Wiener type theorems for Jacobi series with nonnegative coefficients

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Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Most of the Abundant Protein Fractions of Embryonic Cerebrospinal Fluid are Produced Out of the Brain Anlagen

The microenvironment of the central nervous system is important for neuronal function and development. During the early stages of embryo development the cephalic vesicles are filled by embryonic cerebrospinal fluid, a complex fluid containing different protein fractions, which contributes to the regulation of the survival, proliferation and neurogenesis of neuroectodermal stem cells. The protein content of embryonic cerebrospinal fluid from chick and rat embryos at the start of neurogenesis has already been determined. Most of the identified gene products are thought to be involved in the regulation of developmental processes during embryogenesis. However, due to the crucial roles played by embryonic cerebrospinal fluid during brain development, the embryological origin of the gene products it contains remains an intriguing question. According to the literature most of these products are synthesised in embryonic tissues other than the neuroepithelium. In this study we examined the embryological origin of the most abundant embryonic cerebrospinal fluid protein fractions by means of slot-blot analysis and by using several different embryonic and extraembryonic protein extracts, immunodetected with polyclonal antibodies. This first attempt to elucidate their origin is not based on the proteins identified by proteomic methods, but rather on crude protein fractions detected by SDS-PAGE analysis and to which polyclonal antibodies were specifically generated. Despite some of the limitations of this study, i.e. that one protein fraction may contain more than one gene product, and that a specific gene product may be contained in different protein fractions depending on post-translational modifications, our results show that most of the analysed protein fractions are not produced by the cephalic neuroectoderm but are rather stored in the egg reservoir; furthermore, few are produced by embryo tissues, thus indicating that they must be transported from their production or storage sites to the cephalic cavities, most probably via embryonic serum. These results raise the question as to whether the transfer of proteins from these two embryo compartments is regulated at this early developmental stage.