Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Role of the molecular weight and the composition on the hydrolysis kinetics of monolayers of poly(α-hydroxy acid)s

The hydrolysis kinetics of spread insoluble monolayers of poly(α-hydroxy acid)s with various molecular weights and lactic acid–glycolic acid molar ratios was followed by measuring simultaneously the decrease in the surface area at constant surface pressure and the evolution of the surface potential. The interfacial hydrolysis at alkaline pH leads to the progressive fragmentation of the polymer molecules and the appearance of charged insoluble products (detected by measuring the surface potential) and small soluble fragments (detected by measuring the decrease in the surface area). The data obtained by both approaches were interpreted in the framework of the random scission model. The rates of hydrolysis are larger for polymers with smaller initial polymerization numbers and increase with the decrease in the molar ratio of lactic acid units. Received: 7 December 1998 Accepted in revised form: 8 March 1999     

State,electrical and rheological properties of model and dioxan isolated lignin films at the air–water interface

The properties of monolayers of the dioxan lignin and of model dehydrogenation polymers spread at the air-water interface were investigated by the following techniques: surface pressure, surface potential, ellipticity, rheological analysis and molecular modeling. Information about the state of the monolayer was obtained from surface pressure-area and surface potential-area isotherms. At small deposited quantities (1-2 mgm^-2) a quasi-monolayer (2D) structure is formed. The values obtained for the mean area per monomer and for the mean dipole moment are coherent with previously reported data, as well as with the proposed molecular model. At higher deposited quantities (3-6 mgm^-2) a complex 3D network is built. These statements are supported by the results obtained by means of ellipsometry and surface rheology. Ellipsometry provides data for the stability of the 2D structure and for the slightly unstable 3D network. By using an original rheological approach, both structures are distinguished by their mechanical response when a dilatational stress is applied. The quasi-monolayer structure behaves as an elastic 2D medium during the compression, while two relaxation processes with characteristic times of 10 and 100 s were observed. The 3D network behaves as a Maxwell viscoelastic body during the compression, while three relaxation processes with characteristic times of 1, 10 and 100 s were detected.     

Enzymatic hydrolysis by Humicola lanuginosa lipase of polycaprolactone monolayers

The enzymatic hydrolysis by Humicola lanuginosa lipase (HLL) of spread insoluble monolayers of polycaprolactone with various molecular weights was studied by measuring the decrease in surface area and in surface potential, in a barostat surface balance. The interfacial hydrolysis under the action of enzymes leads to the progressive fragmentation of the polymer molecules and to the appearance at the interface of charged insoluble and small soluble products. The solubilization of the small soluble fragments was detected by measuring the decrease in surface area during hydrolysis. An independent study showed that, in contrast to poly(lactic-co-glycolic acid) (PLAGA) oligomers, this solubilization is not instantaneous. Taking into account the solubilization rates, one can determine the kinetics of enzymatic hydrolysis. The specific catalytic activity of HLL was estimated in the framework of the random-scission model and compared to those obtained for the hydrolysis of monolayers built up of PLAGA or of simple di- and triglyceride molecules. Received: 25 July 2000 Revised: 28 November 2000 Accepted: 29 November 2000     

Kinetics and layer organization during the polymerization of coniferyl alcohol at the air-water interface

The initial stage of the polymerization of coniferyl alcohol catalyzed by a peroxydase was studied at the air-water interface. The properties of the monolayers were investigated at constant area and at constant surface pressure by surface pressure, surface potential and ellipticity measurements. On the basis of the results obtained at constant surface area, it is proposed that the formation of a 2D layer occurs up to the inflection point of the surface pressure-area isotherm, and that for larger surface pressures a 3D structure is formed during the polymerization. If the barostat is set at the inflection point (the surface pressure is constant while the surface area increases), the 2D organization of the monolayer is retained. A kinetic model describing the adsorption of the reaction products in a 2D layer is proposed. The kinetic constants were determined from the surface potential, ellipsometry, surface pressure and surface area data.     

Beta-spectroscopic separation of90Sr,90Y and89Sr with a scintillation detector

A -spectroscopic method for measurement of the isotope ratios and absolute activities of⁹⁰Sr,⁹⁰Y and⁸⁹Sr with an organic scintillator is described and tested. The correction factors for absorption in the sample and the detector window are calculated. The method can be used for rapid estimation of ratios and absolute activities of pure -emitters after a nuclear accident.Supported in part by the International Atomic Energy Agency, RC5633 and the National Fund for Scientific Research (Bulgaria).     

Modulation instability in pulsed surface-wave sustained discharges

Experimental results showing development of modulation instability and tendency to soliton formation in pulsed gas discharges sustained by surface waves are presented. The measurements are performed in argon discharges at gas pressure 13-1.3·10³ Pa sustained by pulsed microwave power at 2.45 GHz, The changes along the discharge length of the shape of the pulses of the total light emission, which is an indication for the plasma density, and of the wave electric field creating the discharge, are registrated. The cases when the modulation instability arises from the level of fluctuations in the plasma and when it is forced by the applied signal producing the discharge are demonstrated. The obtained results are discussed in terms of weak nonlinearity superimposed on the mechanism of strong ionization nonlinearity responsible for the discharge creation itself. A separation of a solitary-like wave front the leading edge of the pulse is also reported as an experimental result     

Morphological instabilities of polymer crystals

We present experimental observations at comparatively low supercooling of morphology transitions from dendritic to faceted structures in polymer crystals growing in thin films of a poly-2-vinylpyridineblock-polyethyleneoxid copolymer. Our results are compared with theoretical concepts describing morphological instabilities of single crystals. Although these concepts originally were not developed for polymers, they allow to describe and interpret our experimental results quite well. In particular, the measured temperature dependence of the width W and frequency of dendritic side branches and the radius of curvature ρ of the growth tips of the crystals follow these concepts. We present preliminary evidence for the influence of polymer attachment kinetics and reorganisation processes behind the growth front. Polymer thin films provide valuable model systems for studying general concepts of crystallisation and allow to distinguish at which point the connectivity of the crystallising units within chain-like molecules starts to play a measurable role.