On the structure of P(n)*P(n) for p=2

We show that P(n)*(P(n)) for p = 2 with its geometrically induced structure maps is not an Hopf algebroid because neither the augmentation Epsilon nor the coproduct Delta are multiplicative. As a consequence the algebra structure of P(n)*(P(n)) is slightly different from what was supposed to be the case. We give formulas for Epsilon(xy) and Delta(xy) and show that the inversion of the formal group of P(n) is induced by an antimultiplicative involution Xi : P(n) -> P(n). Some consequences for multiplicative and antimultiplicative automorphisms of K(n) for p = 2 are also discussed

The reactions p + n --> d + omega and p + n --> d + phi near threshold

The reactions p+n-->d+omega and p+n-->d+phi are studied within a relativistic meson-exchange model of hadronic interactions. Predictions for the total cross sections and for the angular distributions of the vector mesons are presented. The resulting cross sections near threshold are around 10 - 30 microb for p+n-->d+omega$ and 200 - 250 nb for p+n-->d+phi. A moderate deviation of the cross section ratio sigma_{p+n-->d+phi} / sigma_{p+n-->d+omega} from that of the Okubo-Zweig-Iizuka rule is predicted.Comment: 12 pages, 7 figure

Logarithmic potentials on Pn\mathbb{P}^n

We study the projective logarithmic potential $\mathbb{G}_{\mu}$ of a Probability measure $\mu$ on the complex projective space $\mathbb{P}^{n}$. We prove that the Range of the operator $\mu\longrightarrow \mathbb{G}_{\mu}$ is contained in the (local) domain of definition of the complex Monge-Amp\`ere operator acting on the class of quasi-plurisubharmonic functions on $\mathbb{P}^n$ with respect to the Fubini-Study metric. Moreover, when the measure $\mu$ has no atom, we show that the complex Monge-Amp\`ere measure of its Logarithmic potential is an absolutely continuous measure with respect to the Fubini-Study volume form on $\mathbb{P}^{n}$Comment: 7 page

P-n junctions formed in gallium antimonide

Vapor phase deposition process forms a heavily doped n-region on a melt-grown p-type gallium antimonide substrate. HCl transports gallium to the reaction zone, where it combines with antimony hydride and the dopant carrier, hydrogen telluride. Temperatures as low as 400 degrees C are required

Separators of fat points in P^n

In this paper we extend the definition of a separator of a point P in P^n to a fat point P of multiplicity m. The key idea in our definition is to compare the fat point schemes Z = m_1P_1 + ... + m_iP_i + .... + m_sP_s in P^n and Z' = m_1P_1 + ... + (m_i-1)P_i + .... + m_sP_s. We associate to P_i a tuple of positive integers of length v = deg Z - deg Z'. We call this tuple the degree of the minimal separators of P_i of multiplicity m_i, and we denote it by deg_Z(P_i) = (d_1,...,d_v). We show that if one knows deg_Z(P_i) and the Hilbert function of Z, one will also know the Hilbert function of Z'. We also show that the entries of deg_Z(P_i) are related to the shifts in the last syzygy module of I_Z. Both results generalize well known results about reduced sets of points and their separators.Comment: 22 pages; minor revisions throughout; to appear in Journal of Algebr