The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.     

Composite ion exchanger with ammonium molybdophosphate and its properties

An organic binding polymer based on polyacrylonitrile (PAN) was used for the preparation of the composite exchanger containing ammonium molybdophosphate (AMP) as the active component. Due to the improvement of granulometric properties of powdered AMP with a binding polymer, an exchanger suitable for the application in column operations was prepared. Study of the properties of the exchanger AMP-PAN proved that kinetics of cesium sorption, capacity of the exchanger for cesium and desorption of cesium are not influenced by the binding polymer. The composite exchanger AMP-PAN described is therefore suitable for the selective separation and concentration of cesium and purification of radioactive wastes from¹³⁷Cs.     

Substituent dependence of the d-d transition band in the electronic absorption spectra of arylferrocenes and the corresponding arylferricenium salts

The electronic absorption spectra of 22 arylferrocenes and their arylferricenium salts with pentacyanopropenide (PCNP) were recorded. The attemptedHammett correlation of _max of the d-d transition bands of arylferrocenes revealed that this band is substituent dependent only for strong electron-withdrawing substituents. Excellent correlation of _max of the d-d transition bands with ⁺ constants was found in the case of arylferricenium cations. Good correlations of _max was also found with theE _1/2 oxidation potentials measured by cyclic voltametry.

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Substituentenabhängigkeit des d-d-Überganges in den Elektronenabsorptions-Spektren von Arylferrocenen und entsprechenden Arylferricenium-Salzen

Zusammenfassung Elektronenabsorptions-Spektren von 22 Arylferrocenen und ihren Arylferricenium-Pentacyanopropenid-Salzen wurden gemessen. VersuchteHammett-Korrelationen des längstwelligen d-d-Überganges (_max) zeigten, daß diese Bande nur von stark elektronenanziehende Substituenten abhängig ist. Im Fall der Arylferricenium-Kationen wurde eine ausgezeichnete Korrelation zwischen _max der d-d-Bande und den ⁺-Konstanten festgestellt. Eine gute Korrelation der _max-Werte wurde auch mit denE _1/2 Oxidationspotentialen gefunden, die durch cyclische Voltametrie meßbar sind.

     

Multiple steady states in a CSTR with total condenser: Comparison of equilibrium and nonequilibrium models

Comparison of equilibrium and nonequilibrium models of a CSTR with total condenser focused on the multiple steady states and dynamic behaviour was carried out. The steady-state behaviour of the model system, MTBE synthesis from methanol and isobutene in a reactive distillation column, was studied in terms of the input parameters, i. e. feed flow rate of methanol or butenes, reflux ratio, and mass of catalyst. The dynamic behaviour of the system during the start-up was investigated and perturbations of manipulated variables were found to cause transitions between the parallel steady states. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Nucleation and growth of Cu onto polycrystalline Pt electrode from acidic CuSO4 solution in the presence of H2SeO3

The early stages of Cu electrodeposition onto Pt(poly) have been investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] ≥ 2×10² using electrochemical and ex situ AFM techniques. The overpotential deposition of Cu has been performed onto a Pt surface precovered independently with Cu in amount close to an equivalent monolayer. Chronoamperometric results have been shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model. The values of diffusion coefficient D for Cu²⁺, number of nuclei N and average nuclei radius r _av have been calculated. In the local regions of the surface, the separate large agglomerates composed of the different diameter clusters have been revealed in both cases, but, in the presence of the H₂SeO₃, they attained a distinct chain-like configuration. Some morphological characteristics have been reported.     

Novel approach to the synthesis of 3-acyl substituted indolizines. The synthesis of 3-(indolizinyl-2)alanine and 4-(indolizinyl-3) homoalanine derivatives

A novel approach to the synthesis of 3-acylindolizines and the transformations of some acids into tryptophane analogues are described. Reaction of ethyl 2-pyridinylacetate and methyl 2-quinolinylacetate with N-trifluoroacetyl-5-bromo-4-oxonorvaline methylester led to N-trifluoroacetyl-3-(1-ethoxycarbonylindolizinyl-2) alanine methyl ester and N-trifluoroacetyl-3-(3-methoxycarbonylpyrrolo [1,2-a]quinolinyl-2) alanine methyl ester, respectively. Treatment of ethyl 2-pyridinylacetate and 2-pyridinylacetonitrile, first with N,N-dimethylformamide dimethyl acetal (DMFDMA), followed by reaction with phenacyl bromide, gave the corresponding 3-benzoylindolizines, while the reaction of ethyl 2-pyridinylacetate and 2-pyridinylacetonitrile with DMFDMA, followed by treatment with (S)-N-trifluoroacetyl-5-bromo-4-oxonorvaline methyl ester, gave the corresponding N-trifluoroacetyl-4-oxo-4-(indolizinyl-3)homoalanine methyl esters.     

Polymerization of methylmethacrylate in presence of tetramethylthiuramdisulphide

The effect of TMTD on the polymerization of methyl methacrylate was studied. The plot of $\text{R}{}_{\mathrm{P}}\text{vs [TMTD]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ shows a maximum ascribed to participation of TMTD-radicals in cross (P′ + RS′) and mutual-termination (RS′ + RS′). The total polymerization rate is then well expressed by a derived relation. Study of the influence of TMTD on the molecular weight of polymethylmethacrylate allows characterization of the transfer process.     

Field and temperature dependence of magnetization of U3P4

Conclusions We conclude that the occurrence of a maximum in the magnetization versus temperature curve observed under certain circumstances on U₃P₄ is not connected with its intrinsic magnetic structure, but substantially depends on the form in which the material is studied (polycrystalline powder, single crystal, single crystal powders with various dimensions of grains). This phenomenon seems to be affected by quenching of the state from the region of low anisotropy at higher temperature in the small particles with a strong tendency to single domain behaviour and thus it may be a consequence of rotation magnetization process in the fields relatively small for U₃P₄. The assertion about transitions between magnetic ordering, sometimes proposed in the literature on the basis of observed anomalies in the temperature course of magnetization without simultaneous confirmation by neutron diffraction, should be accepted with some reservation, especially in the case of simple uranium compounds. However, another situation arises for pseudobinary alloys of ferro- and antiferromagnetic components (e.g. UP_0·75S_0·25) where such transitions were confirmed both by magnetic methods and by neutron diffraction studies [13].The authors would like to express their thanks to Ing. A.Meovský for careful preparation of samples.