Acoustic Scattering and the Extended Korteweg deVries hierarchy

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa-Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.Comment: 18 page

On Soliton Content of Self Dual Yang-Mills Equations

Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map \C^4 \to \C^{\infty } satisfying a simple system of linear equations formulated below one can pull back the (generalized) Drinfeld-Sokolov hierarchies to the Self Dual Yang-Mills equations. This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method. In particular this class contains the solutions obtained via the symmetry reductions of the Self Dual Yang-Mills equations. It also contains genuine 4 dimensional solutions . The method can be used to study the symmetry reductions and as an example of that we get an equation exibiting breaking solitons, formulated by O. Bogoyavlenskii, as one of the $2 + 1$ dimensional reductions of the Self Dual Yang-Mills equations.Comment: 11 pages, plain Te

Multipeakons and a theorem of Stieltjes

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.Comment: 6 page

Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation

In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Padé approximants of a Nikishin system. The study is motivated by a mixed Hermite-Padé approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.This author [G.L.L] was supported by research grant MTM2015-65888-C4-2-P of Ministerio de Economía, Industria y Competitividad. This author [S.M.P.] received support from research grant CONICYT Fondecyt/Postdoctorado/ Proyecto 3170112. [J.S] Partially supported by NSERC

Assessment of Wild Mustard (Sinapis arvensis L.) Resistance to ALS-inhibiting Herbicides

There is an urgent need for rapid, accurate, and economical screening tests that can determine if weeds surviving a herbicide application are resistant. This chapter describes development and application of a simple root length bioassay technique for detection of wild mustard (Sinapis arvensis L.) resistance to ALS-inhibiting herbicides. This bioassay was performed in 2-oz WhirlPak® bags filled with 50 g of soil wetted to 100% moisture content at field capacity. Wild mustard seeds were pre-germinated in darkness in Petri dishes lined with moist filter paper for 2 days. Six seeds with well-developed radicles were planted in the non-treated soil and in soil with added herbicide, and plants were grown in a laboratory under fluorescent lights. After 4 days of growth, WhirlPak® bags were cut open, soil was washed away, intact plants were removed, and root length was measured with a ruler. The concentration of each herbicide in soil at which a significant root inhibition of susceptible biotype, but no root inhibition of a resistant biotype occurred was selected. Susceptibility/resistance of wild mustard populations was estimated by calculating the percentage of uninhibited roots of plants grown in the herbicide-treated soil as compared to the plants grown in the non-treated soil

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Moment determinants as isomonodromic tau functions

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.Comment: 24 page

Effect of soil pH on sulfentrazone phytotoxicity

Non-Peer Reviewe