The scattering off a potential of finite rank (a sum of a finite number of separable potentials) is studied thoroughly in the neighborhood of infinity of potential strength; for this purpose we introduce the "strong coupling representation" by means of a canonical transformation. The same K matrix as for the infinitely strong repulsion is derived for the infinitely strong attraction. The differ...

Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2(A) to H−2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.

Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...

By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...

We prove a version of the O'Nan-Scott Theorem for detinably primitive permutation groups of finite Morley rank. This yields questions about structures of finite Morley rank of the form (F, + , . , / / ) where (F, +,.) is an algebraically closed field and H is a central extension of a simple group with /Y=sGL(rt, F). We obtain partial results on such groups H, and show for example that if char(/...

Introduction Groups of finite Morley rank made their first appearance in model theory as binding groups, which are the key ingredient in Zilber's ladder theorem and in Poizat's explanation of the Picard-Vessiot theory. These are not just groups, but in fact permutation groups acting on important definable sets. When they are finite, they are connected with the model theoretic notion of algebrai...

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovász) base reduction algorithm [20], cryptographic...

Let (rI , r, ,...) be a sequence of non-negative integers summing to n. We determine under what conditions there exists a finite distributive lattice L of rank n with ri join-irreducibles of rank i, for all i = 1,2,.. . . When I. exists, we give explicit expressions for the greatest number of elements L can have of any given rank, and for the greatest total number of elements L can have. The pr...

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovász) base reduction algorithm [20], cryptographic...