Brylawski [2] has shown that loopless principal transversal matroids have critical exponent at most 2. Welsh [4] asks if a similar result holds for all transversal matroids. We answer in the affirmative by proving that all loopless transversal matroids have critical exponent at most 2. The terminology used here for matroids will in general follow Welsh 131. A rank r transversal matroid M is rep...

Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps. To each Whitney stratified manifold we assign transversal homotopy monoids, one for each natural number. The assignment is functorial for a natural class of maps which we call stratified normal submersions. When the stratif...

A distnbuted amplifier based 5-tap tramversai filter using MESFET implementation of the Gilbert Cell as the tap weights has been designed for use as a fractonally spilfed adjustable equaluer in high speed optical c~mmunication systems. The effective tramconductance of the Gilbert Celi can be adjusted h m negative to positive values and therefore the transversal filter designed has adjustable po...

Abstract: The analysis of transversal filters based on a novel cell design in common-source configuration (TF-CS) is presented. Based on this approach, a distributed transversal filter was designed as a monolithic microwave integrated circuit (MMIC) for optical-CDMA receiver systems [1]. In order to assess its performance, a transversal filter based on Gilbert cells (TF-GC) was designed using t...

We classify positive transversal torus knots in tight contact structures up to transversal isotopy.

We analyze the vector magnetograms in several well-developed active regions obtained at Huairou Solar Observing Station, National Astronomical Observatories of China, at Mees Solar Observatory, University of Hawaii, and at National Astronomical Observatory of Japan. It is found that there is a basic agreement on the transversal fields among these magnetographs. The observational error (mutual d...

A P4-transversal of a graph G is a set of vertices T which meets every P4 of G. A P4transversal T is called stable if there are no edges in the subgraph of G induced by T . It has been previously shown by Hoàng and Le that it is NP -complete to decide whether a comparability (and hence perfect) graph G has a stable P4-transversal. In the following we show that the problem is NP -complete for ch...