Construction of Ricci-type connections by reduction and induction

Given the Euclidean space $\R^{2n+2}$ endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, Baguis and Cahen have defined a reduction procedure which yields a symplectic manifold endowed with a Ricci-type connection. We observe that any symplectic manifold of dimension greater than 2 endowed with a symplectic connection of Ricci-type is locally given by a local version of such a reduction. We also consider the reverse of this reduction procedure, an induction procedure: we construct globally on a symplectic manifold endowed with a connection of Ricci-type $(M,\omega,\nabla)$ a circle or a line bundle which embeds in a flat symplectic manifold $(P,\mu ,\nabla^1)$ as the zero set of a function whose third covariant derivative vanishes, in such a way that $(M,\omega,\nabla)$ is obtained by reduction from $(P,\mu ,\nabla^1)$. We further develop the particular case of symmetric symplectic manifolds with Ricci-type connections

On Mpc-structures and Symplectic Dirac Operators

We prove that the kernels of the restrictions of symplectic Dirac or symplectic Dirac-Dolbeault operators on natural subspaces of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute those kernels for the complex projective spaces. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabilizer of a Lagrangian subspace) in the group Mpc and classify G-invariant Mpc-structures on symplectic spaces with a G-action. We prove a variant of Parthasarathy's formula for the commutator of two symplectic Dirac-type operators on a symmetric symplectic space

An integral formulation for wave propagation on weakly non-uniform potential flows

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform

Microstructure and properties of welds between 5754 Al alloys and AZ31 Mg alloys using a Yb:YAG laser

The authors wish to thank Mr. Henri ANDRZEJEWSKI for his technical assistance in laser experiments. The authors wish to place their sincere thanks to Professor Philippe BOURNOT and Dr. Eric VALERIO for helpful discussions.Dissimilar laser beam welding between A5754 Al alloy and AZ31 Mg alloy with the plate thickness of 2 mm was investigated. Complex flow pattern characterized by a large volume of intermetallic compounds Al12Mg17 and Al3Mg2 is formed in the fusion zone. Microhardness measurement of the dissimilar welds presents an uneven distribution due to the complicated microstructure of the weld, and the maximum value of microhardness in the fusion zone is much higher than of the base materials

Fermented mistletoe extract as a multimodal antitumoral agent in gliomas

In Europe, commercially available extracts from the white-berry mistletoe (Viscum album L.) are widely used as a complementary cancer therapy. Mistletoe lectins have been identified as main active components and exhibit cytotoxic effects as well as immunomodulatory activity. Since it is still not elucidated in detail how mistle toe extracts such as ISCADOR communicate their effects, we analyzed the mechanisms that might be responsible for their antitumoral function on a molecular and functional level. ISCADOR-treated glioblastoma (GBM) cells down-regulate central genes involved in glioblastoma progression and malignancy such as the cytokine TGF-β and matrix-metalloproteinases. Using in vitro glioblastoma/immune cell co-cultivation assays as well as measurement of cell migration and invasion, we could demonstrate that in glioblastoma cells, lectin-rich ISCADOR M and ISCADOR Q significantly enforce NK-cell-mediated GBM cell lysis. Beside its immune stimulatory effect, ISCADOR reduces the migratory and invasive potential of glioblastoma cells. In a syngeneic as well as in a xenograft glioblastoma mouse model, both pretreatment of tumor cells and intratumoral therapy of subcutaneously growing glioblastoma cells with ISCADOR Q showed delayed tumor growth. In conclusion, ISCADOR Q, showing multiple positive effects in the treatment of glioblastoma, may be a candidate for concomitant treatment of this cancer

Extrinsic symplectic symmetric spaces

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also build a natural star-quantization on a class of examples