31,909 research outputs found
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 over
with , 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 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 , the subspace
of the Sobolev space for which the weak
derivative .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.
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
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
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
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