A Tree Version of Kőnig's Theorem

Kőnig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalization, in which the point in one fixed side of the graph of each edge is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell [2]. As an application we prove a special case (that of chordal graphs) of a conjecture of B. Reed. Received January 27, 2000/Revised November 2, 2000 RID=" " ID=" " The research of the first author was supported by grants from the Israel Science Foundation, the M. & M.L Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.     

Explicit norm one elements for ring actions of finite abelian groups

It is known that the norm map N _G for the action of a finite groupG on a ringR is surjective if and only if for every elementary abelian subgroupU ofG the norm map N _U is surjective. Equivalently, there exists an elementx _G ∈R satisfying N _G (x _G )=1 if and only if for every elementary abelian subgroupU there exists an elementx _U ∈R such that N _U (x _U )=1. When the ringR is noncommutative, it is an open problem to find an explicit formula forx _G in terms of the elementsx _U . We solve this problem when the groupG is abelian. The main part of the proof, which was inspired by cohomological considerations, deals with the case whenG is a cyclicp-group. Supported by TMR-Grant ERB FMRX-CT97-0100 of the European Union.     

Decay of the diocotron rotation and transport in a new low-density asymmetry-dominated regime

The decay of the diocotron rotation was studied in a new regime in which trap asymmetries dominate. Decay within a few diocotron periods was observed, sometimes orders of magnitude faster than predicted by the traditional "rotational pumping" theory. The decay does not conserve angular momentum, and is strongest for small, low-density columns. The new regime appears when "magnetron-like" rotation from the end confinement fields becomes dominant, and appears to be associated with errors in these fields. Transition to decay dominated by rotational pumping was observed for larger and denser columns. The asymmetry-dominated transport was also studied, and found to depend linearly on the line density (and not the density) over nearly 4 orders of magnitude.     

Quantifying motion in video recordings of neonatal seizures by regularized optical flow methods.

This paper presents the development of regularized optical flow computation methods and an evaluation of their performance in the extraction of quantitative motion information from video recordings of neonatal seizures. A general formulation of optical flow computation is presented and a mathematical framework for the development of practical tools for computing optical flow is outlined. In addition, this paper proposes an alternative formulation of the optical flow problem that relies on a discrete approximation of a family of quadratic functionals. These regularized optical flow computation methods are used to extract motion strength signals from video recordings of neonatal seizures.     

Stable Equilibrium Based on Lévy Statistics:A Linear Boltzmann Equation Approach

To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, we consider stochastic collision models. The models are a generalization of the Rayleigh collision model, for a heavy one dimensional particle M interacting with ideal gas particles with a mass m<<M. Similar to previous approaches we assume elastic, uncorrelated, and impulsive collisions. We let the bath particle velocity distribution function to be of general form, namely we do not postulate a specific form of power-law equilibrium. We show, under certain conditions, that the velocity distribution function of the heavy particle is Lévy stable, the Maxwellian distribution being a special case. We demonstrate our results with numerical examples. The relation of the power law equilibrium obtained here to thermodynamics is discussed. In particular we compare between two models: a thermodynamic and an energy scaling approaches. These models yield insight into questions like the meaning of temperature for power law equilibrium, and into the issue of the universality of the equilibrium (i.e., is the width of the generalized Maxwellian distribution functions obtained here, independent of coupling constant to the bath).     

Solubility and miscibility of poly(ethyl oxazoline)

The solubility of poly(ethyl oxazoline) in aqueous solutions was studied. The cloud point temperatures decreased in the presence of sodium chloride but increased by the addition of tetrabutylammonium bromide or dioxane. Solution-cast films of blends of the polymer and poly(acrylic acid) were miscible, but mutual precipitation occurred in water, methanol, and dioxane. The compositions of the complexes correspond in most cases to simple molar ratios of the interacting groups. The glass transition temperatures of the complexes are higher than the values for blends of the same compositions, and the high values are attributed to hydrogen bonds acting as physical crosslinks. Complex formation also occurs when the polymer is mixed with a styrene-acrylic acid copolymer and with low weight polymers containing phenol groups.     

PROTECTION AGAINST DIHEMATOPORPHYRIN ETHER PHOTOSENSITIVITY

Abstract Amelioration of dihematoporphyrin ether (DHE) induced skin photosensitivity by medications either suspected or known to influence porphyrin metabolism or inflammatory response was evaluated in 357 female athymic NCR-nude mice (308 study animals, 49 controls) in 56 separate study groups. Seventy-two hours after injection with 25 mg/kg of DHE, the study animals'abdomens were irradiated with 4.125-4.25 J/cm² of visible light. Controls were irradiated after receiving either medication, solubilizing agent, or no injection. The abdominal surface burns were examined daily and graded as extensive, partial, or no burn. Statistical comparison was made between irradiated mice injected with DHE only and irradiated mice injected with DHE and medication. Injection of medications which influenced metabolism (hydroxychloroquine, hydrochlorothiazide) produced fewer extensive ( P < 0.01) but greater frequencies of partial burns than DHE controls. Medications which block histamine effect (cimetidine and/or hydroxyzine) resulted in fewer extensive ( P < 0.03) and roughly equal frequencies of partial burns compared with DHE controls. Steroids (dexamethasone, methylpred-nisolone, triamcinolone) which interfere with inflammatory response resulted in similar extensive and partial burn levels. Control animals receiving only medication, solubilizing agent, or no injection had no photosensitivity and consequently showed no burns. The results from this study suggest that inhibition of histamine effect and, to a lesser extent, increased activity of porphyrin catabolic pathways may decrease skin photosensitivity associated with DHE administration.