35,263 research outputs found
Lifting Grobner bases from the exterior algebra
In the article "Non-commutative Grobner bases for commutative algebras",
Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and
initial ideals of those ideals in the free associative algebra which contain
the commutator ideal. We prove similar results for ideals which contains the
anti-commutator ideal (the defining ideal of the exterior algebra). We define
one notion of generic initial ideals in the free assoicative algebra, and show
that gin's of ideals containing the commutator ideal, or the anti-commutator
ideal, are finitely generated.Comment: 6 pages, LaTeX2
Nonlinear equations for p-adic open, closed, and open-closed strings
We investigate the structure of solutions of boundary value problems for a
one-dimensional nonlinear system of pseudodifferential equations describing the
dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar
tachyon field using the method of successive approximations. For an open-closed
string, we prove that the method converges for odd values of p of the form
p=4n+1 under the condition that the solution for the closed string is known.
For p=2, we discuss the questions of the existence and the nonexistence of
solutions of boundary value problems and indicate the possibility of
discontinuous solutions appearing.Comment: 16 pages, 3 figure
Cooperative Chiral Order in Copolymers of Chiral and Achiral Units
Polyisocyanates can be synthesized with chiral and achiral pendant groups
distributed randomly along the chains. The overall chiral order, measured by
optical activity, is strongly cooperative and depends sensitively on the
concentration of chiral pendant groups. To explain this cooperative chiral
order theoretically, we map the random copolymer onto the one-dimensional
random-field Ising model. We show that the optical activity as a function of
composition is well-described by the predictions of this theory.Comment: 13 pages, including 3 postscript figures, uses REVTeX 3.0 and
epsf.st
Old Recipes, New Practice? The Latin Adaptations of the Hippocratic Gynaecological Treatises
There were two main gynaecological traditions in the early Middle Ages: the Soranic and Hippocratic traditions. This article focuses on the latter tradition, which was based on the translations into Latin of the Greek treatises Diseases of Women I and II. These translations, referred to here as Latin Diseases of Women and On the Diverse Afflictions of Women, contain a wealth of recipes, which are examined in detail. I ask whether recipes that had been first written down in the fifth century BC could still form the basis of gynaecological practice in the Middle Ages, and whether the act of translation transformed medical practice
Infinite planar string: cusps, braids and soliton exitations
We investigate infinite strings in space-time, which may be
considered as excitations of straight lines on the spatial plane. We also
propose the hamiltonian description of such objects that differs from the
standard hamiltonian description of the string. The hamiltonian variables are
separated into two independent groups: the "internal" and "external" variables.
The first ones are invariant under space-time transformations and are connected
with the second form of the world-sheet. The "external" variables define the
embedding of the world-sheet into space-time. The constructed phase space is
nontrivial because the finite number of constraints entangles the variables
from these groups. First group of the variables constitute the coefficients for
the pair of first-order spectral problems; the solution of these problems is
necessary for the reconstruction of the string world-sheet. We consider the
excitations, which correspond to "N- soliton" solution of the spectral problem,
and demonstrate that the reconstructed string has cuspidal points. World lines
of such points form braids of various topologies.Comment: 16 pages, 4 figure
Abelian 3-form gauge theory: superfield approach
We discuss a D-dimensional Abelian 3-form gauge theory within the framework
of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and
absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST
symmetry transformations for this theory. To pay our homage to Victor I.
Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form
(antisymmetric tensor) gauge field, we go a step further and discuss the above
D-dimensional Abelian 3-form gauge theory within the framework of BRST
formalism and establish that the existence of the (anti-)BRST invariant
Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form
gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow
Region, Russi
Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom
Hundred twenty years after the fundamental work of Poincar\'e, the statistics
of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom
is studied by numerical simulations. The obtained results show that in a
regime, where the measure of stability islands is significant, the decay of
recurrences is characterized by a power law at asymptotically large times. The
exponent of this decay is found to be . This value is
smaller compared to the average exponent found previously
for two-dimensional symplectic maps with divided phase space. On the basis of
previous and present results a conjecture is put forward that, in a generic
case with a finite measure of stability islands, the Poncar\'e exponent has a
universal average value being independent of number of
degrees of freedom and chaos parameter. The detailed mechanisms of this slow
algebraic decay are still to be determined.Comment: revtex 4 pages, 4 figs; Refs. and discussion adde
TFD Approach to Bosonic Strings and -branes
In this work we explain the construction of the thermal vacuum for the
bosonic string, as well that of the thermal boundary state interpreted as a
-brane at finite temperature. In both case we calculate the respective
entropy using the entropy operator of the Thermo Field Dynamics Theory. We show
that the contribution of the thermal string entropy is explicitly present in
the -brane entropy. Furthermore, we show that the Thermo Field approach
is suitable to introduce temperature in boundary states.Comment: 6 pages, revtex, typos are corrected. Prepared for the Second
Londrina Winter School-Mathematical Methods in Physics, August 25-30, 2002,
Londrina-Pr, Brazil. To appear in a special issue of IJMP
High-field noise in metallic diffusive conductors
We analyze high-field current fluctuations in degenerate conductors by
mapping the electronic Fermi-liquid correlations at equilibrium to their
semiclassical non-equilibrium form. Our resulting Boltzmann description is
applicable to diffusive mesoscopic wires. We derive a non-equilibrium
connection between thermal fluctuations of the current and resistive
dissipation. In the weak-field limit this is the canonical fluctuation-
dissipation theorem. Away from equilibrium, the connection enables explicit
calculation of the excess ``hot-electron'' contribution to the thermal
spectrum. We show that excess thermal noise is strongly inhibited by Pauli
exclusion. This behaviour is generic to the semiclassical metallic regime.Comment: 13 pp, one fig. Companion paper to cond-mat/9911251. Final version,
to appear in J. Phys.: Cond. Ma
- …