A note on rank-additivity

A new criterion is given for rank additivity of a collection of m × n complex matrices.     

Applications of photoconductivity measurements in n-InSb under crossed fields

The photocurrent in n-InSb at 85K was measured as function of the applied longitudinal voltage and an additionally applied transverse magnetic field. In the driftconfiguration the photoionized electron-hole plasma was driven into the sample volume, and negative photocurrents resulted from the negative feedback of this motion. With the magnetic field being reversed, in the Suhl configuration, only positive photocurrents were measured. All results are in agreement with the theory in [1]. They were used to determine recombination coefficients in n-InSb, and, principally, the transverse diffusion coefficientD _⊥. As first observed in [13],D _⊥ proved to be anomalously enhanced above classical values if plasma instabilities were generated in the samples.     

Classification of knot projections

The first step in tabulating the non-composite knots with n crossings is the tabulation of the non-singular plane projections of such knots, where two (piecewise linear) projections are regarded as equivalent, or in the same class, if they agree up to homeomorphism of the extended plane, i.e. two-sphere. This first step is here reduced to a simple algorithm suitable for computer use.     

Magnetoelastic domain wall wave in a ferromagnet

We show that in a magnetically and elastically uniaxial ferromagnetic insulator, a new type of inhomogeneous elastic wave may propagate along a 180° domain wall. A numerical example is given.     

Affine action and Margulis invariant

In this paper, we show that two Zariski dense subgroups consisting of hyperbolic elements in with the same marked Margulis invariant, are conjugate. We also consider in affine deformations an analogue of quasifuchsian deformation of Fuchsian groups.     

Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.     

Automata and Square Complexes

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedońska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.