M. Heath

M. Heath
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Mathematics - Functional Analysis (7)
 
Earth and Planetary Astrophysics (2)
 
Mathematics - Complex Variables (1)
 
Mathematics - Combinatorics (1)
 
Astrophysics (1)
 
Nonlinear Sciences - Chaotic Dynamics (1)
 
Computer Science - Cryptography and Security (1)
 
High Energy Physics - Experiment (1)
 
Nuclear Experiment (1)
 
Mathematics - Numerical Analysis (1)
 
Physics - Instrumentation and Detectors (1)
 
Physics - Materials Science (1)

Publications Authored By M. Heath

The COHERENT collaboration's primary objective is to measure coherent elastic neutrino-nucleus scattering (CEvNS) using the unique, high-quality source of tens-of-MeV neutrinos provided by the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL). In spite of its large cross section, the CEvNS process has never been observed, due to tiny energies of the resulting nuclear recoils which are out of reach for standard neutrino detectors. The measurement of CEvNS has now become feasible, thanks to the development of ultra-sensitive technology for rare decay and weakly-interacting massive particle (dark matter) searches. Read More

In this paper we consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We introduce a notion of 'allocation map' connected with Swiss cheeses, and we develop the theory of such maps. We use this theory to modify examples previously constructed in the literature to solve various problems, in order to obtain examples of Swiss cheese sets homeomorphic to the Sierpinski carpet which solve the same problems. Read More

We give a survey of the known connections between regularity conditions and amenability conditions in the setting of uniform algebras. For a uniform algebra $A$ we consider the set, $A_{lc}$, of functions in $A$ which are locally constant on a (varying) dense open subset of the character space of $A$. We show that, for a separable uniform algebra $A$, if $A$ has bounded relative units at every point of a dense subset of the character space of $A$, then $A_{lc}$ is dense in $A$. Read More

Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality output but are often deemed too slow to be practical for use in large simulations. We combine these two approaches to construct a family of hybrid generators that permit users to choose the desired tradeoff between quality and speed for a given application. Read More

Techniques for mass-production of large area graphene using an industrial scale thin film deposition tool could be the key to the practical realization of a wide range of technological applications of this material. Here, we demonstrate the growth of large area polycrystalline graphene from sputtered films (a carbon-containing layer and a metallic layer) using in-situ or ex-situ rapid thermal processing in the temperature range from 650 to 1000 oC. It was found that graphene always grows on the top surface of the stack, in close contact with the Ni or Ni-silicide. Read More

We use the circumbinary planetary system Kepler-16b as an example to specify some considerations that may be of interest to astrobiologists regarding the dynamic nature of habitable zones around close double star systems. Read More

The concept of the Circumstellar Habitable Zone has served the scientific community well for some decades. It slips easily off the tongue, and it would be hard to replace. Recently, however, several workers have postulated types of habitable bodies which might exist outside the classic circumstellar habitable zone (HZ). Read More

We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, $A$, into its dual module, then there are no compact derivations from $A$ into any symmetric $A$-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra $\ell^1(\Z_+)$ to its dual. Read More

We show that the space of all bounded derivations from the disc algebra into its dual can be identified with the Hardy space $H^1$; using this, we infer that all such derivations are compact. Also, given a fixed derivation $D$, we construct a finite, positive Borel measure $\mu_D$ on the closed disc, such that $D$ factors through $L^2(\mu_D)$. Such a measure is known to exist, for any bounded linear map from the disc algebra to its dual, by results of Bourgain and Pietsch, but these results are highly non-constructive. Read More

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps $T:A\to B$ between Banach algebras that are "close to multiplicative" in the following senses: the failure of multiplicativity, defined by $S_T(a,b)=T(a)T(b)-T(ab)$, is compact [respectively weakly compact]. We call such maps cf-homomorphisms [respectively wcf-homomorphisms]. Read More

We characterize those derivations from the convolution algebra $\ell^1({\mathbb Z}_+)$ to its dual which are weakly compact. In particular, we provide examples which are weakly compact but not compact. The characterization is combinatorial, in terms of "translation-finite" subsets of ${\mathbb Z}_+$, and we investigate how this notion relates to other notions of "smallness" for infinite subsets of ${\mathbb Z}_+$. Read More

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equation's symmetry group. With the method used, relative periodic solutions are represented by a space-time Fourier series modified to include the symmetry group element and are sought as solutions to a system of nonlinear algebraic equations for the Fourier coefficients, group element, and time period. Read More

In \cite{F} J.F. Feinstein constructed a compact plane set $X$ such that $R(X)$ has no non-zero, bounded point derivations but is not weakly amenable. Read More