Nucleation of superconductivity in an overcooled normal domain

Daerah integral R dikatakan perinormal jika untuk setiap overring (lokal) T dari R yang memenuhi kondisi going-down, maka T merupakan lokalisasi dari R pada ideal prima. Perinormalitas merupakan salah satu sifat ketertutupan integral. Dengan memperhatikan bahwa klosur integral dari daerah normal Noether merupakan daerah Krull, akan ditunjukkan bagaimana sifat perinormalitas di daerah Krull.An integral domain R is said to be perinormal if whenever T is a (local) overring of R such that the inclusion R in T satisfies going-down, it follows that T is a localization of R necessarily at a prime ideal. Perinormality is one of integral closedness property. As the integral closure of any Noetherian normal domain is Krull, it will be shown how perinormality behaves on Krull domains.

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Ectopic application of recombinant BMP-2 and BMP-4 can change patterning of developing chick facial primordia

Development ◽

10.1242/dev.124.2.391 ◽

1997 ◽

Vol 124 (2) ◽

pp. 391-398 ◽

Cited By ~ 3

Author(s):

A.J. Barlow ◽

P.H. Francis-West

Keyword(s):

Gene Expression ◽

Cell Proliferation ◽

Bone Morphogenetic Proteins ◽

Skeletal Development ◽

Normal Domain ◽

Spatial Order ◽

Correct Function ◽

Facial Development ◽

Palatine Bone ◽

Signalling Cascade

The facial primordia initially consist of buds of undifferentiated mesenchyme, which give rise to a variety of tissues including cartilage, muscle and nerve. These must be arranged in a precise spatial order for correct function. The signals that control facial outgrowth and patterning are largely unknown. The bone morphogenetic proteins Bmp-2 and Bmp-4 are expressed in discrete regions at the distal tips of the early facial primordia suggesting possible roles for BMP-2 and BMP-4 during chick facial development. We show that expression of Bmp-4 and Bmp-2 is correlated with the expression of Msx-1 and Msx-2 and that ectopic application of BMP-2 and BMP-4 can activate Msx-1 and Msx-2 gene expression in the developing facial primordia. We correlate this activation of gene expression with changes in skeletal development. For example, activation of Msx-1 gene expression across the distal tip of the mandibular primordium is associated with an extension of Fgf-4 expression in the epithelium and bifurcation of Meckel's cartilage. In the maxillary primordium, extension of the normal domain of Msx-1 gene expression is correlated with extended epithelial expression of shh and bifurcation of the palatine bone. We also show that application of BMP-2 can increase cell proliferation of the mandibular primordia. Our data suggest that BMP-2 and BMP-4 are part of a signalling cascade that controls outgrowth and patterning of the facial primordia.

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