• 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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1039-1052
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• 2021

In this paper, we introduce and study the class of 𝜙-w-flat modules which are generalizations of both 𝜙-flat modules and w-flat modules. The 𝜙-w-weak global dimension 𝜙-w-w.gl.dim(R) of a commutative ring R is also introduced and studied. We show that, for a 𝜙-ring R, 𝜙-w-w.gl.dim(R) = 0 if and only if w-dim(R) = 0 if and only if R is a 𝜙-von Neumann ring. It is also proved that, for a strongly 𝜙-ring R, 𝜙-w-w.gl.dim(R) ≤ 1 if and only if each nonnil ideal of R is 𝜙-w-flat, if and only if R is a 𝜙-PvMR, if and only if R is a PvMR.

• Proceedings of the KIPE Conference
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• 1999.07a
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• pp.577-580
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• 1999

High power density on-board power supply is implemented by using flat transformer. In the high frequency switching converters, large leakage inductance increases the switching stress and duty cycle loss, which sometimes limits maximum switching frequency. The flat transformer is designed by using special core structure, which has very low profile and low temperature rise since the thermal loading is spread evenly over a larger area. 100W, 3.3V output on board supply is built and tested and 50.7W/$\textrm{inch}^{3}$ power density is achieved.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.25-35
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• 2013

In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1289-1304
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• 2022

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.711-712
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• 2009

• The Transactions of the Korean Institute of Power Electronics
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• v.10 no.3
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• pp.248-256
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• 2005

This paper presents the design method of the DC/DC converter using flat transformer which is suitable for midium or large capacity and high density power supply. Flat transformer module is composed and manufactured of multi-transformers in parallel and has a number of parallel single turn secondary windings. Therefore, its leakage inductance is highly decreased and it is more suitable for high frequency operation than conventional one. In this paper, we manufactured and tested 750W AC/DC converter with variable output powers to verify the performance of the flat transformer.

• Korean Journal of Remote Sensing
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• v.27 no.4
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• pp.411-420
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• 2011

In this study, a digital elevation model (DEM) in tidal flat of Suncheon Bay, one of the most ecological preserved area in the world, was generated from digital aerial stereo-images. The focal lengths for the aerial stereo-images were adjusted using ground control points (GCPs) in order to improve the accuracy of camera parameters. We proposed matching sizes suitable for generating DEM in tidal flat and a method for eliminating excessive position errors using intersection-distance($P_R$) threshold value. The accuracies of the DEM generated from the proposed method as well as the commercial S/W were compared with the elevation profiles measured by Total Station in the filed. As the results, the DEM generated by the proposed method showed better result (maximum deviation is a -21 centimeters) with detailed topography than DEM by the commercial S/W in the region. These results suggest that the DEM of tidal flat, which hardly obtained with the traditional methods, can be generated from digital aerial images by applying the proposed method in this study. We believe that the generated DEM in tidal flat can be an essential data for monitoring the sediment erosion and deposit of the tidal flat.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1327-1338
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• 2015

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).