Set-valued processes induced by parameterised stochastic differential equations with an application to Tuned Mass Dampers

In this paper ordinary stochastic differential equations whose coefficients depend on uncertain parameters are considered. An approach is presented how to combine both types of uncertainty (stochastic excitation and parameter uncertainty) leading to set-valued stochastic processes. The latter serve as a robust representation of solutions of the underlying stochastic differential equations. The mathematical concept is applied to a problem from earthquake engineering, where it is shown how the efficiency of Tuned Mass Dampers can be realistically assessed in the presence of uncertainty. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of donor-acceptor substitution on the nonlinear optical properties of oligo(1,4-phenyleneethynylene)s studied by third harmonic generation spectroscopy

Third-harmonic generation (THG) spectroscopy was performed for oligo(1,4-phenyleneethynylene)s (OPEs) with terminal donor-acceptor (DA) substitution and compared to the results of merely donor substituted OPEs and regular OPE chains with 2,5-dipropoxy benzene rings. Both, extension of the conjugation and push-pull effect enhance the molecular hyperpolarizability gamma, even for the DAOPEs, which exhibit a hypsochromic shift of the long-wavelength absorption for increasing length L of the conjugated chain.     

Neutrale Bis‐Aziridin‐Komplexe des Typs [M(CO)3XAz2] (M = Mn,Re; X = Cl,Br; Az = N(H)C2H2Me2)

The pentacarbonylhalogene complexes [XM(CO)₅] (M = Mn, Re; X = Cl, Br) ( 1a – 2b ) react with 2,2‐dimethylaziridine by thermally induced substitution reaction to give the neutral bis‐aziridine complexes [M(X)(CO)₃Az₂] (Az = N(H)C₂H₂Me₂) ( 3a – 4b ). As a result of the X‐ray structure analyses, the metal atoms are octahedrally configurated in the facial arrangement; the intact three‐membered rings coordinate through their distorted tetrahedrally configurated N atoms. All compounds 3a – 4b are stable with respect to the directed thermal alkene elimination to give the corresponding nitrene complexes (CO)₄(X)M=NH; their IR, ¹H and ¹³C{¹H} NMR, and MS spectra are reported and discussed.     

Encapsulation of Halocarbons in a Tetrahedral Anion Cage

Caged supramolecular systems are promising hosts for guest inclusion, separation, and stabilization. Well‐studied examples are mainly metal‐coordination‐based or covalent architectures. An anion‐coordination‐based cage that is capable of encapsulating halocarbon guests is reported for the first time. This A₄L₄‐type (A=anion) tetrahedral cage, [(PO₄)₄ L ₄]^12?, assembled from a C₃‐symmetric tris(bisurea) ligand ( L ) and phosphate ion (PO₄^3?), readily accommodates a series of quasi‐tetrahedral halocarbons, such as the Freon components CFCl₃, CF₂Cl₂, CHFCl₂, and C(CH₃)F₃, and chlorocarbons CH₂Cl₂, CHCl₃, CCl₄, C(CH₃)Cl₃, C(CH₃)₂Cl₂, and C(CH₃)₃Cl. The guest encapsulation in the solid state is confirmed by crystal structures, while the host–guest interactions in solution were demonstrated by NMR techniques.     

Synthesis and structure of a ferrocenylboron dication

Treatment of the borane Br 2BFc (Fc = ferrocenyl) with the Lewis base 4-methylpyridine and Na[BAr (f) 4] [Ar (f) = 3,5-(CF 3) 2C 6H 3] afforded the boron dication [FcB(NC 5H 4-4-Me) 3][BAr (f) 4] 2. This compound is a rare example of a structurally characterized boron dication.     

Enantio‐ and Diastereoselective Synthesis of Chiral Allenes by Palladium‐Catalyzed Asymmetric [3+2] Cycloaddition Reactions

A protocol for the asymmetric synthesis of highly substituted chiral allenes with control of point and axial chirality has been developed. A palladium‐catalyzed [3+2] cycloaddition using readily available racemic allenes gives access to densely functionalized chiral allenes with excellent yields and functional group tolerance. The catalytic asymmetric protocol utilizes a broad range of allenyl TMM (trimethylenemethane) donors to form cyclopentanes, pyrrolidines, and spirocycles with very good control of regio‐, enantio‐, and diastereoselectivity. The chiral allene moiety is shown to be a valuable functional group for rapid elaboration towards complex targets.     

