Carboranylmethylene-substituted phosphazenes and polymers thereof

Carboranylmethylene-substituted cyclophosphazenes are described which can be thermally polymerized into carboranylmethylene-substituted phosphazene polymers. The polymers are useful as thermally stable coatings. Also, due to the characteristics of these polymers in acting as a ligand for transition metals, metalocarboranylmethylene phosphazene polymers are described which can act as immobilized catalyst systems, and are electrically conductive and superconductive

Real Cubic Surfaces and Real Hyperbolic Geometry

The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37\pi^2/1080 in the metric of constant curvature -1. Each of the five connected components of the moduli space can be described as the quotient of real hyperbolic four-space by a specific arithmetic group. We compute the volumes of these components.Comment: 4 pages, one figur

Hyperbolic geometry and moduli of real cubic surfaces

Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H^4 and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in PO(4,1). We also derive several new and several old results on the topology of M_0^R. Let M_s^R be the moduli space of real cubic surfaces that are stable in the sense of geometric invariant theory. We show that this space carries a hyperbolic structure whose restriction to M_0^R is that just mentioned. The corresponding lattice in PO(4,1), for which we find an explicit fundamental domain, is nonarithmetic.Comment: Major revision, including several new or completely rewritten sections. 56 page

Process for the preparation of polycarboranylphosphazenes

A process for the preparation of polycarboranylphosphazenes is described. Polydihalophosphazenes are allowed to react at ambient temperatures for at least one hour with a lithium carborane in a suitable inert solvent. The remaining chlorine substituents of the carboranyl polyphosphazene are then replaced with aryloxy or alkoxy groups to enhance moisture resistance. The polymers give a high char yield when exposed to extreme heat and flame and can be used as insulation

Carboranylcyclotriphosphazenes and their polymers

Carboranyl-substituted polyphosphazenes are prepared by heat polymerizing a carboranyl halocyclophosphazene at 250 C for about 120 hours in the absence of oxygen and moisture. The cyclophosphazene is obtained by allowing a lithium carborane, e.g., the reaction product of methyl-o-carborane with n-butyllithium in ethyl ether, to react with e.g., hexachlorocyclotriphosphazene at ambient temperatures and in anhydrous conditions. For greater stability in the presence of moisture, the chlorine substituents of the polymer are then replaced by aryloxy or alkoxy groups, such as CF3CH2O. The new substantially inorganic polymers are thermally stable materials which produce a high char yield when exposed to extreme temperatures, and can thus serve to insulate less heat and fire resistant substances

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Measurement of Time-of-Arrival in Quantum Mechanics

It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.Comment: References added. To appear in Phys. Rev.