• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.611-620
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• 2002

The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\prod_{p\epsilonAtt_R(A)}T-p$, where $Tp$ is the completion of a free R$_{p}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $_AX$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\chiA$. This result leads to a description of the structure of a minimal flat resolution for ${H^n}_{\underline{m}}(R)$, nth local cohomology module of R with respect to the ideal $\underline{m}$, over a local Cohen-Macaulay ring (R, $\underline{m}$) of dimension n.

• Progress in Medical Physics
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• v.19 no.2
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• pp.102-112
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• 2008

We developed a high-resolution micro-CT system based on rotational gantry and flat-panel detector for live mouse imaging. This system is composed primarily of an x-ray source with micro-focal spot size, a CMOS (complementary metal oxide semiconductor) flat panel detector coupled with Csl (TI) (thallium-doped cesium iodide) scintillator, a linearly moving couch, a rotational gantry coupled with positioning encoder, and a parallel processing system for image data. This system was designed to be of the gantry-rotation type which has several advantages in obtaining CT images of live mice, namely, the relative ease of minimizing the motion artifact of the mice and the capability of administering respiratory anesthesia during scanning. We evaluated the spatial resolution, image contrast, and uniformity of the CT system using CT phantoms. As the results, the spatial resolution of the system was approximately the 11.3 cycles/mm at 10% of the MTF curve, and the radiation dose to the mice was 81.5 mGy. The minimal resolving contrast was found to be less than 46 CT numbers on low-contrast phantom imaging test. We found that the image non-uniformity was approximately 70 CT numbers at a voxel size of ${\sim}55{\times}55{\times}X100\;{\mu}^3$. We present the image test results of the skull and lung, and body of the live mice.