Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

Electron diffraction studies of the molecular structures of iron(II) chloride and iron(II) bromide. Evidence on the structure of dimeric species Fe2Br4

An expression for the extreme values of mean-square amplitudes of vibrations in polyatomic molecules has been derived which permits estimation of the mean-square amplitude without solving the vibrational problem. This expression can be improved for the stretching and scissoring modes when the assignment of frequencies is known. In turn, the corresponding vibrational frequency may be estimated from the experimental value of the mean-square amplitude. The mean-square amplitudes of the butadiene-1,3 molecule are considered as an example.     

Réactions des céténes et du dicéténe avec les germyl- et silylphosphines

Ketenes add to germyl- and silylphosphines R₃MPEt₂ with opening of the carbonyl group and formation of phosphorylated alkenoxygermanes or -silanes

(R′H, Ph). These adducts are thermally stable and only the addition derivative of diphenylketene and Me₃SiPEt₂ exhibits metallotropic isomerization to a C-derivative after prolonged heating. Hydrolysis of these addition compounds is a new approach to the acylphosphines R₂CH-CO-PEt₂. Diketene also reacts with germyl- and silylphosphines with acyloxygen bond cleavage and formation of metallated and phosphorylated ketoenolates of the type

. These derivatives isomerize either partially (MSi) or completely (MGe) into R₃MOC(CH₃)CHCOPEt₂. Their hydrolysis constitutes a new method of synthesis of the phosphorylated β-diketone

. The ketoenolates from the addition reaction of the hydrosilylphosphine, Me₂Si(H)PEt₂, cyclize readily after partial isomerization by the intramolecular addition SiH to CO, to give phosphorylated siladioxane and siladioxene. The conformation of these heterocyclic compounds has been studied.     

Calculation of cross sections for positron-Ar collisions

The three-body classical trajectory Monte-Carlo (CTMC) method is used to investigate positron-argon atom collisions. The total ionization cross sections are presented along with singly and doubly differential cross sections. The existence of the cusp-like peak in the triply differential electron and positron spectra at positron impact is predicted.