• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.269-273
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• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.443-456
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• 2005

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $L(G){\rightarrow}G$ denote the exponential mapping. For $S{\subseteq}G$, we define the tangent set of S by $L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras

• Development and Reproduction
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• v.4 no.1
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• pp.67-77
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• 2000

Snailfish usually lives at the bottom of the sea and showed typical retrogressive change with specialized tissue structures of skin and skeletons. In order to obtain the specific genes of snailfish, highly expressed in the body, we made subtracted cDNA library and analyzed 200 clones. Totally 200 clones were obtained and sequenced, and among them 62 clones were turned out to be homologous to the known gene, i.e., thioesterase (9), myosin (8), creatine kinase (7), skeletal alpha-actin (6), parvalbumin b (5), ribosomal protein (5), type I collagen (3), muscle troponin (3), dopamine receptor (2), histatin (2), and heat shock protein (2), cystatin (1), lectin (1), statherin (1), secretory carrier membrane protein (1), keratin type I (1), desmin (1), chloroplast (1), muscle tropomyosin (1), reticulum calcium ATPase (1), ribonucleoprotein (1). The remaining 138 clones were low homologous or non-redundant genes through Genbank search. Especially 5 clones were novel and specifically expressed in the body tissues of Snailfish by in situ hybridization. Therefore, we analysed these 5 clones to identify the C-terminal protein structures and motifs, and partly defined the roles of these proteins in comparison with the expression patterns by in situ hybridization. C9O-77, about 5000 bp, was supposed to be a matrix protein expressed strongly positive in epithelium, myxoid tissue, fibrous tissue and collagenous tissue. C9O-116, about 1500 bp, was supposed to be a transmembrane protein which was weakly expressed in the fibrous tissue, epithelium tissue, and myxoid tissue, but strong in muscle tissue. C9O-130, about 1200 bp, was supposed to be an intracytoplasmic molecule usually in the epithelial cells. C9O-161, about 2000 bp, was weakly expressed in epithelium, muscle tissue and myxoid tissue, but specially strong in epithelium. C9O-171, about 1000 bp, was supposed to be a transcription factor containing zinc finger like domain, which was intensely expressed in the epithelium, muscle tissue, fibrous tissue, and in collagenous tissue.