9,241 research outputs found
Admissible generalizations of examples as rules
International audienc
Dirac--Lie systems and Schwarzian equations
A Lie system is a system of differential equations admitting a superposition
rule, i.e., a function describing its general solution in terms of any generic
set of particular solutions and some constants. Following ideas going back to
the Dirac's description of constrained systems, we introduce and analyse a
particular class of Lie systems on Dirac manifolds, called Dirac--Lie systems,
which are associated with `Dirac--Lie Hamiltonians'. Our results enable us to
investigate constants of the motion, superposition rules, and other general
properties of such systems in a more effective way. Several concepts of the
theory of Lie systems are adapted to this `Dirac setting' and new applications
of Dirac geometry in differential equations are presented. As an application,
we analyze traveling wave solutions of Schwarzian equations, but our methods
can be applied also to other classes of differential equations important for
Physics.Comment: 41 page
Combinatorics of bicubic maps with hard particles
We present a purely combinatorial solution of the problem of enumerating
planar bicubic maps with hard particles. This is done by use of a bijection
with a particular class of blossom trees with particles, obtained by an
appropriate cutting of the maps. Although these trees have no simple local
characterization, we prove that their enumeration may be performed upon
introducing a larger class of "admissible" trees with possibly doubly-occupied
edges and summing them with appropriate signed weights. The proof relies on an
extension of the cutting procedure allowing for the presence on the maps of
special non-sectile edges. The admissible trees are characterized by simple
local rules, allowing eventually for an exact enumeration of planar bicubic
maps with hard particles. We also discuss generalizations for maps with
particles subject to more general exclusion rules and show how to re-derive the
enumeration of quartic maps with Ising spins in the present framework of
admissible trees. We finally comment on a possible interpretation in terms of
branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction
and discussion/conclusion extended, minor corrections, references adde
On the Semantics of Gringo
Input languages of answer set solvers are based on the mathematically simple
concept of a stable model. But many useful constructs available in these
languages, including local variables, conditional literals, and aggregates,
cannot be easily explained in terms of stable models in the sense of the
original definition of this concept and its straightforward generalizations.
Manuals written by designers of answer set solvers usually explain such
constructs using examples and informal comments that appeal to the user's
intuition, without references to any precise semantics. We propose to approach
the problem of defining the semantics of gringo programs by translating them
into the language of infinitary propositional formulas. This semantics allows
us to study equivalent transformations of gringo programs using natural
deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms
(ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke
A System Appallingly out of Balance : Morgan v. State and the Rights of Defendants and Victims in Sexual Assault Prosecutions
In a series of three cases that culminate with Morgan v. State, Alaska\u27s courts established a unique protection for defendants in sexual assault cases. This protection, which allows such defendants to attack their victims in court with previous reports of sexual assault that did not result in prosecution, is not afforded to defendants in other cases and is based on a dubious general principle that the credibility of sexual assault victims has special relevance. The protection is problematic in several ways: it is grounded in erroneous stereotypes about the victims of sex crimes; it is detrimental to victims and the pursuit of truth; it is inconsistent with traditional rules of evidence; and it is unnecessary to protect the rights of defendants. For these reasons, this protection for defendants in sexual assault cases should be abrogated by legislative action as proposed herein
V.M. Miklyukov: from dimension 8 to nonassociative algebras
In this short survey we give a background and explain some recent
developments in algebraic minimal cones and nonassociative algebras. A good
deal of this paper is recollections of my collaboration with my teacher, PhD
supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that
motivated the present research. This paper is dedicated to his memory.Comment: 19 page
- …