428 research outputs found
The multicomponent 2D Toda hierarchy: Discrete flows and string equations
The multicomponent 2D Toda hierarchy is analyzed through a factorization
problem associated to an infinite-dimensional group. A new set of discrete
flows is considered and the corresponding Lax and Zakharov--Shabat equations
are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix
types are proposed and studied. Orlov--Schulman operators, string equations and
additional symmetries (discrete and continuous) are considered. The
continuous-discrete Lax equations are shown to be equivalent to a factorization
problem as well as to a set of string equations. A congruence method to derive
site independent equations is presented and used to derive equations in the
discrete multicomponent KP sector (and also for its modification) of the theory
as well as dispersive Whitham equations.Comment: 27 pages. In the revised paper we improved the presentatio
S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies
We introduce an S-function formulation for the recently found r-th
dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also
a connection of these -functions with the Orlov functions of the
hierarchies. Then, we discuss a reduction scheme for the hierarchies that
together with the -function formulation leads to hodograph systems for the
associated solutions. We consider also the connection of these reductions with
those of the dispersionless KP hierarchy and with hydrodynamic type systems. In
particular, for the 1-component and 2-component reduction we derive, for both
hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel
package
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
The multicomponent 2D Toda hierarchy: dispersionless limit
The factorization problem of the multi-component 2D Toda hierarchy is used to
analyze the dispersionless limit of this hierarchy. A dispersive version of the
Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators
is introduced and the corresponding additional symmetries and string equations
are discussed. Then, it is shown how KP and Toda pictures of the dispersionless
Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional
symmetries and string equations for the dispersive Whitham hierarchy are
studied in this limit.Comment: Revised version with an overall improved presentatio
Mechanism of the synergistic inactivation of Escherichia coli by UV-C light at mild temperatures
UV light only penetrates liquid food surfaces to a very short depth, thereby limiting its industrial application in food pasteurization. One promising alternative is the combination of UV light with mild heat (UV-H), which has been demonstrated to produce a synergistic bactericidal effect. The aim of this article is to elucidate the mechanism of synergistic cellular inactivation resulting from the simultaneous application of UV light and heat. The lethality of UV-H treatments remained constant below ~45ĀŗC, while lethality increased exponentially as the temperature increased. The percentage of synergism reached a maximum (40.3%) at 55ĀŗC. Neither the flow regimen nor changes in the dose delivered by UV lamps contributed to the observed synergism. UV-H inactivation curves of the parental Escherichia coli strain obtained in a caffeic acid selective recovery medium followed a similar profile to those obtained with uvrA mutant cells in a nonselective medium. Thermal fluidification of membranes and synergistic lethal effects started around 40 to 45ĀŗC. Chemical membrane fluidification with benzyl alcohol decreased the UV resistance of the parental strain but not that of the uvrA mutant. These results suggest that the synergistic lethal effect of UV-H treatments is due to the inhibition of DNA excision repair resulting from the membrane fluidification caused by simultaneous heating
Additional symmetries and solutions of the dispersionless KP hierarchy
The dispersionless KP hierarchy is considered from the point of view of the
twistor formalism. A set of explicit additional symmetries is characterized and
its action on the solutions of the twistor equations is studied. A method for
dealing with the twistor equations by taking advantage of hodograph type
equations is proposed. This method is applied for determining the orbits of
solutions satisfying reduction constraints of Gelfand--Dikii type under the
action of additional symmetries.Comment: 21 page
Vectorial Ribaucour Transformations for the Lame Equations
The vectorial extension of the Ribaucour transformation for the Lame
equations of orthogonal conjugates nets in multidimensions is given. We show
that the composition of two vectorial Ribaucour transformations with
appropriate transformation data is again a vectorial Ribaucour transformation,
from which it follows the permutability of the vectorial Ribaucour
transformations. Finally, as an example we apply the vectorial Ribaucour
transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package
Markov Chains and Multiple Orthogonality
In this work we survey on connections of Markov chains and the theory of
multiple orthogonality. Here we mainly concentrate on give a procedure to
generate stochastic tetra diagonal Hessenberg matrices, coming from some
specific families of multiple orthogonal, such as the ones of Jacobi--Pi\~neiro
and Hypergeometric Lima--Loureiro. We show that associated with a positive
tetra diagonal nonnegative bounded Hessenberg matrix we can construct two
stochastic tetra diagonal ones. These two stochastic tridiagonal nonnegative
Hessenberg matrices are shown to be, enlightened by the Poincar\'e theorem,
limit transpose of each other
Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials
This paper explores a factorization using bidiagonal matrices of the
recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is
expressed in terms of ratios involving the generalized hypergeometric function
and is proven using recently discovered contiguous relations.
Moreover, employing the multiple Askey scheme, a bidiagonal factorization is
derived for the Hahn descendants, including Jacobi-Pi\~neiro, multiple Meixner
(kinds I and II), multiple Laguerre (kinds I and II), multiple Kravchuk, and
multiple Charlier, all represented in terms of hypergeometric functions. For
the cases of multiple Hahn, Jacobi-Pi\~neiro, Meixner of kind II, and Laguerre
of kind I, where there exists a region where the recurrence matrix is
nonnegative, subregions are identified where the bidiagonal factorization
becomes a positive bidiagonal factorization.Comment: 14 pages, 2 figure
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