• Journal of the Korean Mathematical Society
• /
• v.42 no.6
• /
• pp.1153-1167
• /
• 2005

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.2
• /
• pp.68.1-68.1
• /
• 2019

Turbulence plays a crucial role in controlling star formation as it produces density fluctuation as well as non-thermal pressure against gravity. Therefore, turbulence controls the mode and tempo of star formation. However, despite a plenty of previous studies, the properties of turbulence remain poorly understood. As part of the Taeduk Radio Astronomy Observatory (TRAO) Key Science Program (KSP), "mapping Turbulent properties In star-forming MolEcular clouds down to the Sonic scale (TIMES; PI: Jeong-Eun Lee)", we mapped the Orion A and the Ophiuchus clouds, in three sets of lines (13CO 1-0/C18O 1-0, HCN 1-0/HCO+ 1-0, and CS 2-1/N2H+ 1-0) with a high-velocity resolution (~0.1 km/s) using the TRAO 14-m telescope. The mean Trms for the observed maps are less than 0.25 K, and all these maps show uniform Trms values throughout the observed area. These homogeneous and high signal-to-noise ratio data provide the best chance to probe the nature of turbulence in two different star-forming clouds, the Orion A and Ophiuchus clouds. We present comparisons between the line intensities of different molecular tracers as well as the results of a Principal Component Analysis (PCA).

• Investigative Magnetic Resonance Imaging
• /
• v.1 no.1
• /
• pp.119-124
• /
• 1997

Purpose: To assess the utility of magnetic resonance(MR) cerebral blood volume (CBV) map in the evaluation of brain tumors. Materials and Methods: We performed perfusion MR imaing preoperatively in the consecutive IS patients with intracranial masses(3 meningiomas, 2 glioblastoma multiformes, 3 low grade gliomas, 1 lymphoma, 1 germinoma, 1 neurocytoma, 1 metastasis, 2 abscesses, 1 radionecrosis). The average age of the patients was 42 years (22yr -68yr), composed of 10 males and S females. All MR images were obtained at l.ST imager(Signa, CE Medical Systems, Milwaukee, Wisconsin). The regional CBV map was obtained on the theoretical basis of susceptibility difference induced by first pass circulation of contrast media. (contrast media: IScc of gadopentate dimeglumine, about 2ml/sec by hand, starting at 10 second after first baseline scan). For each patient, a total of 480 images (6 slices, 80 images/slice in 160 sec) were obtained by using gradient echo(CE) single shot echo-planar image(EPI) sequence (TR 2000ms, TE SOms, flip angle $90^{\circ}$, FOV $240{\times}240mm,{\;}matrix{\;}128{\times}128$, slice-thick/gap S/2.S). After data collection, the raw data were transferred to CE workstation and rCBV maps were generated from the numerical integration of ${\Delta}R2^{*} on a voxel by voxel basis, with home made software (${\Delta}R2^{*}=-ln (S/SO)/TE). For easy visual interpretation, relative RCB color coding with reference to the normal white matter was applied and color rCBV maps were obtained. The findings of perfusion MR image were retrospectively correlated with Cd-enhanced images with focus on the degree and extent of perfusion and contrast enhancement. Results: Two cases of glioblastoma multiforme with rim enhancement on Cd-enhanced Tl weighted image showed increased perfusion in the peripheral rim and decreased perfusion in the central necrosis portion. The low grade gliomas appeared as a low perfusion area with poorly defined margin. In 2 cases of brain abscess, the degree of perfusion was similar to that of the normal white matter in the peripheral enhancing rim and was low in the central portion. All meningiomas showed diffuse homogeneous increased perfusion of moderate or high degree. One each of lymphoma and germinoma showed homogenously decreased perfusion with well defined margin. The central neurocytoma showed multifocal increased perfusion areas of moderate or high degree. A few nodules of the multiple metastasis showed increased perfusion of moderate degree. One radionecrosis revealed multiple foci of increased perfusion within the area of decreased perfusion. Conclusion: The rCBV map appears to correlate well with the perfusion state of brain tumor, and may be helpful in discrimination between low grade and high grade gliomas. The further study is needed to clarify the role of perfusion MR image in the evaluation of brain tumor.