Forcing revisited

The purpose of this paper is to propose and explore a general framework within which a wide variety of model construction techniques from contemporary set theory can be subsumed. Taking our inspiration from presheaf constructions in category theory and Boolean ultrapowers, we will show that generic extensions, ultrapowers, extenders and generic ultrapowers can be construed as examples of a single model construction technique. In particular, we will show that Łoś's theorem can be construed as a specific case of Cohen's truth lemma, and we isolate the weakest conditions a filter must satisfy in order for the truth lemma to work.     

Strong Direct Magnetic Coupling in a Dinuclear CoII Tetrazine Radical Single‐Molecule Magnet

The ligand‐centered radical complex [(CoTPMA)₂‐μ‐bmtz^.?](O₃SCF₃)₃ ? CH₃CN (bmtz=3,6‐bis(2′‐pyrimidyl)‐1,2,4,5‐tetrazine, TPMA=tris‐(2‐pyridylmethyl)amine) has been synthesized from the neutral bmtz precursor. Single‐crystal X‐ray diffraction studies have confirmed the presence of the ligand‐centered radical. The Co^II complex exhibits slow paramagnetic relaxation in an applied DC field with a barrier to spin reversal of 39 K. This behavior is a result of strong antiferromagnetic metal–radical coupling combined with positive axial and strong rhombic anisotropic contributions from the Co^II ions.     

The weighted Grammar constraint

We introduce the WeightedGrammar constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on this connection, we prove the correctness and complexity of these algorithms. Specifically, these algorithms enforce domain consistency on the WeightedGrammar constraint in time O(n ³). Further, we propose that the WNNF constraint can be decomposed into a set of primitive arithmetic constraint without hindering propagation.     

Direct electrochemistry of an [FeFe]-hydrogenase on a TiO2 electrode

[FeFe]-hydrogenases are efficient natural catalysts that can be exploited for hydrogen production. Immobilization of the recombinant [FeFe]-hydrogenase CaHydA was achieved for the first time on an anatase TiO(2) electrode. The enzyme is able to interact and exchange electrons with the electrode and to catalyze hydrogen production with an efficiency of 70%.     

Practical manganese-catalysed highly enantioselective cis-dihydroxylation of electron-deficient alkenes and detection of a cis-dioxomanganese(V) intermediate by high resolution ESI-MS analysis

A practical protocol has been developed for asymmetric cis-dihydroxylation of electron-deficient alkenes with Oxone catalysed by a manganese complex bearing a chiral tetradentate N(4)-donor ligand affording cis-diols in up to 95% yield with up to 96% ee. Analysis of the reaction mixture by high resolution ESI-MS revealed the formation of a cis-dioxomanganese(V) intermediate.     

Tetra‐μ2‐acetato‐diacetatodi‐μ3‐hydroxido‐tetrakis[piperidinecopper(II)] dihydrate

The title complex, [Cu₄(C₂H₃O₂)₆(OH)₂(C₅H₁₁N)₄]·2H₂O, possesses an unusual inversion‐symmetric tetranuclear copper framework, with each Cu^II atom displaying a square‐pyramidal geometry and one additional long Cu...O contact. The four piperidine ligands are terminal, one at each Cu^II atom, and the two hydroxide ligands are triply bridging. The six acetate ligands exhibit two distinct coordination modes, namely as two monodentate acetates and four bridging acetates that bridge the two inequivalent copper centres. The noncoordinating acetate O atom is involved in intramolecular hydrogen bonding with H atoms from the hydroxide and one piperidine ligand. In addition, extensive intermolecular hydrogen bonding involving the solvent water molecules is observed.     

On the weights of mod <Emphasis Type="Italic">p</Emphasis> Hilbert modular forms

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Hodge theory.     

Numerical Kähler-Einstein Metric on the Third del Pezzo

The third del Pezzo surface admits a unique Kähler-Einstein metric, which is not known in closed form. The manifold’s toric structure reduces the Einstein equation to a single Monge-Ampère equation in two real dimensions. We numerically solve this nonlinear PDE using three different algorithms, and describe the resulting metric. The first two algorithms involve simulation of Ricci flow, in complex and symplectic coordinates respectively. The third algorithm involves turning the PDE into an optimization problem on a certain space of metrics, which are symplectic analogues of the “algebraic” metrics used in numerical work on Calabi-Yau manifolds. Our algorithms should be applicable to general toric manifolds. Using our metric, we compute various geometric quantities of interest, including Laplacian eigenvalues and a harmonic (1,1)-form. The metric and (1,1)-form can be used to construct a Klebanov-Tseytlin-like supergravity solution.