Let g0(N) be the genus of the modular curve X0(N). We record several properties of the sequence {g0(N)}. Even though the average size of g0(N) is (1.25/π )N , a random positive integer has probability zero of being a value of g0(N). Also, if N is a random positive integer then g0(N) is odd with probability one.

Let g0(N) be the genus of the modular curve X0(N). We record several properties of the sequence {g0(N)}. Even though the average size of g0(N) is (1.25/π)N , a random positive integer has probability zero of being a value of g0(N). Also, if N is a random positive integer then g0(N) is odd with probability one.

Let M0 = G0/H be a (n+1)-dimensional Cahen-Wallach Lorentzian symmetric space associated with a symmetric decomposition g0 = h + m and let S(M0) be the spin bundle defined by the spin representation ρ : H → GLR(S) of the stabilizer H . This article studies the superizations of M0, i.e. its extensions to a homogeneous supermanifold M = G/H whose sheaf of superfunctions is isomorphic to Λ(S∗(M0))...

Here we classify finite non-Dedekindian p-groups which are not generated by their non-normal subgroups. (Theorem 1). The purpose of this paper is to classify non-Dedekindian finite p-groups which are not generated by their non-normal subgroups. It is surprising that such p-groups must be of class 2 with a cyclic commutator subgroup. We consider here only finite p-groups and our notation is stan...

In comparing gene expression of normal and CML CD34+ quiescent (G0) cell, 292 genes were downregulated and 192 genes upregulated in the CML/G0 Cells. The differentially expressed genes were grouped according to their reported functions, and correlations were sought with biological differences previously observed between the same groups. The most relevant findings include the following. (i) CML ...

A possible notion of superspace associated to a given 3-dimensional Lie algebra g0 might be a Lie superalgebra g g0 ⊕ g1. If one is to introduce a minimal set of assumptions, it seems quite natural to consider those superalgebras for which g1 g0 and for which the g0 action on g1 is the adjoint representation. A complete classification of the real and complex 3, 3 -dimensional Lie superalgebras ...

We report here the isolation of 44 genes that are upregulated after serum starvation and/or contact inhibition. These genes have been termed TIGA, after Transcript Induced by Growth Arrest. We found that there are two kinds of G0 phases caused by serum starvation, namely, the shallow G0 (or G0/G1) and the deep G0 phases. The shallow G0 is induced by only a few hours of serum starvation, while d...

The CCAAT enhancer-binding protein (C/EBP) family of transcription factors is implicated in the regulation of cell proliferation and differentiation in a variety of tissues. C/EBPd is involved in regulating G0 growth arrest and apoptosis of mouse mammary epithelial cells. This study shows that activation of signal transducer and activator of transcription 3 (Stat3), but not activation of Stat1 ...

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra over k and σ an involutory automorphism of g. Then g = g0 ⊕ g1 is the direct sum of σ-eigenspaces. Here g0 is a reductive subalgebra and g1 is a g0-module. Let G be the adjoint group of g and G0 ⊂ G a connected subgroup with LieG0 = g0. The commuting variety of (g, g0) is the follow...

We report that eucaryotic cells were induced to synthesize a specific class of heat shock proteins (hsps) when they entered the resting state, G0. This finding was originally made with Saccharomyces cerevisiae cells by taking advantage of the system in which we can distinguish between G1 arrests leading to G0 and those that do not result in G0 (Iida, H., and I. Yahara, 1984, J. Cell Biol. 98:11...