Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a representation of the $n$th minor as an $n\times n$ determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit formula for the functional derivative of a Fredholm minor of order $n$ with respect to the kernel. Our formula is a linear combination of the $n$th and the $n\pm 1$th minors.Comment: 17 pages, Latex, no figures connection to supplementary compound matrices mentioned, references added, typos correcte

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Exploratory study on the behaviour of glass/PDCPD composites

© 2015 International Committee on Composite Materials. All rights reserved. The potential of the tough thermoset polydicyclopentadiene (PDCPD) as a matrix for composite materials was explored in this study. A range of properties was compared for a composite with a PDCPD formulation matrix and an equivalent epoxy composite. The PDCPD composite showed higher interlaminar fracture toughness and reduced damage development during tensile loading. Improved fatigue life and higher compressive strength were observed. Impact damage was greatly reduced and substantial improvement in compression after impact strength was noted. Based on the obtained results, the PDCPD formulation used in this work can be considered an interesting alternative for brittle thermosets.status: publishe

4-(1H-Pyrazol-1-yl) Benzenesulfonamide Derivatives: Identifying New Active Antileishmanial Structures for Use against a Neglected Disease

Submitted by Sandra Infurna ([email protected]) on 2018-11-06T10:52:31Z No. of bitstreams: 1 marilene_cavalheiro_etal_IOC_2012.pdf: 293836 bytes, checksum: 67e35006a093a0701d7d6684125401b8 (MD5)Approved for entry into archive by Sandra Infurna ([email protected]) on 2018-11-06T11:04:44Z (GMT) No. of bitstreams: 1 marilene_cavalheiro_etal_IOC_2012.pdf: 293836 bytes, checksum: 67e35006a093a0701d7d6684125401b8 (MD5)Made available in DSpace on 2018-11-06T11:04:44Z (GMT). No. of bitstreams: 1 marilene_cavalheiro_etal_IOC_2012.pdf: 293836 bytes, checksum: 67e35006a093a0701d7d6684125401b8 (MD5) Previous issue date: 2012Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal Fluminense. Instituto de Biologia. Programa de Pós-graduação em Ciências e Biotecnologia. Niterói, RJ, Brasil.Fundação Oswaldo Cruz. Instituto Oswaldo Cruz. Laboratório de Bioquímica de Tripanosomatídeos. Rio de Janeiro, RJ. Brasil.Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal do Rio de Janeiro. Faculdade de Farmácia. ModMolQSAR. Rio de Janeiro, RJ, Brasil.Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Química. Niterói, RJ, Brasil.Universidade Federal do Rio de Janeiro. Faculdade de Farmácia. ModMolQSAR. Rio de Janeiro, RJ, Brasil.Fundação Oswaldo Cruz. Instituto Oswaldo Cruz. Laboratório de Bioquímica de Tripanosomatídeos. Rio de Janeiro, RJ. Brasil.Fundação Oswaldo Cruz. Instituto Oswaldo Cruz. Laboratório de Bioquímica de Tripanosomatídeos. Rio de Janeiro, RJ. Brasil.Universidade Federal Fluminense. Instituto de Biologia. Programa de Pós-graduação em Ciências e Biotecnologia. Niterói, RJ, Brasil.Leishmaniasis is a neglected disease responsible for about 56,000 deaths every year. Despite its importance, there are no effective, safe and proper treatments for leishmaniasis due to strain resistance and/or drug side-effects. In this work we report the synthesis, molecular modeling, cytotoxicity and the antileishmanial profile of a series of 4-(1H-pyrazol-1-yl)benzenesulfonamides. Our experimental data showed an active profile for some compounds against Leishmania infantum and Leishmania amazonensis. The profile of two compounds against L. infantum was similar to that of pentamidine, but with lower cytotoxicity. Molecular modeling evaluation indicated that changes in electronic regions, orientation as well as lipophilicity of the derivatives were areas to improve the interaction with the parasitic target. Overall the compounds represent feasible prototypes for designing new molecules against L. infantum and L. amazonensis