Superconducting strings

It is known that certain spontaneously broken gauge theories give rise to stable strings or vortex lines. In this paper it is shown that under certain conditions such strings behave like superconducting wires whose passage through astrophysical magnetic fields would generate a variety of striking and perhaps observable effects. The superconducting charge carriers may be either bosons (if a charged Higgs field has an expectation value in the core of the string) or fermions (if charged fermions are trapped in zero modes along the string, as is known to occur in certain circumstances). They might be observable as synchrotron sources or as sources of high-energy cosmic rays. If the charge carriers are ordinary quarks and leptons, the strings have important baryon number violating interactions with magnetic fields; such a string, traversing a galactic magnetic field of 10^?6 G, creates baryons (or antibaryons) at a rate of order 10¹² particles/cm of string per second.     

The mathematical miscellany (1836–1839)

Charles Gill (1805–1855), who immigrated to the United States from England in 1830, began to edit The Mathematical Miscellany (1836–1839) while teaching on Long Island (New York, U.S.A.). Most of America's best mathematicians of the day were contributors, including Benjamin Peirce, Theodore Strong, and William Lenhart. The contents of the journal and the correspondence between Gill and its contributors, as well as the journal's troubles, give insights into American mathematics in the middle of the 19th century.     

On the convergence of quadratic spline interpolants

Characterization and uniqueness of minimax approximation by the product PQ of two finite dimensional subspaces P and Q is studied. Some approximants may have no standard characterization since PQ may not be a sun, but interior points do have the standard linear characterization.     

On point-halfspace graphs

The following definition is motivated by the study of circle orders and their connections to graphs. A graphs G is called a point-halfspace graph (in R ^k) provided one can assign to each vertex v ? (G) a point p _v R ^k and to each edge e ? E(G) a closed halfspace H_e ? R ^k so that v is incident with e if and only if p _v ? H_e. Let H ^k denote the set of point-halfspace graphs (in R ^k). We give complete forbidden subgraph and structural characterizations of the classes H ^k for every k. Surprisingly, these classes are closed under taking minors and we give forbidden minor characterizations as well. © 1996 John Wiley & Sons, Inc.     

Quantum field theory,Grassmannians, and algebraic curves

This paper is devoted in part to clarifying some aspects of the relation between quantum field theory and infinite Grassmannians, and in part to pointing out the existence of a close analogy between conformal field theory on Riemann surfaces and the modern theory of automorphic representations. Along the way we develop a multiplicative analog of the usual additive Ward identities of current algebra. We also reformulate the additive Ward identities in a way which may be useful, in terms of the residues of operator-valued differential forms. A concluding section is devoted to some remarks on string field theory. In an appendix, we attempt to clarify the recent construction by Beilinson, Manin, and Schechtman of what might be called global Virasoro algebras.Supported in part by NSF Grants PHY80-19754 and 86-16129     

The asymptotic enumeration of rooted convex polyhedra

An asymptotic formula is obtained for the number of rooted c-nets with m vertices and n edges as m, n → ∞ with $\text{1}\text{2}\text{+ ε <}\text{n}\text{m}\text{< 2 ? ε}$ for some ε > 0.