Inverse Problems for Identification of Memory Kernels in Viscoelasticity

Inverse problems for identification of the memory kernel in the linear constitutive stress–strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.     

Cyclothiazeno-Komplexe des Wolframs mit Phosphaniminatound tertiär-Butoxyliganden

Cyclothiazeno Complexes of Tungsten with Phosphoraneiminato and t-Butoxy Ligands The cyclothiazeno complex [WCl₃(N₃S₂)]₂ reacts with the silylated phosphaneimine Me₃SiNPPh₃ in THF solution forming the cyclothiazenophosphoraneiminato complex [Cl₂W(N₃S₂)(NPPh₃)]_n which forms green crystals of [Cl₂W(N₃S₂)(NPPh₃)(Py)] ( 1 ) when pyridine is added. The corresponding reaction with Me₃SiNPMe₃ leads to the methyl derivative which is analogous to 1 and which is obtained as dark green crystals along with the tetrakis(phosphoraneiminato) complex of the crystal composition [W(NPMe₃)₄]Cl₂ · 2 [Cl₂W(N₃S₂)(NPMe₃)(Py)] · 2 CH₂Cl₂ ( 2 ). According to the crystal structure analyses the phosphoraneiminato ligands NPR₃^– cause as a result of the short WN bonds of approximately 180 pm a strong trans influence on one of the WN bonds of the planar WN₃S₂ rings and alternatingly long SN bonds. With LiOCMe₃ [WCl₃(N₃S₂)]₂ reacts forming the centrosymmetrically dimeric cyclothiazeno alkoxy complex [(Me₃CO)₄W(N₃S₂)Li₂Cl]₂ ( 3 ) the ion ensemble of which is linked via the lithium and the chlorine atoms.     

Modern Variants of the Mannich Reaction

Important building blocks for the synthesis of drugs or natural products are found in Mannich bases and their derivatives. Modern variants of the Mannich reaction that expand the potential of the classical intermolecular reaction significantly and enable efficient control of the regioselectivity and stereoselectivity are therefore the topic of intensive research. Intramolecular reactions, in particular as part of domino reaction sequences, often afford astoundingly simple and elegant approaches to complex target compounds.     

Sesquialkoxide von Gallium und Indium

Sesquialkoxides of Gallium and Indium Treatment of GaMe₃ with one equivalent of HO^cHex in toluene at 20 °C leads to [Me₂GaO^cHex]₂ ( 4 ) under evolution of methane. The reaction of InMe₃ with two equivalents of HO^cHex leads under similar conditions not to [MeIn(O^cHex)₂]_n but to the sesquialkoxide [In{Me₂In(O^cHex)₂}₃] ( 5 ). 5 can be described also as [{Me₂InO^cHex)}₂{MeIn(O^cHex)₂}₂]. The use of an excess of cyclohexanol in boiling toluene gives the same result. Under these reflux conditions, the reaction of GaMe₃ with an excess of PhCH₂OH leads exclusively to another type of sequialkoxides, [Ga{MeGa(OCH₂Ph)₃}₃] ( 6 ). 4 — 6 were characterized by NMR, vibrational and MS spectra, as well as by X‐ray structure determinations. According to this, 4 forms centrosymmetrical and therefore planar Ga₂O₂ four‐membered rings. 5 and 6 possess basically the same structural motif, central M³⁺ ion ( 5 : In³⁺; 6 : Ga³⁺) coordinated by three metalate units ( 5 : [Me₂In(O^cHex)₂]^—; 6 : [MeGa(OCH₂Ph)₃]^—). The central M³⁺ ions have always coordination number (CN) six while the three surrounding metal ions possess CN 4. Because of the spectroscopic findings 6 must exist in two isomers (1:1). The C₃‐symmetrical isomer C₃‐ 6 was characterized by X‐ray analysis, while the isomer C₁‐ 6 could by described mainly by the complex NMR data.