904 research outputs found
On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains
International audienceThis paper provides an algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists. A regularity test for polynomials modulo regular chains is revisited in the nondifferential setting and lifted to differential algebra. A new characterization of regular chains is provided
Algorithmic Thomas Decomposition of Algebraic and Differential Systems
In this paper, we consider systems of algebraic and non-linear partial
differential equations and inequations. We decompose these systems into
so-called simple subsystems and thereby partition the set of solutions. For
algebraic systems, simplicity means triangularity, square-freeness and
non-vanishing initials. Differential simplicity extends algebraic simplicity
with involutivity. We build upon the constructive ideas of J. M. Thomas and
develop them into a new algorithm for disjoint decomposition. The given paper
is a revised version of a previous paper and includes the proofs of correctness
and termination of our decomposition algorithm. In addition, we illustrate the
algorithm with further instructive examples and describe its Maple
implementation together with an experimental comparison to some other
triangular decomposition algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1008.376
Thomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear
partial differential systems of equations and inequations into so-called simple
subsystems. We exploit Thomas decomposition ideas and develop them into a new
algorithm. For algebraic systems simplicity means triangularity, squarefreeness
and non-vanishing initials. For differential systems the algorithm provides not
only algebraic simplicity but also involutivity. The algorithm has been
implemented in Maple
A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations
This paper deals with the index reduction problem for the class of
quasi-regular DAE systems. It is shown that any of these systems can be
transformed to a generically equivalent first order DAE system consisting of a
single purely algebraic (polynomial) equation plus an under-determined ODE
(that is, a semi-explicit DAE system of differentiation index 1) in as many
variables as the order of the input system. This can be done by means of a
Kronecker-type algorithm with bounded complexity
Computing differential characteristic sets by change of ordering
submitted to the Journal of Symbolic ComputationWe describe an algorithm for converting a characteristic set of a prime differential ideal from one ranking into another. This algorithm was implemented in many different languages and has been applied within various software and projects. It permitted to solve formerly unsolved problems
Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
We construct a four-parameter family of Markov processes on infinite
Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures.
Any process in the family induces a Feller Markov process on the
infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently,
the space of extreme characters of the infinite-dimensional unitary group
U(infinity). The process has a unique invariant distribution which arises as
the decomposing measure in a natural problem of harmonic analysis on
U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194,
this measure can also be described as a determinantal point process with a
correlation kernel expressed through the Gauss hypergeometric function
A Short Contribution to the Theory of Regular Chains
International audienceThis paper contains short contributions to the theory of regular chains which follow a recent JSC paper by the same authors. These contributions apply to both the nondifferential and the differential context. They deal with the computation of normal forms and with the membership problem to ideals defined by regular chains
- …