 제한적인 관측 시간 내에 관측자의 판단으로 이루어지고 있는 실정이다. 특히 제한적인 관측시간은 관측자의 상당한 신중함을 요구하고 있어 노출시간 조절 및 시작 시간을 지나게 되면 Sky Flat 영상을 얻지 못하는 경우도 있다. 이러한 제약 조건에서 효율적인 Flat관측을 하기위해 AutoFlat 프로그램을 개발하였다. AutoFlat 프로그램은 5초 노출로 빈 하늘을 찍으며 관측된 이미지에서 정해진 하늘의 밝기가 되면 자동으로 노출 시간을 계산하고, 각각의 필터별로 관측을 하는 동시에 적절한 이름을 주어 자동으로 저장하게 되어 있다. 이번 연구에서 개발한 AutoFlat 프로그램은 관측자가 Flat 관측을 진행하지 않아도 안정적이면서 효율적인 Flat 관측을 수행하여 앞으로 CCD를 이용한 측광 관측에서 유용하게 사용될 것으로 기대된다.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.203-218
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• 2013

Let R be a ring. A right R-module M is called GI-flat if $Tor^R_1(M,G)=0$ for every Gorenstein injective left R-module G. It is shown that GI-flat modules lie strictly between flat modules and copure flat modules. Suppose R is an $n$-FC ring, we prove that a finitely presented right R-module M is GI-flat if and only if M is a cokernel of a Gorenstein flat preenvelope K ${\rightarrow}$ F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various results in [6] are developed, some new characterizations of von Neumann regular rings are given.

• Journal of the Korean Association of Geographic Information Studies
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• v.3 no.1
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• pp.44-56
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• 2000

Through the ISODATA method of unsupervised classification, the micro-landform of Gomso-Bay tidal flat was classified into mud, mixed, and sand flats by using Landsat TM image. Each tidal flat shows on apparent differences in its topographical characteristics and grain size compositions. Mud flat is occupied the innermost part of the tidal flat. Sand flat is distributed adjacent to the entrance of the bay, while the mixed one is located in the central part of the bay. Mud flat deposits have fine grain size, more than 4 in average mean phi, bad sorting, more than 1 phi in standard devation, and positive skewness. Mixed and sand flat deposits have coarse grain size, less than 4 average mean phi, good sorting, less than 1 phi in standard daviation, and negative skewness. Topographically, the mud flat consists of flat surfaces and dissected channels. The average depth of dissected channels is about 2 meters. Meanwhile, sand flat has a very flat landform with well-developed ripple marks of less than 10 centimeters in average relief. And the mixed one shows the intermediate topographical characteristics of those of mud and sand flats.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05a
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• pp.111-114
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• 2005

While the existing reinforced concrete flat plate(RC flat plate) has a lot of advantages including reduced building height, it has some weak points such as many steel bars and the brittle rupture by punching shear. Compared with the RC flat plate, the post-tensioned flat plate (PT flat plate) has not only the same merits, but it also makes longer span possible and induces slab-column connections to be failed with the ductile behavior rather than with the brittle behavior by means of post-tensioning. However, it is difficult to define the joint behavior of PT flat plate under vertical and lateral loads since there are limit experimental results. For this reason, the experimental study is undertaken to investigate the comparison of behavior of PT flat plate and RC flat plate, and how flat plate(Gravity Load Resisting System) is displaced as lateral loads, like the wind and the earthquake, are occur. The result of this experiment shows that PT flat plate is generally superior to RC flat plate in terms of controlling crack, postponing stiffness deterioration, energy dissipation, etc.

• Journal of the Semiconductor & Display Technology
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• v.9 no.1
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• pp.61-66
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• 2010

A flat luminaire utilizing 32" flat fluorescent lamp was developed and its optical characteristics were compared with that of the troffer using three T8 regular fluorescent tubes. The optical characteristics of the 32" flat luminaire was similar to that of the troffer.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1359-1370
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• 2022

In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1483-1494
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• 2021

Let A and B be rings and U be a (B, A)-bimodule. If _BU has finite flat dimension, U_A has finite flat dimension and U ⊗_A C is a cotorsion left B-module for any cotorsion left A-module C, then the Gorenstein flat-cotorsion modules over the formal triangular matrix ring $T=\(\array{A&0\\U&B}\)$ are explicitly described. As an application, it is proven that each Gorenstein flat-cotorsion left T-module is flat-cotorsion if and only if every Gorenstein flat-cotorsion left A-module and B-module is flat-cotorsion. In addition, Gorenstein flat-cotorsion dimensions over the formal triangular matrix ring T are studied.

• Journal of Astronomy and Space Sciences
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• v.30 no.4
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• pp.327-334
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• 2013

The purpose of this study is to develop an observation program for obtaining effective flat images that are necessary for photometric observation. The development of the program was achieved by improving the existing method for obtaining twilight flat images. The existing method for obtaining twilight flat images acquires flat images by observing the sky light after sunset or light before sunrise. The decision of when to observe flat images at each night is solely dependent on the judgment of an observer, and thus the obtained flat images for particular nights may not be clean. Especially, in the case of the observatories where an automated observation system is in operation, there is a difficulty that an observer should pay attention during sunrise and sunset in order to obtain flat images. In this study, a computer program is developed to improve this inconvenience and to efficiently perform photometric observation in the observatories where an automated observation system is applied. This program can obtain flat images by calculating the time for obtaining flat images automatically and the exposure time using a numerically calculated function. When obtaining twilight flat images at dusk and at dawn, the developed program performs automated observation and provides effective flat images by acquiring appropriate exposure time considering the sunrise and sunset times that vary depending on the day of observation. The code for performing this task was added to Obs Tool II (Yoon et al. 2006), which is the automated observation system of the Chungbuk National University Observatory, and the usefulness of the developed program was examined by performing an actual automated observation. If this program is applied to other observatories where automated observation is in operation, it is expected that stable and high-quality flat images could be obtained, which can be used for the pre-processing of photometric observation data.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.611-620
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• 2002

The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\prod_{p\epsilonAtt_R(A)}T-p$, where $Tp$ is the completion of a free R$_{p}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $_AX$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\chiA$. This result leads to a description of the structure of a minimal flat resolution for ${H^n}_{\underline{m}}(R)$, nth local cohomology module of R with respect to the ideal $\underline{m}$, over a local Cohen-Macaulay ring (R, $\underline{m}$) of dimension n.