Bi-Hamiltonian structure of N-component Kodama equations

The author presents a simple way of constructing the second Hamiltonian operators for N-component Kodama equations. Using dimensional analysis he is led to an ansatz for the Hamiltonian operator as well as the conserved quantities in terms of ratios of polynomials. The coefficients of these polynomials are determined from the Jacobi identities. The resulting bi-Hamiltonian structure consists of generalization of Cavalcante and McKean's work (1982) for N=2 and his earlier results for N=3,4

Poisson structure of dynamical-systems with 3 degrees of freedom

Cataloged from PDF version of article.It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure. © 1993 American Institute of Physics

Successful Medical Management of Recalcitrant Fusarium solani Keratitis: Molecular Identification and Susceptibility Patterns

PubMedID: 22528742Fungal keratitis is a rare but sight-threatening infection of the cornea that may be caused by several fungal pathogens. A delay in diagnosis and inadequate treatment may even lead to loss of the affected eye. Fungal keratitis is often misdiagnosed as bacterial keratitis because isolation and identification of the fungal pathogen is difficult and requires experience, and fungal growth in culture requires time. In this report, a 14-year-old boy with recalcitrant Fusarium solani keratitis, unresponsive to initial therapy, is presented. CLSI M38-A2 in vitro antifungal susceptibility tests demonstrated that only amphotericin B (0. 5 µg/ml) had potent activity against F. solani; however, fluconazole (>64 µg/ml), itraconazole (>16 µg/ml), voriconazole (8 µg/ml), and posaconazole (>16 µg/ml) had high minimum inhibitory concentrations. In addition, caspofungin (>16 µg/ml) and anidulafungin (>16 µg/ml) exhibited high minimum effective concentrations. Repeated intrastromal voriconazole injections, topical voriconazole, and caspofungin combined with systemic antifungal agents improved of the corneal lesion with a significant increase in visual acuity. Intrastromal voriconazole injection may be used as an adjunctive treatment method for recalcitrant fungal keratitis with no prominent complications. The intrastromal route could be an effective route of administration of antifungal agents, especially for F. solani keratitis, as in this case. A combination of various antifungal agents administered by different routes prevented loss of the eye. © 2012 Springer Science+Business Media B.V

Cigarette smoke causes caspase-independent apoptosis of bronchial epithelial cells from asthmatic donors

Our results show that PBECs from asthmatic donors are more susceptible to CSE-induced apoptosis. This response involves AIF, which has been implicated in DNA damage and ROS-mediated cell-death. Epithelial susceptibility to CSE may contribute to the impact of environmental tobacco smoke in asthm

First integrals of a generalized Darboux–Halphen system

This pre-print has been submitted, and accepted, to the journal, Journal of Mathematical Physics [© American Institute of Physics]. The definitive version: HALBURD, R. and CHAKRAVARTY, S., 2003. First integrals of a generalized Darboux-Halphen system. Journal of Mathematical Physics, 44(4), pp. 1751-1762, is available at: http://jmp.aip.org/jmp/.A third-order system of nonlinear, ordinary differential equations depending on 3 arbitrary parameters is analyzed. The system arises in the study of SU(2)-invariant hypercomplex manifolds and is a dimensional reduction of the self-dual Yang-Mills equation. The general solution, first integrals and the Nambu-Poisson structure of the system are explicitly derived. It is shown that the first integrals are multi-valued on the phase space even though the general solution of the system is single-valued for special choices of parameters