• 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.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.

• 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).

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.97-112
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• 2023

In this paper, we introduce and study the u-S-weak global dimension u-S-w.gl.dim(R) of a commutative ring R for some multiplicative subset S of R. Moreover, the u-S-weak global dimensions of factor rings and polynomial rings are investigated.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.563-589
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• 2019

Let W and V be manifolds of dimension m + 2, M a locally flat submanifold of V whose dimension is m. Let $f:W{\rightarrow}V$ be a homotopy equivalence. The problem we study in this paper is the following: When is f homotopic to another homotopy equivalence $g:W{\rightarrow}V$ such that g is transverse regular along M and such that $g{\mid}g^{-1}(M):g^{-1}(M){\rightarrow}M$ is a simple homotopy equivalence? $L{\acute{o}}pez$ de Medrano (1970) called this problem the weak h-regularity problem. We solve this problem applying the codimension two surgery theory developed by the author (1973). We will work in higher dimensions, assuming that $$m{\geq_-}5$$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• The Research Journal of the Costume Culture
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• v.16 no.5
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• pp.852-862
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• 2008

The purpose of this paper is to find how to do the width of skirt and the girth of the waist in the adequate pattern making for the obese women's skirt. Appearance test of the five experimental skirts was evaluated by the four experts in clothing construction. At the same time, 3D clothing air volume was observed for the five types of experimental skirt with different size specifications. The results from the appearance test were as follows; when the width of skirt pattern is set for(the shell girth/2), it was suggested w/4+1(front), w/4(back) for girth of the waist. On one hand, in case of (the shell girth of front)/2+(the shell girth of back)/2, it was suggested(the waist girth of front)/2 and(waist girth of back)/2 for obese women's skirt with the best appearance. As results, it was found that the width of skirt pattern for the obese women should be the greatest shell girth instead of hip girth. In the case of the hip girth, the amount of ease on hip was suggested 6cm. It was found that pattern with the wrinkle of ease was full of the gaps between body and skirt in 3D clothing air volume. In spreading out to 2D flat pattern from 3D scan data, when the width of skirt pattern was set for(the shell girth of front)/2+(the shell girth of back)/2, it was suggested(the waist girth of front/2)+(the waist girth of back/2) than the shell girth/2 in girth of the waist for the best appearance. And the conversion of 3D scan data into 2D flat pattern in curve shape of crosswise had to spread out of the plane in straight line. The obese women's clothing should be manufactured with systematical consideration of the diversity and scarcity of the obese women's body shape.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2130-2135
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• 2007

Operating characteristics of a loop heat pipe (LHP) having a bypass line was investigated experimentally. The LHP had a sintered metal wick as a capillary structure and methanol as a working fluid. The sintered metal wick was made of stainless steel of which the average pore size was 5 ${\mu}m$and porosity of 47%. A bypass line of a small diameter was attached between the vapor escape passage and the liquid reservoir. The dimension of the flat evaporator was $50(L){\times}40(W){\times}30(H)$ mm and that of the condenser was $50(L){\times}40(W){\times}11(H)$ mm. Wall and pipe material of the LHP was stainless steel and heating area was 35(W) mm${\times}$35(L) mm. The inner diameters of vapor and liquid transport lines were 4.0 mm and 2.0 mm, and the lengths of the two lines were both 0.5 m. The LHP was tested for three different tilt angles of horizontal, favorite tilt, and adverse tilt. The thermal load range was up to 290 W at the condenser above evaporation position. Furthermore, the effect of a bypass line on the start-up transient as well as steady-state operation was presented and discussed.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.11 no.1
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• pp.41-55
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• 2003

A calibration jet system using separate blower is developed to calibrate a flow sensor effectively. Designed open circuit type mini calibration jet system, which has the dimension of $0.5m(W){\times}1.17m(H)$ is small compared with conventional calibration jet systems. The exit of nozzle has exchangeable contractions with a cross section area of $38.5cm^2$ , and a cross section area of $113.1cm^2$, respectively. The ranges of wind speed at exit of exchangeable nozzles are $7.5{\sim}42\;m/s$ and $1.8{\sim}16.5\;m/s$, respectively. The input power for the high pressure blower is 1.18kW. The turning vanes for corner was rolled flat plate parallel to the flow direction. The flow conditioning screen was located immediately downstream of the wide-angle diffuser. The honeycomb and two flow conditioning screens were located in the stagnation chamber. From the economical point of view and the simplicity of the calibration jet system set up and handling, it can be said that the developed calibration jet system is an effective calibration jet system. This system can also be used to calibrate the flow sensor with high resolution.