On the zeros of a polynomial and its derivatives

If is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk, then the Gauss-Lucas theorem states that all zeros of lie in the same disk. We study the following question: what is the maximum distance from the arithmetic mean of all zeros of to a nearest zero of ? We obtain bounds for this distance depending on degree. We also show that this distance is equal to for polynomials of degree 3 and polynomials with real zeros.

     

New classes of self-similar symmetric stable random fields

We construct two new classes of symmetric stable self-similar random fields with stationary increments, one of the moving average type, the other of the harmonizable type. The fields are defined through an integral representation whose kernel involves a norm on ⁿ . We examine how the choice of the norm affects the finite-dimensional distributions. We also study the processes which are obtained by projecting the random fields on a one-dimensional subspace. We compare these projection processes with each other and with other well-known self-similar processes and we characterize their asymptotic dependence structure.The research was done at Boston University while the first author was on leave from the Hugo Steinhaus Center, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation.     

On “hyperboloidal” Cauchy data for vacuum einstein equations and obstructions to smoothness of Scri

The relationship between the geometric properties of hyperboloidal Cauchy data for vacuum Einstein equations at the conformal boundary of the initial data surface and between the space-time geometry is analyzed in detail. We prove that a necessary condition for existence of a smooth or a polyhomogeneous Scri (i.e., a Scri around which the metric is expandable in terms ofr ^–j log ⁱ r rather than in terms ofr ^–j ) is the vanishing of the shear of the conformal boundary of the initial data surface. We derive the boundary constraints which have to be satisfied by an initial data set for compatibility with Friedrich's conformal framework. We show that a sufficient condition for existence of a smooth Scri (not necessarily complete) is the vanishing of the shear of the conformal boundary of the initial data surface and smoothness up to boundary of the conformally rescaled initial data. We also show that the occurrence of some log terms in an asymptotic expansion at the conformal boundary of solutions of the constraint equations is related to the non-vanishing of the Weyl tensor at the conformal boundary.Supported in part by KBN grant #2 1047 91 01     

Interactions in water of alkyl and perfluoroalkyl surfactants with fluorocarbon- and hydrocarbon-modified poly(N-isopropylacrylamides)

Fluorescence spectroscopy and isothermal titration calorimetry (ITC) have been used to study the interactions in water at 25 degrees C of two anionic surfactants--sodium dodecyl sulfate (SDS) and sodium perfluorononanoate (SPFN)--with various pyrene-labeled hydrophobically modified poly(N-isopropylacrylamides) (HM-PNIPAM) grafted at random with small amounts of fluorocarbon chains (1H,1H-perfluorooctyl, CH2C7F15); (PNIPAM-F), or (n-octadecyl, C18H37) (PNIPAM-HPy) or both (PNIPAM-F/HPy). In aqueous solution, the copolymers form micellar structures consisting of a loose corona of hydrated poly(N-isopropylacrylamide) chains and a hydrophobic core rich in hydrocarbon or fluorocarbon groups. From fluorescence studies based on changes in the ratio of pyrene excimer to monomer emission intensity, it has been established (1) that mixed SDS/C18H37 clusters form along the polymer chain upon addition of SDS to either PNIPAM-HPy or PNIPAM-F/HPy and (2) that SPFN does not interact with the hydrocarbon-rich microdomains of the polymeric micelles. The conclusions were corroborated by ITC experiments, which yield the overall enthalpy change associated with polymer/surfactant interactions. They provided strong evidence (1) that SDS molecules adsorb along the PNIPAM main chain but do not mix with the fluorocarbon-rich microdomains of PNIPAM-F or PNIPAM-F/HPy and (2) that SPFN associates with the perfluorocarbon substituents of PNIPAM-F and PNIPAM-F/HPy but has a poor affinity for the polymer chain.     