Characterization of Two-Component Metal Coatings (Al/Sn) with SIMS

 Vacuum deposited films of immiscible metal–metal systems can be applied as tribological coatings for plain bearings in high performance diesel engines. These industrially manufactured coatings show higher lifetimes than conventional electroplated coatings. For our investigations we used aluminum-tin coatings of 1 μm thickness on a glass substrate produced by sequential deposition from two separate targets under working gas pressure of 0.4 Pa. The tough Al matrix takes high mechanical loads and the soft inclusions of Sn act as solid lubricant. While Sn is deposited it migrates on the Al surface and grows as islands. We characterized the conformation and the distribution of the Sn islands on the surface and to the interstitial area between the islands with 3-D secondary ion mass spectroscopy (SIMS). The existence of a Sn layer between the islands (“wetting layer”) has been detected by SIMS and verified by measurements with Auger electron spectroscopy (AES).     

Trichloropalladate(II) Complexes with Pyridine Ligands – Molecular Structure and Conformational Analysis of [K(18C6)][PdCl3(py)]

[K(18C6)]₂[Pd₂Cl₆] ( 1 ) (18C6 = 18‐crown‐6) was found to react with pyridines in a strictly stoichiometric ratio 1 : 2 in methylene chloride or nitromethane to yield trichloropalladate(II) complexes [K(18C6)][PdCl₃(py*)] (py* = py, 2a ; 4‐Bnpy, 2b ; 4‐tBupy, 2c ; Bn = benzyl; tBu = tert‐butyl). The reaction of 1 with pyrimidine (pyrm) in a 1 : 1 ratio led to the formation of the pyrimidine‐bridged bis(trichloropalladate) complex [K(18C6)]₂[(PdCl₃)₂(μ‐pyrm)] ( 3 ). The identities of the complexes were confirmed by means of NMR spectroscopy (¹H, ¹³C) and microanalysis. The X‐ray structure analysis of 2a reveals square‐planar coordination of the Pd atom in the [PdCl₃(py)]^? anion. The pyridine plane forms with the complex plane an angle of 55.8(2)°. In the [K(18C6)]⁺ cation the K⁺ lies outside the mean plane of the crown ether (defined by the 6 O atoms) by 0.816(1) Å. There are tight K···Cl contacts between the cation and the anion (K···Cl1 3.340(2) Å, K···Cl2 3.166(2) Å). To gain an insight into the conformation of the [PdCl₃(py)]^? anion, DFT calculations were performed showing that the equilibrium structure ( 6eq ) has an angle between the pyridine ligand and the complex plane of 35.3°. Rotation of the pyridine ligand around the Pd–N vector exhibited two transition states where the pyridine ligand lies either in the complex plane ( 6TS _pla, 0.87 kcal/mol above 6eq ) or is perpendicular to it ( 6TS _per, 3.76 kcal/mol above 6eq ). Based on an energy decomposition analysis the conformation of the anion is discussed in terms of repulsive steric interactions and of stabilizing σ and π orbital interactions between the PdCl₃^? moiety and the pyridine ligand.     

Synthesis and characterization of silver(I), gold(I), and gold(III) complexes bearing a bis-dialkylamino functionalized N-heterocyclic carbene

Bis-1,3-[2-(diisopropylamino)ethyl]-imidazolium chloride, 1, has been prepared and used as a precursor for the synthesis of the corresponding silver(I) chloride complex 2. The single crystal structure analysis reveals that the complex dimerizes in the solid state. Transmetalation of 2 with (tht)AuBr (tht = tetrahydrothiophene) yields the (NHC)Au(I)Br complex 3. By treatment with bromine it is oxidized to (NHC)AuBr₃, 4, which is obtained as a yellow, microcrystalline powder. The UV-vis spectra of 4 are dependent on the pH-value and suggest a square-pyramidal structure in solution.     

Darstellung und Eigenschaften von 2-Acyl-1,2-thiazetidin-1,1-dioxiden

Title compounds3a–3i were synthesized by acylation of 1,2-thiazetidine 1,1-dioxide by various methods. Spectroscopic data elucidate the conformation and geometry of the fourmembered ring. An X-ray analysis of3i is presented.