Reaction of N‐Heterocyclic Silylenes with Thioketone: Formation of Silicon–Sulfur Three (Si‐C‐S)‐ and Five (Si‐C‐C‐C‐S)‐Membered Ring Systems

Three‐ and five‐membered rings that bear the (Si‐C‐S ) and (Si‐C‐C‐C‐S ) unit have been synthesized by the reactions of L SiCl ( 1 ; L =PhC(NtBu)₂) and L′ Si ( 2 ; L′ =CH{(C?CH₂)(CMe)(2,6‐iPr₂C₆H₃N)₂}) with the thioketone 4,4′‐bis(dimethylamino)thiobenzophenone. Treatment of 4,4′‐bis(dimethylamino)thiobenzophenone with L SiCl at room temperature furnished the [1+2]‐cycloaddition product silathiacyclopropane 3 . However, reaction of 4,4′‐bis(dimethylamino)thiobenzophenone with L′ Si at low temperature afforded a [1+4]‐cycloaddition to yield the five‐membered ring product 4 . Compounds 3 and 4 were characterized by NMR spectroscopy, EIMS, and elemental analysis. The molecular structures of 3 and 4 were unambiguously established by single‐crystal X‐ray structural analysis. The room‐temperature reaction of 4,4′‐bis(dimethylamino)thiobenzophenone with L′ Si resulted in products 4 and 5 , in which 4 is the dearomatized product and 5 is formed under the 1,3‐migration of a hydrogen atom from the aromatic phenyl ring to the carbon atom of the C? S unit. Furthermore, the optimized structures of probable products were investigated by using DFT calculations.     

A priori error estimates for nonstationary optimal control problems with gradient state constraints

We are concerned with the discretization of semilinear parabolic optimization problems subject to constraints on the first derivative of the solution of the PDE. Constructing sequences of feasible controls for the dG(0)-cG(1) discretization of the problem and relying on a quadratric growth condtion, we show convergence orders as temporal and spatial mesh tends to zero. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrocatalysis by Polyoxometalate-Protected Gold Nanoparticles

Electrocatalysis by polyoxometalate (POM)-monolayer protected gold nanoparticles is herein demonstrated using a newly discovered phenomenon that makes it possible to observe the electrochemistry of dilute aqueous solutions of these colloidal nanostructures. To preserve the integrity of the gold nanoparticles’ electrostatically-stabilized POM-monolayer structures, deposition and drying of the POM-protected metal(0) NPs on the electrode surface must be avoided. Overcoming this constraint, we here show that POM-monolayer protected gold nanoparticles can be induced to reversibly associate with electrode surfaces, resulting in dramatic current amplification and well behaved, quasi-reversible cyclic voltammetric behavior at remarkably small electrolyte concentrations, thus making it possible to investigate electrocatalysis by dilute aqueous solutions of POM-protected gold NPs.     

Phase Transition of [2,2]‐Paracyclophane – An End to an Apparently Endless Story

In this contribution, the solid‐state low‐temperature phase structure of [2,2]‐paracyclophane is unambiguously characterised by single‐crystal X‐ray analysis. Additionally, a heat capacity measurement was undertaken, which proves the existence of a λ‐type phase transition at 45 K, a transition that is connected with the formation of a secondary C_p/T feature at 60 K. The low‐temperature phase (<45 K) crystallises in the lower symmetry space group P$\bar 4$ n2, whereas the high‐temperature phase (>60 K) crystallises in space group P4₂/mnm. This proves what has been postulated both by experimental and theoretical chemists but has repeatedly been dismissed as speculation many times.     

Dilation analyticity in constant electric field

The resolvent of the operatorH ₀(ε, θ)=?Δe ^-20+εx ₁ e ^θ is not analytic in θ for θ in a neighborhood of a real point, if the electric field ε is non-zero. (One manifestation of this singular behavior is that for 0<|Im θ|<π/3,H ₀(ε, θ) has no spectrum in the finite plane.) Nevertheless it is shown that the techniques of dilation analyticity still can be used to discuss the long-lived states (resonances) of a system described by a Hamiltonian of the formH=?Δ+εx ₁+V(x).     

Growth and application of [01·4] LiNbO3

We have successfully grown large, high quality LiNbO₃ boules in the [0.1·4] direction which lies in the yz plane 38° to the z. Following annealing and poling the material is strain free, striation free and of high optical quality. It has been used to fabricate an electro-optic switch, for second harmonic generation and tunable parametric generation over the 1.4 μm to 4.4 μm spectral range.     

Precision model independent determination of |Vub| from B --> pilnu

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.