Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Multiscale variety in complex systems

The Law of Requisite Variety is a mathematical theorem relating the number of control states of a system to the number of variations in control that is necessary for effective response. The Law of Requisite Variety does not consider the components of a system and how they must act together to respond effectively. Here we consider the additional requirement of scale of response and the effect of coordinated versus uncoordinated response as a key attribute of complex systems. The components of a system perform a task, with a number of such components needed to act in concert to perform subtasks. We apply the resulting generalization—a Multiscale Law of Requisite Variety—to understanding effective function of complex biological and social systems. This allows us to formalize an understanding of the limitations of hierarchical control structures and the inadequacy of central control and planning in the solution of many complex social problems and the functioning of complex social organizations, e.g., the military, healthcare, and education systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 37–45, 2004     

Femtosecond dynamics of secondary radiation formation from quantum well excitons

The time-resolved secondary emission of resonantly created excitons in GaAs quantum wells is studied using femtosecond up-conversion spectroscopy. The behaviour of the rise and decay of the secondary emission and reflectivity in quantum wells is strongly dependent upon the disorder at the interfaces, the exciton density and the temperature. In the case of low densities and temperatures the emission is independent of the exciton density and rises quadratically in time, in excellent agreement with recent theory for Rayleigh scattering from two-dimensional excitons subjected to disorder. These rise times are compared directly with times measured by time-integrated four-wave mixing (FWM). The comparison of the dynamics displayed in time-resolved secondary radiation and time-integrated FWM provide a clear understanding of the coherence properties of QW excitons in the first few picoseconds after excitation. High-contrast oscillations that are due to quantum beats between the heavy- and light-hole 1s-states are seen. The visibility decay at very low densities is long ps and is related to the action of potential fluctuations on the scattering of heavy-hole and light-hole excitons.     

High-frequency (140-GHz) time domain EPR and ENDOR spectroscopy: the tyrosyl radical-diiron cofactor in ribonucleotide reductase from yeast

High-frequency pulsed EPR and ENDOR have been employed to characterize the tyrosyl radical (Y*)-diiron cofactor in the Y2-containing R2 subunit of ribonucleotide reductase (RNR) from yeast. The present work represents the first use of 140-GHz time domain EPR and ENDOR to examine this system and demonstrates the capabilities of the method to elucidate the electronic structure and the chemical environment of protein radicals. Low-temperature spin-echo-detected EPR spectra of yeast Y* reveal an EPR line shape typical of a tyrosyl radical; however, when compared with the EPR spectra of Y* from E. coli RNR, a substantial upfield shift of the g(1)-value is observed. The origin of the shift in g(1) was investigated by 140-GHz (1)H and (2)H pulsed ENDOR experiments of the Y2-containing subunit in protonated and D(2)O-exchanged buffer. (2)H ENDOR spectra and simulations provide unambiguous evidence for one strongly coupled (2)H arising from a bond between the radical and an exchangeable proton of an adjacent residue or a water molecule. Orientation-selective 140-GHz ENDOR spectra indicate the direction of the hydrogen bond with respect to the molecular symmetry axes and the bond length (1.81 A). Finally, we have performed saturation recovery experiments and observed enhanced spin lattice relaxation rates of the Y* above 10 K. At temperatures higher than 20 K, the relaxation rates are isotropic across the EPR line, a phenomenon that we attribute to isotropic exchange interaction between Y* and the first excited paramagnetic state of the diiron cluster adjacent to it. From the activation energy of the rates, we determine the exchange interaction between the two irons of the cluster, J(exc) = -85 cm(-)(1). The relaxation mechanism and the presence of the hydrogen bond are discussed in terms of the differences in the structure of the Y*-diiron cofactor in yeast Y2 and other class I R2s.     

Crystallization kinetic studies: A means to evaluate time-temperature-transformation curves. Application to metallic glasses

It is shown that the study of the kinetics of crystallization of an amorphous alloy may be used to obtain the correct form of the low temperature part of the time-temperature-transformation (T-T-T) curves. A unified review of the current kinetics of crystallization studies is presented and the general kinetic equation which gives the reaction rate as a function of temperature and crystalline fraction is shown to contain information related to theT-T-T-curves. Finally examples of application to two metallic glasses, Nd₃Fe₇₇B₂₀ and Fe_67.5Co₁₅Nb_1.5B₁₆, obtained by rapid solidification techniques are presented. The comparison between theory and experiment is satisfactory.

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Zusammenfassung Es wird gezeigt, daß die Untersuchung der Kristallisationskinetik von amorphen Legierungen genutzt werden kann, die korrekte Form des Niedertemperaturbereiches der Zeit-Temperatur-Transformation (T-T-T) Kurven zu erhalten. Es wird ein einheitlicher Überblick über die jüngsten Untersuchungen von Kristallisationskinetiken gegeben und an der allgemeinen Gleichung der Reaktionsgeschwindigkeit als eine Funktion von Temperatur und Kristallanteil wird gezeigt, daß sie Informationen bezüglich der T-T-T-Kurven beinhaltet. Letztlich wird eine Anwendung an zwei, durch schnelles Erstarren gewonnenen metallischen Gläsern Nd₃Fe₇₇B₂₀ und Fe_67.5Co₁₅Nb_1.5B₁₆ dargelegt. Zwischen Theorie und Praxis konnte eine ausreichende Übereinstimmung festgestellt werden.

