Continuous Quotients for Lattice Actions on Compact Spaces

Let < SL _n ( ) be a subgroup of finite index, where n 5. Suppose acts continuously on a manifold M, where ₁(M) = ⁿ , preserving a measure that is positive on open sets. Further assume that the induced action on H ¹(M) is non-trivial. We show there exists a finite index subgroup < and a equivariant continuous map : M ⁿ that induces an isomorphism on fundamental group. We prove more general results providing continuous quotients in cases where ₁(M) surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with actions.     

Free actions of -groups on products of lens spaces

Let be an odd prime number. We prove that if acts freely on a product of equidimensional lens spaces, then . This settles a special case of a conjecture due to C. Allday. We also find further restrictions on non-abelian -groups acting freely on a product of lens spaces. For actions inducing a trivial action on homology, we reach the following characterization: A -group can act freely on a product of lens spaces with a trivial action on homology if and only if and has the -extension property. The main technique is to study group extensions associated to free actions.

     

Polar and coisotropic actions on Kähler manifolds

The main result of the paper is that a polar action on a compact irreducible homogeneous Kähler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

     

Accessibility of the matrix Riccati differential equation

A known result on the classification of transitive Lie group actions on complex Grassmann manifolds is exploited to derive a necessary and sufficient accessibility criterion for the complex matrix differential Riccati equation. We treat both cases, the symmetric as well as the non-symmetric Riccati equation. Corresponding accessibility results for the real Riccati equation are also available, but not stated here. An application to the accessibility of generalized double bracket flows is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Locally Weyl Invariant Massless Bosonic and Fermionic Spin-1/2 Action in the (Y4, g) Space-Time

We search for a real bosonic and fermionic action in four dimensions which both remain invariant under local Weyl transformations in the presence of contortion and non-metricity tensor. In the presence of the non-metricity tensor the investigation is extended to (W _n, g) space-time while when the torsion is encountered we are restricted to the (U ₄, g) space-time. Our results hold in general for the (Y ₄, g) space-time and we also calculate extra contributions to the conformal gravity.     

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility.The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells.The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.     

Von Neumann Algebras Associated with the Group SL2（R）

Let M\mathcal{M} and N\mathcal{N} be the von Neumann algebras induced by the rational action of the group SL ₂(ℝ) and its subgroup P on the upper half plane \mathbbH\mathbb{H}. We have shown that N\mathcal{N} is spatial isomorphic to the group von Neumann algebra L_P\mathcal{L}_P and characterized M\mathcal{M} and its commutant M￠\mathcal{M}' and gotten a generalization of the Mautner’s lemma. It is also shown that the Berezin operator commutates with the Laplacian operator.     

Slice theorem and orbit type stratification in infinite dimensions

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which the assumptions of this theorem are fulfilled. First, using Glöckner's inverse function theorem, we show that the linear action of a compact Lie group on a Fréchet space admits a slice. Second, using the Nash–Moser theorem, we establish a slice theorem for the tame action of a tame Fréchet Lie group on a tame Fréchet manifold. For this purpose, we develop the concept of a graded Riemannian metric, which allows the construction of a path-length metric compatible with the manifold topology and of a local addition. Finally, generalizing a classical result in finite dimensions, we prove that the existence of a slice implies that the decomposition of the manifold into orbit types of the group action is a stratification.     

Clove Essential Oil and Its Main Constituent,Eugenol, as Potential Natural Antifungals against Candida spp. Alone or in Combination with Other Antimycotics Due to Synergistic Interactions

The occurrence of candidiasis, including superficial infections, has recently increased dramatically, especially in immunocompromised patients. Their treatment is often ineffective due to the resistance of yeasts to antimycotics. Therefore, there is a need to search for new antifungals. The aim of this study was to determine the antifungal effect of clove essential oil (CEO) and eugenol (EUG) towards both reference and clinical Candida spp. strains isolated from the oral cavity of patients with hematological malignancies, and to investigate their mode of action and the interactions in combination with the selected antimycotics. These studies were performed using the broth microdilution method, tests with sorbitol and ergosterol, and a checkerboard technique, respectively. The CEO and EUG showed activity against all Candida strains with a minimal inhibitory concentration (MIC) in the range of 0.25–2 mg/mL. It was also found that both natural products bind to ergosterol in the yeast cell membrane. Moreover, the interactions between CEO and EUG with several antimycotics—cetylpyridinium chloride, chlorhexidine, silver nitrate and triclosan—showed synergistic or additive effects in combination, except nystatin. This study confirms that the studied compounds appear to be a very promising group of phytopharmaceuticals used topically in the treatment of superficial candidiasis. However, this requires further studies in vivo.     

Bimetallic catalysts for hydrogenation in liquid phase

Activity and selectivity of bimetallic catalysts for two model reactions, citral hydrogenation in isopropanol and nitrate reduction in water, are reviewed on the basis of results obtained over bimetallic systems prepared in our laboratory, notably by redox techniques. The parent metal is generally a noble metal (Rh, Pd, Pt), while the additive is most often a non-noble metal (Ge, Sn, Cu…) whose oxidation state plays an important role in hydrogenation. Dramatic improvements of the selectivity to unsaturated alcohols are observed in citral hydrogenation with adequate deposition of the additive and pretreatment of the final catalyst. In nitrate reduction, the second metal essentially affects the first step of the process (conversion of nitrate to nitrite) but the global selectivity (limitation of NH₃ formation) may be significantly improved by tuning the couple parent metal–additive. Other aspects such as the choice of the support and the optimization of reaction conditions (temperature, pressure, pH effects in water) are also discussed.