Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

N=0 Supersymmetry and the Non-Relativistic Monopole

We study some of the algebraic properties of the non-relativistic monopole. We find that we can construct theories that possess an exotic conserved fermionic charge that squares to the Casimir of the rotation group, yet do not possess an ordinary supersymmetry. This is in contrast to previous known examples with such exotic fermionic charges. We proceed to show that the presence of the exotic fermionic charge in the non-supersymmetric theory can nonetheless be understood using supersymmetric techniques, providing yet another example of the usefulness of supersymmetry in understanding non-supersymmetric theories.Comment: 9 pages, harvmac, no figure

A Simple Method for Computing Soliton Statistics

I provide an extremely simple argument that the kink-type solitons in certain theories are fermionic. The argument is based on the Witten index, but can in fact be used to determine soliton statistics in non-supersymmetric theories as well.Comment: 9 pages, harvmac, HWS-92/09. (Added substantial details in one section.

Asians, Jews, and the Legacy of Midas

In much of the U.S. media today, Asian-Americans are being hailed as the new wonder group. Local newspapers seem to be filled with articles about how this student from Pakistan won the spelling bee and that student from Japan won the math contest. Weekly news magazines carry articles extolling this phenomenon, and many liberals and conservatives alike enthusiastically promote the stereotype: liberals because it combats the racist myth that people of color are intellectually inferior to Euro-Americans ( whites ) and conservatives because it can be used to promote the idea that any ethnic group can make it if only they work hard.[1] Therein lies one of the negative aspects of this media campaign

On a Spector ultrapower of the Solovay model

We prove that a Spector--like ultrapower extension \gN of a countable Solovay model \gM (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension \gM[\al] where \al is a random real over \gM. The proof involves an almost everywhere uniformization theorem in the Solovay model

Obscene division: Feminist liberal assessments of prostitution versus feminist liberal defenses of pornography

In assessing ethical issues concerning the sex-industry, feminist liberalism ought to combine the concern for the worker that is central to its treatment of prostitution, with sensitivity to the social and cultural embeddedness of self that is central to its treatment of pornography. That would enable us to then look at live-actor pornography as a form of prostitution that raises additional questions about third party consumption — and analysis both more theoretically coherent and practically useful

Duality, Partial Supersymmetry, and Arithmetic Number Theory

We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to this after first developing the notion of partial supersymmetry-in which some, but not all, of the operators of a theory have superpartners-and using it to construct fermionic and parafermionic thermal partition functions, and to derive some number theoretic identities. In the process, we also find a bosonic analogue of the Witten index, and use this, too, to obtain some number theoretic results related to the Riemann zeta function.Comment: 14 pages, harvmac, no figures; revised to add references, fix typos, add paragraph in Section

[Review of] Joseph Rothschild, Ethnopolitics, A Conceptual Framework

Whether ethnicity stems from certain intrinsic group characteristics or whether it is a definition conferred upon various groups because of their political, social, and economic environment has been a fundamental debate within the field of ethnic studies. Most students of ethnic studies would agree that ethnicity today embraces both factors, and more, that it is the result of the interactions between both sets of influences. How these factors interact in the political sphere is the core of Rothschild\u27s ambitious new book