A quantitative estimate of agglutinins in three Shigella flexneri antisera.

Thesis (Ph.D.)--Boston University.The Flexner group of dysentery organisms contains a number of strains classified together because of their close physiological and serological properties. The serological relationships of this group have been determined qualitatively by Boyd and Wheeler. According to these investigators, each Flexner type is distinguished by the presence in the cell of an antigen characteristic of that type. This antigen is called the "type-specific" antigen. Those antigens, possessed in common by several types, which are responsible for the serological cross reactions are designated as "group antigens". The purpose of this investigation was to study quantitatively (using the method of Heidelberger and Kabat to measure agglutinin nitrogen) the serological cross reactions that occur among Shigella flexneri types Ia, Ib and III. In so far as it seemed practical, a quantitative serological analysis was made of types Ia, Ib and III antisera. The type-specific antibody in each serum and the group "6" antibody in types Ib and III antisera was measured. It is this "group 6" factor, possessed in common by both Ib and III cells, which is responsible for the close serological relationship of these two types. [TRUNCATED

Formal groups arising from formal punctured ribbons

We investigate Picard functor of a formal punctured ribbon. We prove that under some conditions this functor is representable by a formal group scheme. Formal punctured ribbons were introduced in arXiv:0708.0985.Comment: 42 pages, minor change

Formal Contexts, Formal Concept Analysis, and Galois Connections

Formal concept analysis (FCA) is built on a special type of Galois connections called polarities. We present new results in formal concept analysis and in Galois connections by presenting new Galois connection results and then applying these to formal concept analysis. We also approach FCA from the perspective of collections of formal contexts. Usually, when doing FCA, a formal context is fixed. We are interested in comparing formal contexts and asking what criteria should be used when determining when one formal context is better than another formal context. Interestingly, we address this issue by studying sets of polarities.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Factoring Formal Maps into Reversible or Involutive Factors

An element $g$ of a group is called reversible if it is conjugate in the group to its inverse. An element is an involution if it is equal to its inverse. This paper is about factoring elements as products of reversibles in the group $\mathfrak{G}_n$ of formal maps of $(\mathbb{C}^n,0)$, i.e. formally-invertible $n$-tuples of formal power series in $n$ variables, with complex coefficients. The case $n=1$ was already understood. Each product $F$ of reversibles has linear part $L(F)$ of determinant $\pm1$. The main results are that for $n\ge2$ each map $F$ with det$(L(F))=\pm1$ is the product of $2+3c$ reversibles, and may also be factored as the product of $9+6c$ involutions, where $c$ is the smallest integer $\ge \log_2n$.Comment: 20 page

Realising formal groups

We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-8.abs.htm

Formal symplectic groupoid

The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function in the direction of a non-trivial Poisson structure so that the multiplication remains associative. We prove that such a deformation is unique under some reasonable conditions and we give the explicit formula for it. This formula turns out to be the semi-classical approximation of Kontsevich's deformation formula. For the case of a linear Poisson structure, the deformed generating function reduces exactly to the CBH formula of the associated Lie algebra. The methods used to prove existence are interesting in their own right as they come from an at first sight unrelated domain of mathematics: the Runge--Kutta theory of the numeric integration of ODE's.Comment: 28 pages, 4 figure