Polyurethane anionomers synthesised with aromatic, aliphatic or cycloaliphatic diisocyanates, polyoxyethylene glycol and 2,2-bis-(hydroxymethyl)propionic acid. Part 3. Electrical properties of polyurethane coatings

The following electrical properties were found for polymer coatings obtained from polyurethane anionomers synthesised with the use of various diisocyanates: volume resistivity, permittivity and dielectric dissipation factor. The effects were discussed from the molecular structures and phase structures of those anionomers on the value of their ionic conductivity and polarizability. The anionomer prepared from the aliphatic diisocyanate was found to offer ionic conductivity; hence, that material can be considered to be a solid electrolyte, which exhibits a considerable susceptibility to structural modifications in the alternating electric field.     

Method of moments approach and coupled cluster theory

Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.Killam Research Fellow 1987–89     

Intercomparison on measurements of PCBs in pork fat during the Belgian PCB-crisis

During the Belgian PCB crisis (1999/2000) the quality of the data from the PCB monitoring were studied with a proficiency testing experiment. Pork fat that was spiked at the Institute for Reference Materials and Measurements (EC-JRC-IRMM) was sent out as unknown to all laboratories that participated in the monitoring. In parallel, the material was certified on the basis of the results of several leading PCB laboratories throughout Europe that did not participate in the monitoring. During the first round 15 to 25% deviation was experienced, while in the end of this multistep intercalibration procedure the average deviation for the respective PCBs was 10.9% (PCB 28), 13.1% (PCB 52), 10.1% (PCB 101), 10.7% (PCB 118), 10.7% (PCB 138), 9.1% (PCB 153), 8.1% (PCB 180) and 8.2% for the sum of the 7 PCBs. The concentrations measured for the higher volatile PCB 28 had a tendency to show lower levels, while for PCB 180 this was less pronounced. On the other hand, PCB 153 showed results rather to the higher side. During this exercise the material was also tested for stability by one of the certifying laboratories.     

ConjugatedSchiff's bases, 19 Cycloaddition of heterocumulenes to sterically congested 1,4-diazabutadiene 4N-oxides

Reactions of aryl isocyanates with sterically congested 1,4-diazabutadiene 4N-oxides representing bifunctional nitrones, proved to be 1,3-dipolar cycloadditions in which the nitrone 1,3-dipol manifested its predominant reactivity in comparison with the 1,4-diazabutadiene system. 3-Substituted 5-oxadiazolidinones resulted from these cycloadditions. Acidic hydrolysis of these products was also investigated.

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Konjugierte Schiff-Basen, 19. Mitt.: Cycloaddition von Heterokumulene an sterisch gehinderten 1,4-Diazabutadien-4N-oxiden

Zusammenfassung Die Reaktionen von Arylisocyanaten mit sterisch gehinderten 1,4-Diazabutadien-4N-oxiden als Vertretern bifunktioneller Nitrone erwies sich als eine 1,3-dipolare Cycloaddition, bei der sich der Nitron-1,3-Dipol in seiner Reaktivität im Vergleich mit dem 1,4-Diazabutadiensystem bevorzugt zeigte. Es wurden bei diesen Cycloadditionen 3-substituierte 5-Oxadiazolidinone erhalten. Die saure Hydrolyse dieser Produkte wurde ebenfalls untersucht.

     

Theoretical calculation of the coiled-coil stability in water in the context of its possible use as a molecular rack

The coiled-coil stability and rigidity may be of importance for molecular electronics (electronically bistable molecules). The coiled-coil binding free energy has been calculated using molecular dynamics (MD). The energy has been computed as a difference of the appropriate free energies; derived for the coiled-coil and isolated alpha-helices separately. All MD simulations have been performed using an explicit model of the solvent, whereas the continuum solvent approach has been applied to analyze the MD trajectories. The computed stability of the coiled-coil is of the order of -87 kcal/mol, i.e., about -1.2 kcal/mol per amino acid residue, and arises mainly from the electrostatic interactions and hydrophobic effect. The entropy term has been roughly estimated to be of the order of -22 kcal/mol. This assures that coiled-coil polypeptides may be used as a stable molecular scaffolding.