SO(p, q) = {g ∈ SLp+q(R) : g>Qg = Q} (where Q = ( 1p 0 0 −1q ) )  SU(2) −→ SO(3) SL2(R) −→ SO(2, 1) SU(2)× SU(2) −→ SO(4) SL2(C) −→ SO(3, 1) SL2(R)× SL2(R) −→ SO(2, 2) Sp∗(2, 0) −→ SO(5) Sp∗(1, 1) −→ SO(4, 1) Sp2(R) −→ SO(3, 2) SU(4) −→ SO(6) SL2(H) −→ SO(5, 1) SU(2, 2) −→ SO(4, 2) SL4(R) −→ SO(3, 3) Thus, these are small examples...

Proof of Proposition 1. Under (H2) we have g := infω,xG(x) > 0. Now consider the sequence of random variables {κn ;n ≥ 1} defined by κn := νQ ω n−1(1)g −. From (2.8) it is straightforward to establish by induction the following semigroup property: for any ω ∈ Ω, and p, n ≥ 0, Qp+n = Q ω pQ θpω n . Combined with (H2), this gives κp+n = νQ ω pQ θpω n−1(1)g − = νQp−1Q θωQθ pω n−1(1)g − ≥ κpκ pω n ...

Burkitt lymphomas (BLs) frequently show secondary chromosomal abnormalities. Here, the authors describe a case of BL with an unusual dual translocation of chromosome 14, t(8;14) and t(14;15), and partial duplication of 1q. This 5-yr-old female patient had several unfavorable prognostic factors including elevated serum lactate dehydrogenase activity and involvement of the central nervous system ...

Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdős, Joó and Komornik in 1990, is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y| : y = 0 + 1q + · · ·+ nq, i ∈ {±1, 0}, y 6= 0). Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. ...

The quality of the 20 in . photomultiplier tubes (Hamamatsu R1449) has been greatly improved over the required specifications for using them m the 50000 ton imaging water Cherenkov detector, Super-Kamiokande . In particular, the resolution of the timing response for single-photoelectron light has been reduced to 3 ns (1Q width), and a clear single-photoelectron peak can be seen in the pulse hei...

Let c : C → X×X be a correspondence with C and X quasi-projective schemes over an algebraically closed field k. We show that if u` : c ∗ 1Q` → c2Q` is an action defined by the localized Chern classes of a c2-perfect complex of vector bundles on C, where ` is a prime invertible in k, then the local terms of u` are given by the class of an algebraic cycle independent of `. We also prove some rela...