On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.Comment: to appear in Journal of Mathematical Physics, 17 pages, Late

Deformed Harry Dym and Hunter-Zheng Equations

We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the non-standard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a non-standard description will involve a pseudo-differential operator of infinite order.Comment: Latex file, 15 page

Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time

A classification of all possible realizations of the Galilei, Galilei-similitude and Schroedinger Lie algebras in three-dimensional space-time in terms of vector fields under the action of the group of local diffeomorphisms of the space \R^3\times\C is presented. Using this result a variety of general second order evolution equations invariant under the corresponding groups are constructed and their physical significance are discussed

Telomerase activation cooperates with inactivation of p16 in early head and neck tumorigenesis

Alteration of the p16/pRb pathway may cooperate with telomerase activation during cellular immortalization and tumour progression. We studied p16 expression status by immunohistochemistry and telomerase activity using the TRAP assay in 21 premalignant lesions of the head and neck epithelium as well as 27 squamous-cell carcinomas. We also examined expression of other components of the pathway (cyclin D1 and pRb) as well as presence of human papillomavirus genomes which can target these molecules. 4 of 9 mild dysplastic lesions (44%), 8 of 12 moderate/severe dysplastic lesions (67%), and 25 of 27 squamous-cell carcinomas (92%) demonstrated high telomerase activity (P = 0.009). There was a parallel increase with severity of lesions for the trend in proportions of cases demonstrating p16 inactivation or cyclin D1 overexpression (P = 0.02 and P = 0.01, respectively). For Ki67, a marker of cell proliferation, this trend was not significant (P = 0.08). Human papillomavirus infection was only found in 4 cases among the 48 samples tested (8.3%). In conclusion, progression of disease is accompanied by a parallel and continuous increase in telomerase activity and alterations in cell cycle regulators (p16, cyclin D1), as proposed by in vitro models. © 2001 Cancer Research Campaign http://www.bjcancer.co

Local and non-local equivalent potentials for p-12C scattering

A Newton-Sabatier fixed energy inversion scheme has been used to equate inherently non-local p-${}^{12}$C potentials at a variety of energies to pion threshold, with exactly phase equivalent local ones. Those energy dependent local potentials then have been recast in the form of non-local Frahn-Lemmer interactions.Comment: 15 pages plus 9 figures submitted to Phys. Rev.

Action versus Result-Oriented Schemes in a Grassland Agroecosystem: A Dynamic Modelling Approach

Effects of agri-environment schemes (AES) on biodiversity remain controversial. While most AES are action-oriented, result-oriented and habitat-oriented schemes have recently been proposed as a solution to improve AES efficiency. The objective of this study was to compare action-oriented, habitat-oriented and result-oriented schemes in terms of ecological and productive performance as well as in terms of management flexibility. We developed a dynamic modelling approach based on the viable control framework to carry out a long term assessment of the three schemes in a grassland agroecosystem. The model explicitly links grazed grassland dynamics to bird population dynamics. It is applied to lapwing conservation in wet grasslands in France. We ran the model to assess the three AES scenarios. The model revealed the grazing strategies respecting ecological and productive constraints specific to each scheme. Grazing strategies were assessed by both their ecological and productive performance. The viable control approach made it possible to obtain the whole set of viable grazing strategies and therefore to quantify the management flexibility of the grassland agroecosystem. Our results showed that habitat and result-oriented scenarios led to much higher ecological performance than the action-oriented one. Differences in both ecological and productive performance between the habitat and result-oriented scenarios were limited. Flexibility of the grassland agroecosystem in the result-oriented scenario was much higher than in that of habitat-oriented scenario. Our model confirms the higher flexibility as well as the better ecological and productive performance of result-oriented schemes. A larger use of result-oriented schemes in conservation may also allow farmers to adapt their management to local conditions and to climatic variations

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.Comment: submitted to Math.Meth.Appl.Sc

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. Darboux-Crum transformations are applied to connect the well-known shape invariant Hamiltonians of the radial oscillator and the Darboux-P\"oschl-Teller potential to the shape invariant potentials of Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of generalised Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure

Democratic cultural policy : democratic forms and policy consequences

The forms that are adopted to give practical meaning to democracy are assessed to identify what their implications are for the production of public policies in general and cultural policies in particular. A comparison of direct, representative, democratic elitist and deliberative versions of democracy identifies clear differences between them in terms of policy form and democratic practice. Further elaboration of these differences and their consequences are identified as areas for further research

On Integrable Doebner-Goldin Equations

We suggest a method for integrating sub-families of a family of nonlinear {\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries. Since the method of integration involves non-local transformations of dependent and independent variables, general solutions obtained include implicitly determined functions. By properly specifying one of the arbitrary functions contained in these solutions, we obtain broad classes of explicit square integrable solutions. The physical significance and some analytical properties of the solutions obtained are briefly discussed.Comment: 23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.st