A note on the radical of a Banach algebra

Relying on the results of the paper [5], we show that the Jacobson radical of a Banach algebra can be characterized as the set of exactly those elements perturbations by which leave the spectrum invariant. A number of corollaries are listed.     

Sur la forme canonique des formes extérieures

Sans résumé

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The article is the text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.     

Estimation of bond energies from mulliken overlap populations

Estimations of the bond energies from Mulliken overlap populations are taken. The strength of a bond is undoubtedly connected with the density of electrons constituting this bond. In the present paper the electron densities _i ^bond belonging to the particular bonds are represented by the total overlap populations defined byMulliken. The heat of atomization of the molecule is subdivide in the ratio of these electron densities _i ^bond belonging to the individual bond.My thanks are due to Drs. S.erný, Z.Knor, J.Pancí and R.Zahradník for their interest and stimulating discussions.     

Magnetic moments and the high field susceptibilities of MnFe2O4

An extended version of the noncollinear spin model bySawatzky et al. is developed to derive a dependence of the differential high field susceptibility on the degree of inversion of the ferrite MnFe₂O₄. Using the available data on the main molecular field coefficients it is shown that the present model imposes restrictions on values of. Determination of from the measurements of the field dependence of the saturated moments at low temperatures on samples with varying degrees of inversion reveals good quantitative agreement with the present model.     

Triplet losses in dye lasers

The expression for losses due to triplet states in dye laser considered as a six-level system is given. It is shown that triplet losses depend on pumping parameters and photon number. Depending on molecular and cavity parameters two different behaviours of dye lasers are expected. Physical conditions are discussed in which triplet losses as well as photon number undergo a jump at the threshold.     

Determination of trap parameters by simultaneous measurement of thermostimulated luminescence and thermostimulated conductivity

A method is proposed for processing of thermostimulated luminescence (TSL) curve in the presence of thermostimulated conductivity (TSC) in which no assumption is made as to the smallness of dn_c/dt (n_c is the conduction electron concentration). Results of the theory are applied to study of ZnSAg, Al and ZnSCu single crystals, in which elementary traps are revealed, and their activation energy and the value of the frequency factor determined. For ZnSCu the radiative transition recombination section is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 94–101, June, 1977.     

Effects in high-performance liquid chromatography of a high pH in the mobile phase on poly(methyloctylsiloxane) immobilized by gamma-radiation on titanium-grafted silica

Effects of high-pH environments on a stationary phase prepared by gamma-radiation immobilization of poly(methyloctylsiloxane) on titanium-grafted silica were investigated by HPLC testing with standard sample mixtures. The HPLC parameters indicate good stationary phase stability to 10000 column volumes each of mobile phases with pH of 7, 9 and 12. At pH 13, the efficiency decreases slowly, although reasonably good separations are still possible until increasing flow resistance no longer allows easy passage of the mobile phase.     

Effects of non-ionic surfactants on isotachophoretic separations of 2-arylpropionic acids

Non-ionic surfactant (Brij 35, Tween 20, Tween 80 and Tergitol NPX) modified capillary isotachophoresis was investigated for the separation of 2-arylpropionic acids (fenoprofen, flurbiprofen, ibuprofen, ketoprofen and naproxen) and benzoic acid and its derivatives (salicylic, acetylsalicylic and gallic acids). The relative step height (RSH) values of analytes were found to be dependent on the type and concentration of the surfactant. The strength of the affinity of the 2-arylpropionic acids to the non-ionic micelles was found to be as follows: flurbiprofen > fenoprofen > ibuprofen > naproxen > ketoprofen. In general, the RSH values of 2-arylpropionic acids increase with an increase in the concentration of surfactants. However, the RSHs of benzoic, salicylic and gallic acids are not considerably affected. Separation of all acids was obtained with the Tween 20 (1.5%, w/v) in the leading electrolyte 10 mmol L(-1) hydrochloric acid/L-histidine (pH 6.0). Changes in the fluorescence intensity of fenoprofen, flurbiprofen and naproxen were also investigated in micellar media (Tween 20, Tween 80 and Brij 35). The strength of the affinity of the 2-arylpropionic acids to the Tweens micelles was found to be as follows: flurbiprofen > fenoprofen > naproxen, which is consistent with the isotachophoretic results. On the contrary, the strength of the affinity to the Brij micelles was found to be as follows: fenoprofen > naproxen > flurbiprofen.     

Constituents of labiatae—XIV: Vierol and powerol,two new diterpenes from Sideritis canariensis

The two new diterpenes, vierol (1) [(?)kaurane-16α,18-diol] and powerol (3) [(?)kaurane-7β,16α-diol] have been isolated from Sideritis canariensis Ait. 1 was obtained by partial synthesis from epicandicandiol (7), and 3 was related with (?)kauranol (6) and (?)kauren-7β-ol acetate (11). Reduction of the acetoxy-aldehyde 14 by the method of Huang-Minlon and posterior acetylation gave 11, (?)isokauren-7β-ol acetate (17) and (?)kauran-7β-ol acetate (18).     

The volumetric analysis of phosphates

A method has been developed for the volumetric determination of orthophosphate, and a simple variation permits the determination of the average number of phosphorus atoms per molecule in condensed phosphates. For total P₂O₅ the phosphates are converted to the diacid orthosalt and precipitated as silver phosphate. The liberated acid is then titrated. For determination of chain length the condensed phosphate is converted to the diacid form and treated similarly, then hydrolysed and determined as orthophosphate. The ratio of the two titrations is equal to the average number of phosphorus atoms per molecule.