(Meta)stabiles CaC2

(Meta)stable CaC₂ One out of four modifications of CaC₂ is the so‐called metastable Calcium Carbide, CaC₂‐III, which was synthesized as pure material. It forms by heating monoclinic CaC₂‐II (C2/c) above 150 °C and remains stable after cooling down to room temperature. The structure was refined from X‐ray powder patterns (C2/m, Z = 4, a = 722.6(1) pm, b = 385.26(7) pm, c = 737.6(1) pm, β = 107.345(2)°). After grinding CaC₂‐III transforms back into CaC₂‐II. Heating CaC₂‐III induces a reversible phase transition into the cubic modification (CaC₂‐IV) at 460 °C. Differences between the three different structures of CaC₂ I–III, being stable at ambient conditions are also shown by ¹³C‐MAS‐NMR measurements, especially the presence of two distinct types of carbon atoms in the structure of the title compound.     

A C2 Fragment as Four‐Electron σ Donor

The formation and X‐ray structure analysis of the Pt^IV complex [(CH₂C{PPh₂C₆H₄}₂)PtI₂] is reported. The molecule possesses the orthometalated ligand (PPh₃)₂C→CH₂, which serves via its C₂ fragment as an unprecedented four‐electron σ donor.     

Anwendung von 2D-NMR-Techniken zur Analyse komplexer Spektren. Maleopimarsäuremethylester

A combination of 2D-NMR-techniques including 2D-J-resolved spectroscopy, SECSY and¹H-¹³C-shift correlation is used to assign the¹H- and¹³C-spectrum of Maleopimaric acid methylester [17,19-Dinoratis-15-ene-4,13,14-tricarboxylic acid 4-methylester, 16-(1-methylethyl)cyclic-13,14-anhydrid (4, 8, 12)] (1).

     

Die Kristallstruktur von Na2NiAlF7—ein Beitrag zum Problem der wahren Raumgruppe orthorhombischer Weberite

The Crystal Structure of Na₂NiAlF₇ — a Contribution to the Problem of the True Space Group of Orthorhombic Weberites The X-ray single crystal structure determination of the orthorhombic weberite Na₂NiAlF₇ (a = 707.4(2), b = 1003.8(2), c = 731.5(1) pm; Z = 4) was performed in space group Imma, after all reflections hk0 with h(k) = 2n + 1 could be eliminated, as they proved simulated by Renninger effect and/or λ/2 reflections. The alternative space groups Imm2 resp. I2₁2₁2₁ of former weberite structure determinations thus became obsolete. The refinement using 880 independent reflections ended at wR = 0.0232. The resulting average distances within the framework of octahedra are Ni? F = 197.3, Al? F = 180.4 pm.     

Certificates of infeasibility via nonsmooth optimization

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem.     

A memetic algorithm for the team orienteering problem

The team orienteering problem (TOP) is a generalization of the orienteering problem. A limited number of vehicles is available to visit customers from a potential set. Each vehicle has a predefined running-time limit, and each customer has a fixed associated profit. The aim of the TOP is to maximize the total collected profit. In this paper we propose a simple hybrid genetic algorithm using new algorithms dedicated to the specific scope of the TOP: an Optimal Split procedure for chromosome evaluation and local search techniques for mutation. We have called this hybrid method a memetic algorithm for the TOP. Computational experiments conducted on standard benchmark instances clearly show our method to be highly competitive with existing ones, yielding new improved solutions in at least 5 instances.     

On the existence of local strong solutions for the Navier-Stokes equations in completely general domains

There are only very few results on the existence of unique local in time strong solutions of the Navier-Stokes equations for completely general domains Ω⊆R³, although domains with edges and corners, bounded or unbounded, are very important in applications. The reason is that the L^q-theory for the Stokes operator A is available in general only in the Hilbert space setting, i.e., with q=2. Our main result for a general domain Ω is optimal in a certain sense: Consider an initial value and a zero external force. Then the condition is sufficient and necessary for the existence of a unique local strong solution u∈L⁸(0,T;L⁴(Ω)) in some interval [0,T), 0<T≤∞, with u(0)=u₀, satisfying Serrin’s condition . Note that Fujita-Kato’s sufficient condition u₀∈D(A^1/4) is strictly stronger and therefore not optimal.