Deriving bases for Abelian functions

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.Comment: 35page

BCG treatment of human tumour xenografts in athymic nude mice.

Xenografts of 3 human malignant cell lines in congenitally athymic nude mice have been examined for susceptibility to BCG. Growth of all 3 tumours, a bladder carcinoma, a melanoma and a colon carcinoma, was suppressed when cells were injected in admixture with BCG. Distant injection of BCG was ineffective. Mice with progressive growths had no detectable anti-human antibody, and rejection of cells and BCG failed to confer protection against subsequent tumour challenge. These studies indicate that human malignant cells are susceptible to local BCG-activated host responses, and that athymic mouse xenografts may be a useful model for assessing the response of human tumours to such agents

Serological aspects of rat tumour xenograft growth in athymic nude mice.

The serum of athymic nude mice bearing rat tumour xenografts has been examined for tumour-specific antigen. With a sarcoma and a hepatoma, tumour-specific antigen expression continued in xenograft growths, and sera of tumour-bearing mice contained free antigen, assayed by its ability to neutralise reactivity of tumour-immune rat sera against tumour target cells in an indirect membrane-immunofluorescence test. In contrast, no anti-rat antibody was detectable in sera of mice bearing the xenografts, or rejecting cells injected in admixture with BCG

Superfluid and Mott Insulator phases of one-dimensional Bose-Fermi mixtures

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the Canonical Worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and inter-species interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.Comment: 8 pages, 12 figure