• Bulletin of the Korean Chemical Society
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• v.33 no.12
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• pp.4079-4083
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• 2012

The mechanism of the cycloaddition reaction between singlet state dichlorosilylene germylidene ($Cl_2Si=Ge:$) and acetone has been investigated with B3LYP/6-$31G^*$ and B3LYP/6-$31G^{**}$ method, from the potential energy profile, we predict that the reaction has one dominant reaction pathway. The presented rule of the reaction is that the two reactants firstly form a Si-heterocyclic four-membered ring germylene through the [2+2] cycloaddition reaction. Because of the 4p unoccupied orbital of Ge atom in the Si-heterocyclic four-membered ring germylene and the ${\pi}$ orbital of acetone forming a ${\pi}{\rightarrow}p$ donor-acceptor bond, the Si-heterocyclic four-membered ring germylene further combines with acetone to form an intermediate. Because the Ge atom in the intermediate hybridizes to an $sp^3$ hybrid orbital after the transition state, then, the intermediate isomerizes to spiro-heterocyclic ring compound involving Si and Ge (P4) via a transition state.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.97-103
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• 2010

It is well known that the group ring K[G] has the nontrivial Jacobson radical if K is a field of characteristic p and G is a finite group of which order is divided by a prime p. This paper is concerned with the structure of the Jacobson radical of such a group ring.

• Cement Symposium
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• no.1
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• pp.64-68
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• 1973

One of the most difficult problems in cement rotary kiln operation must be ring and coating formation. In the Dopol kiln with the capacity of 1,500 t/d($4.4m\phi\times70mL$, meal rings have been accreted on transit zone and end of the kiln and

• Clinical and Experimental Pediatrics
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• v.51 no.4
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• pp.426-430
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• 2008

We report clinical, cytogenetic, and fluorescence in situ hybridization (FISH) studies of a patient with ring chromosome 9. She presented with failure to thrive, facial dysmorphysm and mild psychomotor development delay in the absence of major malformations. Peripheral blood karyotype of the patient was 46,XX,r(9)(p24q34). G-band analysis suggested no loss of material in the ring chromosomes. FISH analysis using the subtelomere-specific sequences on chromosome 9p and 9q, revealed 46,XX,r(9)(p24q34),ish r(9)(D9S913-,D9S325+). Failure to detect any hybridization of a probe for the subtelomeric sequences in the ring 9p terminal suggested that this ring arose from breakage in the distal short arm. The cytogenetic and FISH data in our case provided further evidence for the existence of a "complete ring" phenotype with incomplete subtelomeric sequences.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.381-401
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• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• Bulletin of the Korean Chemical Society
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• v.23 no.11
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• pp.1629-1634
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• 2002

Reaction of tetrahomodioxa p-phenylcalix[4]arene with alkyl halide and NaH in DMF leads to the title tetra-alkylated derivatives, 7,13,21,27-tetra-phenyl-29,30,31,32-tetraalkyloxy-2,3,16,17-tetrahomo-3,17-dioxacalix [4]arenes, their preferred conformations were determined by NMR spectra as C-1,2-alternate. The molecular structure of allyl derivative has been solved by X-ray diffraction methods. The molecules have a conformation with pseudo center of symmetry. The benzene ring A is up, ring C is down, B and D rings are flat with respect to the plane of the macrocyclic ring.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.61-64
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• 1993

In this paper, we show that if R is a local-global domain then the Question holds. McDonald and Waterhouse in [6] and Estes and Guralnick in [5] introduced the concept of local-global rings (so called rings with many units) independently. A local-global ring is a commutative ring R with 1 satisfying; if a polynomial f in R[ $x_{1}$, .., $x_{n}$] represents a unit over $R_{P}$ for every maximal ideal P in R, then f represents a unit over R. Such rings include semilocal rings, or more generally, rings which are von Neumann regular mod their Jacobson radical, and the ring of all algebraic integers.s.s.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.727-735
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• 2021

In this paper, we will study the structure of the quotient ring R/P of an arbitrary ring R by a prime ideal P. We do so using differential identities involving generalized derivations of R. We enrich our results with examples that show the necessity of their assumptions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.311-317
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• 2018

Let (R, m) be a commutative Noetherian local ring and I be an ideal of R. In this paper it is shown that if cd(I, R) = t > 0 and the R-module $Hom_R(R/I,H^t_I(R))$ is finitely generated, then $$t={\sup}\{{\dim}{\widehat{\hat{R}_p}}/Q:p{\in}V(I{\hat{R}}),\;Q{\in}mAss{_{\widehat{\hat{R}_p}}}{\widehat{\hat{R}_p}}\;and\;p{\widehat{\hat{R}_p}}=Rad(I{\wideha{\hat{R}_p}}=Q)\}$$. Moreover, some other results concerning the cohomological dimension of ideals with respect to the rings extension $R{\subset}R[X]$ will be included.

• The Journal of Korean Academy of Prosthodontics
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• v.16 no.1
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• pp.45-47
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• 1978

We use investment to retain the mould of the wax pattern in making dental metal castings. A fin on the metal casting is occasionally formed due to several factors. The factors making the fin are improper burn out time and temperature, improper W/P ratio of investment and lining of asbestos in casting ring. The purpose of this study is to investigate the effect of W/P ratio of investment on the fin formation. Except the W/P ratio of investment which used to invest the wax pattern, the study was done under same condition; burn out time and temperature, W/P ratio of refractory cast(W/P=0.12) and asbestos lining in casting ring. The obtained result is that the fin is more likely to be formed on the casting which invested with higher W/P ratio of investment to that of refractory cast.