Implications of the τ and b spins for theories of quarks and leptons

We argue that the present evidence that the spin of the τ is $\text{1}\text{2}$ is circumstantial, and that a spin of $\text{3}\text{2}$ is not excluded. If the τ spin were $\text{3}\text{2}$, it would have important implications for the idea that leptons and quarks were composite states, perhaps allowing an explanation of the existence of three generations. Supergravity ideas could also be affected. Similar ideas suggest the b-quark could have spin-$\text{3}\text{2}$; we give several ways to test this.     

Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-spacehas been considered. A suitable coordinate transformation hasallowed the region near the leading edge of the front to beexamined for both a maintained planar surface and with surfacecollapse due to material shrinkage. The change in the oxidizerconcentration for a small increment in the propagation speedfor large time and surface collapse has been determined. Theinfluence of two types of nonlinear diffusion on the shape ofthe smouldering front has been found; other cases can be dealtwith in a similar manner.     

On the possibility of finding light uncolored supersymmetric partners at present and future machines

Supersymmetric models allow the possibility of finding new light $\text{spin}\text{-}\text{1}\text{2}$ fermions (m <m_w, and perhaps m < 10–15 GeV, charged or neutral) that are (apart from mixing effects) the supersymmetric partners of W, Z⁰, and Higgs bosons. We provide a detailed analysis of their expected properties, production mechanisms, and signatures, with emphasis on detection at e⁺e^- colliders. Although the charged, $\text{spin}\text{-}\text{1}\text{2}$ particles resemble sequential leptons, it turns out that their properties differ enough that they might have been missed in the standard searches with normal cuts, and they still might be found with m < 18 GeV. A neutral, $\text{spin}\text{-}\text{1}\text{2}$ particle with m below about 30 GeV could exist with a clear decay signature and be singly produced at detectable rates at present machines (picobarn cross sections).     

A constraint from B decay on models with no t quark

We show that if the b quark is assigned to a singlet representation of the weak interaction SU(2) symmetry and if it decays through the usual weak bosons W^± and Z⁰, then neutral current decays occur at such a rate that Λ(B→X?⁺?^?)/Λ(B→X?⁺ν)?0.12, even allowing arbitrarily many quarks with which the b can mix. We discuss the manner in which the experimental exlusion of this inequality would constrain the possibilities for t-free models.     

Which rational numbers are binding numbers?

The concept of the binding number of a graph was introduced by Woodall in 1973. in this paper we characterize the set F_n of all pairs (a, b) of integers such that there is a graph G with n vertices and binding number a/b that has a realizing set of b vertices.     

Surface-catalyzed growth of polymethylene-rich copolymer films on gold

We report the preparation of a new class of copolymer films that consist of polymethylene (PM) with a low percentage ( approximately 1-4%) of randomly distributed ethyl ester side groups, consistent with poly(methylene-co-ethyl acetate). The films are prepared through a surface-catalyzed polymerization on gold surfaces upon exposure to a dilute solution of diazomethane (DM) and ethyl diazoacetate (EDA) in ether at 0 degrees C. While EDA alone does not polymerize at gold surfaces but DM does decompose on gold to grow PM films, the combined presence of EDA and DM results in dramatic enhancements in film growth and promotes an alternative mechanism for propagation as compared with that for the PM homopolymerization. The rate of copolymer film growth is constant over a approximately 24 h period, consistent with a controlled polymerization in which chain terminations are minimized. Carefully controlled experiments indicate that chain propagation does not occur at the outer film-solvent interface, but more likely, at the film-metal interface, suggesting a catalyzed insertion mechanism that extends the chain and pushes the outer chain termini further away from the metal-polymer interface. The results also suggest that adsorbed intermediates of EDA function as co-catalysts to promote the propagation reaction. Of particular importance for materials modification is that the ester side chains of these copolymer films can be hydrolyzed to carboxylate groups that exhibit pH-dependent wettability.