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Dedicated to Professor Dr. H. J. Seifert on the occasion of his 60^th birthday

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This work was supported by the Comision Interdepartamental de Cienca y Tecnologia, CICYT (project No. MAT88-0439) which are acknowledged.     

Real-time measurement and control of particle-number density and size of the detonation products of lead azide

Time-resolved measurement and modeling of the number density and size of lead particles produced following the detonation of Lead Azide (LA) are presented. Particles expanding freely into vacuum through a supersonic nozzle or interacting with a barrier placed above the LA sample are monitored via attenuation of laser beams at 0.67, 1.3 and 10.6 µm. The attenuation depends on the conditions of expansion, but is always much more pronounced at 0.67 µm and 1.3 µm. From the ratio between the attenuations at 0.67 µm and 10.6 µm, the radius and number density of the particles are calculated applying Beer's law and Mie's theory. It is found that 20–90 µs following the detonation the attenuation at 32–36 mm above the LA sample is due to particles with radii of 0.9, 0.7 and 0.1 µm for free expansion into vacuum through the nozzle or near the barrier, respectively. Also, the expansion through the nozzle results in a transparent medium above the nozzle exit for the first few µs following the detonation. The effect of the nozzle is attributed to the fact that the velocity of the expanding detonation products is supersonic, which leads to compression and heating in the throat region, in contrast to the more familiar phenomenon of cooling at subsonic velocities. The dynamics of particles expanding under the different conditions and the mechanism of size reduction and elimination of particles is discussed.     

Metal complexes of a homopolymer system containing diethanolamine side group: synthesis and dielectrical behaviors

In this work, 4-diethanolaminomethyl styrene (DEAMSt) monomer was prepared by modification of 4-chloromethyl styrene with diethanolamine. The homopolymerization of styrene modificated was carried out by free radical polymerization method at 60?°C in presence of 1,4-dioxane and AIBN. The metal complexes were prepared by reaction of the homopolymer used as ligand P(DEAMSt)L^l and Ni(II), Co(II) metal ions in presence of ethanol and dilute NaOH at 65?°C for 48?h in pH 6.

The structure of modificated monomer, homopolymer used as ligand and polymer-metal complexes were characterized by (FT-IR), ¹H-NMR, ¹³C-NMR, Raman spectroscopy tecniques, elemental analysis, SEM, XRD and magnetic measurements. Their geometric structures according to magnetic measurements of Co(II) and Ni(II) complexes were estimated that have a tetrahedral structure. P(DEAMSt)L^l polymer has a transition state between amorphous and crystalline, whereas metal complexes (Co(II) and Ni(II) are with a large crystal structure. The molecular weight of P(DEAMSt)L¹ homopolymer was determined by gel permeation chromatography (GPC). The glass transition temperature (Tg) of homopolymer was measured by differantial scanning calorimeter (DSC). The thermal behaviors of both ligand and polymer-metal complexes were investigated by thermogravimetric analysis (TGA) and (DTA). The results obtained were compared with each other. Then, the dielectrical measurements (dielectric constant, dielectric loss and conductivity) of the ligand and polymer-metal complexes were investigated as a function of temperature and frequency. The activation energies (Ea) of the ligand and metal complexes were determined from the conductivity measurements.     

Thermosensitive mucoadhesive gel formulation loaded with 5-Fu: cyclodextrin complex for HPV-induced cervical cancer

Human Papilloma Virus (HPV) infections are the major cause of cervical cancers. To achieve a better therapeutic efficacy and patient compliance in the treatment for HPV-induced cervical cancers, anticancer agent 5-fluorouracil has been formulated in a vaginal gel using the thermosensitive polymer Pluronic^® F127 together with alternative mucoadhesive polymers e.g., hyaluronic acid, Carbopol 934 and hydroxypropylmethylcellulose. To increase its aqueous solubility and to achieve the complete release of 5-FU from the gel, the drug was incorporated as its inclusion complex with 1:1 molar ratio with either β-cyclodextrin or hydroxypropyl-β-cyclodextrin. Following the characterization of drug:CD complexes, thermosensitive gel formulations containing different mucoadhesive polymers and the drug in free or complexed form were characterized in vitro by determining the gelation temperature and the rheological behavior of different formulations along with the in vitro release profiles of these formulations in pH 5.5 citrate buffer. It was observed that complexation with cyclodextrin accelerated the release of 5-FU with the exception of formulation containing Carbopol 934 as mucoadhesive polymer. As far as rheological properties are concerned, favorable thermosensitive in situ gelling properties were obtained with formulations containing HPMC as mucoadhesive polymer. Complete release of 5-FU from gels were obtained with both complexes of β-CD and HP-β-CD and cytotoxicity studies against HeLa human cervical carcinoma cells demonstrated that 1% 5-FU:CD complexes were equally effective as 1% free 5-FU indicating better therapeutic efficacy with lower dose.