Controllability of linear systems,differential geometry curves in grassmannians and generalized grassmannians,and riccati equations

We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators e^t B. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in ⁿ. We then view (t)=Im(e^t B) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(ⁿ). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(ⁿ), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit.     

Monotonicity properties of zeros of generalized Airy functions

Summary We show, among other things, that the positive zeros of a solution ofy +x y=0,y(0)=0 decrease to 1 as increases, 0.

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Sommario Si dimostra, tra l'altro, che gli zeri positivi d'una soiuzione diy +x y=0,y(0)=0 decrescono al limite 1, quando cresce, 0.

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To the memory of Milo Háik

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This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino.     

Algorithmic aspects of intersection graphs and representation hypergraphs

Let be a family of sets. The intersection graph of is obtained by representing each set in by a vertex and connecting two vertices by an edge if and only if their corresponding sets intersect. Of primary interest are those classes of intersection graphs of families of sets having some specific topological or other structure. The grandfather of all intersection graphs is the class of interval graphs, that is, the intersection graphs of intervals on a line.The scope of research that has been going on in this general area extends from the mathematical and algorithmic properties of intersection graphs, to their generalizations and graph parameters motivated by them. In addition, many real-world applications involve the solution of problems on such graphs.In this paper a number of topics in algorithmic combinatorics which involve intersection graphs and their representative families of sets are presented. Recent applications to computer science are also discussed. The intention of this presentation is to provide an understanding of the main research directions which have been investigated and to suggest possible new directions of research.     

The search for top quarks at hadron colliders: a realistic appraisal

We study means of identifying top quarks of mass in the range 70–120 GeV at the CERN and FNAL \(\bar pp\) colliders. We show that “W+dijet” production presents a serious background to the conventional “isolated electron+dijet” signature of top. We study an improved signature, calculate the expected event rates, and discuss the determination of the mass of the top quark.     

Conductivity relaxation in glass: Compositional contributions to non-exponentiality

That ionic conductivity in glass is a non-exponential process and has been known for many years. The amorphous structure of glass and hence a distribution of cation sites has often been thought to be the cause for the non-exponentiality. Almost completely unresearched, however, has been the effect of glass composition on the nature of the relaxation process. In this paper, we review the observations that have been made of the relationships between glass composition and the non-exponential character of the conductivity relaxation as well combine our recent wide composition range studies of sodium aluminoborate and lithium phosphate glasses to delineate the major features of the correlation. By examining glass compositions ranging from 0.02 to 60 mole% alkalioxide, it is observed that the rapid development of non-exponentiality within 1% Na₂O is accompanied by a similar rapid decrease in the average cation-cation separation distance, this being calculated using the composition and density. Other quantities such as the dc conductivity or activation energy are observed to vary too slowly with composition to produce a linear correlation with the extent of non-exponentiality as monitored in the parameter of the stretched exponentialkww function.     

Mixed C18 and C1 modification on an optical fiber for chromatographic sensing

An optical fiber-chromatographic sensor, aiming at simultaneous and selective response to multiple components following a chromatographic separation, is described. We report an improved approach for immobilization of octadecyl (C(18)) and methyl (C(1)) moieties as stationary phase on an optical fiber suitable as a sensing phase for organic solutes. By this approach, the stability and lifetime of the sensing layer as well as the detectability and retention behavior of the chromatographic sensor could be improved. Infrared spectroscopy was employed to confirm the presence of C(18) and C(1) moieties on the modified surface of the optical fiber. The chromatographic sensor was applied, with good sensitivity and chemical selectivity, to the simultaneous separation and detection of bromobenzene and toluene, using water as the mobile phase.