The Goldman bracket characterizes homeomorphisms

We show that a homotopy equivalence between compact, connected, oriented surfaces with non-empty boundary is homotopic to a homeomorphism if and only if it commutes with the Goldman bracket. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Potential ultrastructural changes in rat epididymal cell types induced by Boswellia papyrifera and Boswellia carterii incense

Boswellia papyrifera and Boswellia carterii, known as Arabian incense, diffuses smoke, contaminating the air, which adversely affects human health. Therefore, this study was designed to ascertain the effect of these plants on histopathological and ultrastructure changes in cauda epididymis of Albino rats. Animals were exposed to 4 g/kg body weight of B. papyrifera and B. carterii daily for 120 days along with suitable controls. Our study indicates a significant reduction in epithelial heights. Cells showed signs of degeneration. The ultrastructural study revealed that the cauda epididymis was affected, including its cell types. Furthermore, a decrease in the size of mitochondria, Golgi complex, and both ERs was observed. In all treated groups, plasma fructose decreased considerably, indicating the sign of reduced energy, vital for motility and other sperm functions. The results of this study suggest that these plants systematically affect cauda epididymal cell types and its lumen through its potential toxicity. (C) 2013 Published by Elsevier Masson SAS on behalf of Academie des sciences.

The projective plane, J-holomorphic curves and Desargues' theorem

By a theorem of Gromov, for an almost complex structure J on CP2 tamed by the standard symplectic structure, the J-holomorphic curves representing the positive generator of homology form a projective plane. We show that this satisfies the Theorem of Desargues if and only if J is isomorphic to the standard complex structure. This answers a question of Ghys. (C) 2013 Published by Elsevier Masson SAS on behalf of Academie des sciences.

Ultrastructural and hormonal changes in rat cauda epididymal spermatozoa induced by Boswellia papyrifera and Boswellia carterii

Boswellia papyrifera and Boswellia carterii diffuses smoke polluting air that adversely affects indoor environment that certainly harm human health. Therefore, this study aims at ascertaining the effect of these plants on gonadal hormones and molecular changes in rat spermatozoa. The animals were exposed to 4 g/kg body weight of B. papyrifera and B. carterii daily for 120 days along with suitable controls. Significant decreases in FSH, LH and testosterone levels were evidenced, along with a reduction of protein, sialic acid, and carnitine levels. In sperm physiology, sperm count, motility, speed decrease, whereas sperm anomalies increase. TEM observation indicates morphological changes in plasma and acrosomal membranes, cytoplasmic droplet in the tail region, vacuolated, and disorganization of the mitochondrial sheath. These findings demonstrate that B. papyrifera and B. carterii smoke affects the process of sperm formation and maturation, which indicates the detrimental effects of these plants on the reproductive system. (c) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.d

Flag structure for operators in the Cowen-Douglas class

The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the flag structure is rigid in the sense that the unitary equivalence class of the operator and the flag structure determine each other. We obtain a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the Cowen-Douglas class. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.