793,871 research outputs found
Classification of Multidimensional Darboux Transformations: First Order and Continued Type
We analyze Darboux transformations in very general settings for
multidimensional linear partial differential operators. We consider all known
types of Darboux transformations, and present a new type. We obtain a full
classification of all operators that admit Wronskian type Darboux
transformations of first order and a complete description of all possible
first-order Darboux transformations. We introduce a large class of invertible
Darboux transformations of higher order, which we call Darboux transformations
of continued Type I. This generalizes the class of Darboux transformations of
Type I, which was previously introduced. There is also a modification of this
type of Darboux transformations, continued Wronskian type, which generalize
Wronskian type Darboux transformations
Scalar Levin-Type Sequence Transformations
Sequence transformations are important tools for the convergence acceleration
of slowly convergent scalar sequences or series and for the summation of
divergent series. Transformations that depend not only on the sequence elements
or partial sums but also on an auxiliary sequence of so-called remainder
estimates are of Levin-type if they are linear in the , and
nonlinear in the . Known Levin-type sequence transformations are
reviewed and put into a common theoretical framework. It is discussed how such
transformations may be constructed by either a model sequence approach or by
iteration of simple transformations. As illustration, two new sequence
transformations are derived. Common properties and results on convergence
acceleration and stability are given. For important special cases, extensions
of the general results are presented. Also, guidelines for the application of
Levin-type sequence transformations are discussed, and a few numerical examples
are given.Comment: 59 pages, LaTeX, invited review for J. Comput. Applied Math.,
abstract shortene
Transformations of -Type Entangled States
The transformations of -type entangled states by using local operations
assisted with classical communication are investigated. For this purpose, a
parametrization of the -type states which remains invariant under local
unitary transformations is proposed and a complete characterization of the
local operations carried out by a single party is given. These are used for
deriving the necessary and sufficient conditions for deterministic
transformations. A convenient upper bound for the maximum probability of
distillation of arbitrary target states is also found.Comment: 7 page
Inferring Program Transformations from Type Transformations for Partitioning of Ordered Sets
In this paper I introduce a mechanism to derive program transforma- tions
from order-preserving transformations of vector types. The purpose of this work
is to allow automatic generation of correct-by-construction instances of
programs in a streaming data processing paradigm suitable for FPGA processing.
We show that for it is possible to automatically derive instances for programs
based on combinations of opaque element- processing functions combined using
foldl and map, purely from the type transformations.Comment: This work is supported by the EPSRC through the TyTra project
(EP/L00058X/1
Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences
The conserved densities of hydrodynamic type system in Riemann invariants
satisfy a system of linear second order partial differential equations. For
linear systems of this type Darboux introduced Laplace transformations,
generalising the classical transformations in the scalar case. It is
demonstrated that Laplace transformations can be pulled back to the
transformations of the corresponding hydrodynamic type systems. We discuss
periodic Laplace sequences of with the emphasize on the simplest nontrivial
case of period 2. For 3-component systems in Riemann invariants a complete
discription of closed quadruples is proposed. They turn to be related to a
special quadratic reduction of the (2+1)-dimensional 3-wave system which can be
reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of
the Lame and rotation coefficients Laplace transformations have a natural
interpretation as the symmetries of the Dirac operator, associated with the
(2+1)-dimensional n-wave system. The 2-component Laplace transformations can be
interpreted also as the symmetries of the (2+1)-dimensional integrable
equations of Davey-Stewartson type. Laplace transformations of hydrodynamic
type systems originate from a canonical geometric correspondence between
systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late
On application of Liouville type equations to constructing B\"acklund transformations
It is shown how pseudoconstants of the Liouville-type equations can be
exploited as a tool for construction of the B\"acklund transformations. Several
new examples of such transformations are found. In particular we obtained the
B\"acklund transformations for a pair of three-component analogs of the
dispersive water wave system, and auto-B\"acklund transformations for coupled
three-component KdV-type systems.Comment: 11 pages, no figure
Vector supersymmetry in topological field theories
We present a simple derivation of vector supersymmetry transformations for
topological field theories of Schwarz- and Witten-type. Our method is similar
to the derivation of BRST-transformations from the so-called horizontality
conditions or Russian formulae. We show that this procedure reproduces in a
concise way the known vector supersymmetry transformations of various
topological models and we use it to obtain some new transformations of this
type for 4d topological YM-theories in different gauges.Comment: 19 page
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