20,891 research outputs found

### Program for the 18th Annual John F. Sonnett Memorial Lecture Series: Bill of Rights

Program for the 18th Annual John F. Sonnett Memorial Lecture Series: Bill of Rights by Judge John J. Gibbons, Chief Judge of the U.S. Court of Appeals for the Third Circuit (1987-1990).https://ir.lawnet.fordham.edu/events_programs_sonnett_miscellaneous/1004/thumbnail.jp

### A genus six cyclic tetragonal reduction of the Benney equations

A reduction of Benney’s equations is constructed corresponding to Schwartz–Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated
Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve

### Complex Numbers, Quantum Mechanics and the Beginning of Time

A basic problem in quantizing a field in curved space is the decomposition of
the classical modes in positive and negative frequency. The decomposition is
equivalent to a choice of a complex structure in the space of classical
solutions. In our construction the real tunneling geometries provide the link
between the this complex structure and analytic properties of the classical
solutions in a Riemannian section of space. This is related to the Osterwalder-
Schrader approach to Euclidean field theory.Comment: 27 pages LATEX, UCSBTH-93-0

### Localized Activation of Bending in Proximal, Medial and Distal Regions of Sea-Urchin Sperm Flagella

Spermatozoa from the sea urchin, Colobocentrotus atratus, were partially demembranated by extraction with solutions containing Triton X-100 at a concentration which was insufficient to solubilize the membranes completely. The resulting suspension was a mixture containing some spermatozoa in which a proximal, medial, or distal portion of the flagellum was membrane-covered, while the remaining portion was naked axoneme. In reactivating solutions containing 12 µM ATP, only the naked portions of the flagellum became motile. In reactivating solutions containing 0.8 mM ADP, the membrane-covered regions became motile and beat at 6-10 beats/s, while the naked regions remained immobile, or beat very slowly at about 0.3 beat/s. Activation of membrane-covered regions in ADP solutions probably results from the membrane restricting the diffusion of ATP which is formed from ADP by the axonemal adenylate kinase. The results indicate that any region of the flagellum has the capacity for autonomous beating, and that special properties of the basal end of the flagellum are not required for bend initiation. However, the beating of different regions of the flagellum is not completely independent, for in a fair number of spermatozoa the beating of the distal, membrane-covered region in 0.8 mM ADP was intermittent, and was turned on and off in phase with the much slower bending cycle in the proximal region of naked axoneme

### WHAT IS A HERPETOLOGIST AND HOW CAN I BECOME ONE?

The following is the first in the JNAH series in which we address a variety of topics on herpetology based on essays from our upcoming book “How to Be a Herpetologist,”. We will also answer frequently asked questions we and other professional herpetologists receive from students, colleagues, and the general public about herpetology as a career or an avocation

### Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions

The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well
known example of geodesic motion on the Diff group of smooth invertible maps
(diffeomorphisms). Its recent two-component extension governs geodesic motion
on the semidirect product ${\rm Diff}\circledS{\cal F}$, where $\mathcal{F}$
denotes the space of scalar functions. This paper generalizes the second
construction to consider geodesic motion on ${\rm Diff} \circledS\mathfrak{g}$,
where $\mathfrak{g}$ denotes the space of scalar functions that take values on
a certain Lie algebra (for example,
$\mathfrak{g}=\mathcal{F}\otimes\mathfrak{so}(3)$). Measure-valued delta-like
solutions are shown to be momentum maps possessing a dual pair structure,
thereby extending previous results for the EPDiff equation. The collective
Hamiltonians are shown to fit into the Kaluza-Klein theory of particles in a
Yang-Mills field and these formulations are shown to apply also at the
continuum PDE level. In the continuum description, the Kaluza-Klein approach
produces the Kelvin circulation theorem.Comment: 22 pages, 2 figures. Submitted to Proc. R. Soc.

### The Physics of 2-d Stringy Spacetimes

We examine the two-dimensional spacetimes that emerge from string theory. We
find all the solutions with no tachyons, and show that the only non-trivial
solution is the black hole spacetime. We examine the role of duality in this
picture. We then explore the thermodynamics of these solutions which is
complicated by the fact that only in two spacetime dimensions is it impossible
to redefine the dilaton field in terms of a canonical scalar field. Finally, we
extend our analysis to the heterotic string, and briefly comment on exact, as
opposed to perturbative, solutions

### Branes as BIons

A BIon may be defined as a finite energy solution of a non-linear field
theory with distributional sources. By contrast a soliton is usually defined to
have no sources. I show how harmonic coordinates map the exteriors of the
topologically and causally non-trivial spacetimes of extreme p-branes to BIonic
solutions of the Einstein equations in a topologically trivial spacetime in
which the combined gravitational and matter energy momentum is located on
distributional sources. As a consequence the tension of BPS p-branes is
classically unrenormalized. The result holds equally for spacetimes with
singularities and for those, like the M-5-brane, which are everywhere
singularity free.Comment: Latex, 9 pages, no figure

### Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black
hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq +
\chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show
that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli
fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric
and magnetic charges. It follows that the least mass of any black hole with
fixed conserved electric and magnetic charges is given by the mass of the
double-extreme black hole with these charges. Our work allows us to interpret
the previously established result that for all extreme black holes the moduli
fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only
on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such
that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio

### Sigma, tau and Abelian functions of algebraic curves

We compare and contrast three different methods for the construction of the
differential relations satisfied by the fundamental Abelian functions
associated with an algebraic curve. We realize these Abelian functions as
logarithmic derivatives of the associated sigma function. In two of the
methods, the use of the tau function, expressed in terms of the sigma function,
is central to the construction of differential relations between the Abelian
functions.Comment: 25 page

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