• 대한수학회보
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• 제59권5호
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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.

• 대한수학회보
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• 제22권2호
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• East Asian mathematical journal
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• 제24권2호
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• pp.139-144
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• 2008

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal($\phi$). Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope E[$x^{-1}$] of an inverse polynomial module M[$x^{-1}$] as a left R[x]-module and we can define an associative Galois group Gal(${\phi}[x^{-1}]$). In this paper we extend the Galois group of inverse polynomial module and can get Gal(${\phi}[x^{-s}]$), where S is a submonoid of $\mathds{N}$ (the set of all natural numbers).

• 약학회지
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• 제24권3_4호
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• pp.151-157
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• 1980

Color transition mechanism of shikonin as an acid-alkali indicator was studied. It was confirmed that the presence of phenolic hydroxy radical was essential for the color change of shikonin. But in accordance with shikonin sodium salt (blue color), which was presumed to make chelation as six membered rings. Shikonin in alkaline solution, by dissociated phenolic protons of naphthoquinone nucleous, converted to the corresponding anion and instead of disappearance tautomerization, electron delocalization occurred and an additional pair of nonbonding electrons in the anion was available for interaction with .phi. electron system of the ring with further extension of the conjugation. It was responsible for its blue color(corresponding color: orange) with needs less energy difference (${\phi}{\rarw}{\phi}^{*}$) because of conjugation extension. Shikonin sodium salt seems to have similar nuclear structure as shikonin anion.

• 대한수학회지
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• 제58권6호
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 하계학술대회 논문집 A
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• pp.92-94
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• 1995

This paper is to describe a method for calculating resistance of cage rotor end-ring, based on 3-D finite element method using magnetic vector potential $\vec{A}$ and electric scalar potential ${\phi}$. The induced current of a cage rotor flows through the bars of a cage rotor. The current completes their closed paths by passing around the end-ring. The end-ring may contribute a significant influence to the performance of machine. The resistance under consideration of skin effect is calculate by using Joule's loss equation.

• 대한금속재료학회지
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• 제49권1호
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• pp.85-91
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• 2011

Alnico magnets can be used as magnetic bearings for the precise electric power measuring instruments such as watt-hour meters because they have high remanence ($B_r$), relatively high maximum energy product ($(BH)_{max}$), and excellent temperature stability. In this study, Alnico composite magnets were fabricated by appropriately mixing alnico alloy powders with epoxy resin and binder. The Alnico powders mixed with epoxy resin and a hardening agent with a mixing ratio of 96:4 were pressed and then cured to be a toroid-type ring magnet with an outer diameter (${\Phi}_{out}$) of 15 mm, an inner diameter (${\Phi}_{in}$) of 6.5 mm and a thickness (t) of 2.5 mm, respectively. The magnetic properties of the Alnico ring magnets were varied with the mixing ratio of Alnico powders that possess different average particle sizes. The Alnico ring magnet prepared by mixing 5 wt% of $50{\mu}m$ (small size) powder, 15~20 wt% of $150{\mu}m$ (medium size) powder, and 75~80 wt% of $300{\mu}m$ (large size) powder showed the best magnetic properties (remanent induction, coercive force, maximum energy product, and surface flux density). In addition, measurements of temperature and moisture characteristics for the Alnico ring magnets showed that the surface flux densities of the N and S poles decreased little and the repulsive distance between the magnets decreased as small as 0.05 mm after 10 days.

• 대한수학회보
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• 제30권1호
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• International Journal of Naval Architecture and Ocean Engineering
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• 제8권5호
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• pp.456-465
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• 2016

In order to optimize the performance of a Wells turbine with fixed guide vanes, the designs of an end plate and a ring on the tip of the turbine rotor are proposed as penetrating blade tip treatments. In this study, numerical investigations are made using computational fluid dynamics (CFD)-based ANSYS Fluent software, and validated by corresponding experimental data. The flow fields are analyzed and non-dimensional coefficients $C_A$, $C_T$ and ${\eta}$ are calculated under steady-state conditions. Numerical results show that the stalling phenomenon on a ring-type Wells turbine occurs at a flow coefficient of ${\phi}=0.36$, and its peak efficiency can reach 0.54, which is 16% higher than that of an unmodified turbine and 9% higher than in the case of an endplate-type turbine. In addition, quasi-steady analysis is used to calculate the mean efficiency and output work of a wave cycle under sinusoidal flow conditions. As a result, it has been found that the ring-type turbine is superior to other types of Wells turbines.

• Bulletin of the Korean Chemical Society
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• 제13권2호
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• pp.155-157
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• 1992

Extensive search over the energy surface of bicyclo[4.2.2]decapentaene with MMP2 molecular mechanics method and AM1 semiempirical MO method revealed only one, deep energy minimum structure, which corresponds to 1. The alternative structure 2 could not be identified as a stationary point. Although the deviation of benzenoid ring from planarity is large in the energy minimum structure (${\phi} = 26^{\circ}$(MMP2), $37^{circ}$ (AM1)), the bond lengths show no severe alternation.