• Nuclear Engineering and Technology
• /
• v.31 no.4
• /
• pp.423-431
• /
• 1999

A radiotracer technique has been developed to monitor the rotational movement of two piston rings in one cylinder during engine operation. The rings were labeled with two different kinds of radioisotopes, i.e. $^{60}$ Co and $^{192}$ Ir, for identification of the top ring from the second ring. The radiotracers were implanted in a small hole bored on the inner side of each piston ring. The rings were installed in a single cylinder hydrogen engine and three Nal scintillation detectors were mounted around the engine block to measure the gamma radiation. The angle of ring-gap orientation was determined from the radiation counts measured with the three detectors during engine operation. Two windows (upper window for $^{60}$ Co and lower window for $^{192}$ Ir) were set on each ratemeter to count radiation from the two isotopes separately. Procedure to convert the radiation counts to the position of the ring gap was established. With the software programmed with MS-Visualbasic, radiation counts were compared with the reference responses that were measured at angular intervals of 10$^{\circ}$for each piston ring in advance of the experiment. The result was used for the evaluation of the relationship between the orientation of ring-gaps and oil consumption. It was found that an increase in the oil consumption rate of a specific operation condition was closely related to the relative phase angle of the two piston rings.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1603-1608
• /
• 2011

Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.

• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.77-85
• /
• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.21-28
• /
• 2015

Let R be a prime ring with center Z, I a nonzero ideal of R, and ${\sigma}$ a non-trivial automorphism of R such that $\{(x{\circ}y)^{\sigma}-(x{\circ}y)\}^n{\in}Z$ for all $x,y{\in}I$. If either char(R) > n or char (R) = 0, then R satisfies $s_4$, the standard identity in 4 variables.

• Journal of the Korean Chemical Society
• /
• v.13 no.4
• /
• pp.341-346
• /
• 1969

The synthesis and pyrolysis of trans-2-butenedial ditosylhydrazone with sodium methoxide in aprotic solvents have been studied to investigate the products of pyrolysis. The pyrolysis of dry lithium salt of tosylhydrazone also has been made, one of its products was acetylene which might come from a certain strained ring compound.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.101-106
• /
• 2006

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.819-826
• /
• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• Nuclear Medicine and Molecular Imaging
• /
• v.41 no.2
• /
• pp.118-131
• /
• 2007

Neurotransmitter imaging with radiopharmaceuticals plays major role for understanding of neurological and psychiatric disorders such as Parkinson's disease and depression. Radiopharmaceuticals for neurotransmitter imaging can be divided to dopamine transporter imaging radiopharmaceuticals and serotonin trnasporter imaging radiopharmaceuticals. Many kinds of new dopamine transporter imaging radiopharmcaeuticals has a tropane ring and they showed different biological properties according to the substituted functional group on tropane ring. After the first clinical trials with $[^{123}I]{\beta}-CIT$, alkyl chain substituent introduced to tropane ring amine to decrease time for imaging acquisition and to increase selectivity. From these results, $[^{123}I]PE2I$, [18F]FE-CNT, $[^{123}I]FP-CIT$ and $[^{18}F]FP-CIT$ were developed and they showed high uptake on the dopamine transporter rich regions and fast peak uptake equilibrium time within 4 hours after injection. $[^{11}C]McN$ 5652 was developed for serotonin trnasporter imaging but this compound showed slow kinetics and high background radioactivity. To overcome these problems, new diarylsulfide backbone derivatives such as ADAM, ODAM, AFM, and DASB were developed. In these candidates, $[^{11}C]AFM$ and $[^{11}C]DASB$ showed high binding affinity to serotonin transporter and fast in vivo kinetics. This paper gives an overview of current status on dopamine and serotonin transporter imaging radiopharmaceuitcals and the development of new lead compounds as potential radiopharmaceuticals by medicinal chemistry.

• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1253-1270
• /
• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.407-417
• /
• 2020

Let (R, m) be a d-dimensional Cohen-Macaulay local ring with infinite residue field. Let I be an ideal of R that has analytic spread ℓ(I) = d, satisfies the G_d condition, the weak Artin-Nagata property AN^-_d-2 and m is not an associated prime of R/I. In this paper, we show that if j₁(I) = λ(I/J) + λ[R/(J_d-1 :_RI+(J_d-2 :_RI+I):_R m^∞)] + 1, then I has almost minimal j-multiplicity, G(I) is Cohen-Macaulay and r_J(I) is at most 2, where J = (x₁, _…, x_d) is a general minimal reduction of I and J_i = (x₁, _…, x_i). In addition, the last theorem is in the spirit of a result of Sally who has studied the depth of associated graded rings and minimal reductions for m-primary ideals.