Interpretation of the Lavrentiev phenomenon by relaxation

We consider functionals of the calculus of variations of the form F(u)= ∝₀¹ f(x, u, u′) dx defined for u ε W^1,∞(0, 1), and we show that the relaxed functional with respect to weak W^1,1(0, 1) convergence can be written as

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, where the additional term L(u), called the Lavrentiev term, is explicitly identified in terms of F.     

A Water Rich Crystalline Hydrate Formed by 1,4,7,10-Tetraazacyclododecane, Siliconhydrofluoric Acid and Water: Structure and Properties

Novel complementary associations have been found in a crystalline ternarycomplex of the macrocyclic tetramine, [12]aneN₄ (e.g. =1,4,7,10-tetraazacyclododecane, cyclen, L), hexafluorosilicate ions andwater (I). The final compound belongs to the host—guest type with themacrocycle as the host (H), the inorganic entity as a guest (G) and watermolecules. It was characterized by X-ray techniques, IR spectroscopy andthermogravimetric study. X-ray crystal analysis revealed that the structureis built of the charged entities, with a 3D-network uniting thequadriprotonated form of the macrocycle, hexafluorosilicate as counterionsand lattice water molecules viaN—H⁺...F^-,N—H⁺...O(w),OH...F^- and O—-H(w)...O(w)hydrogen bonds. The overall complex stoichiometry comprises fourSiF₆ ^2- anions and seven water molecules per two[LH₄]⁴⁺ cations. Crystals of (I) are monoclinic,space group P2₁/n with a = 14.585(3), b = 16.384(2), c =16.500(3) Å, = 92.84(3)°, V = 3938(1)ų and Z = 8 forC₈H₃₁F₁₂N₄O_3.5Si₂.     

[1,2,5]Oxadiazolo[3,4-d]pyridazine 1,5,6-trioxides: efficient synthesis via the reaction of 3,4-bis(hydroxyimino)methyl)-1,2,5-oxadiazole 2-oxides with a mixture of concentrated nitric and trifluoroacetic acids and structural characterization

An efficient synthesis of [1,2,5]oxadiazolo[3,4-d]pyridazine 1,5,6-trioxides (1) from 3,4-bis(hydroxyimino)methyl)-1,2,5-oxadiazole 2-oxides using a mixture of concentrated nitric and trifluoroacetic acids has been developed. The scope of the unconventional reaction was established. The 4,7-dinitro[1,2,5]oxadiazolo[3,4-d]pyridazine 1,5,6-trioxide 1f represents a new high energy compound, unfortunately with low thermal stability. The parent [1,2,5]oxadiazolo[3,4-d]pyridazine 1,5,6-trioxide 1c was studied by single-crystal X-ray diffraction analysis which revealed a planar molecule with an unusually long intracyclic NN bond of 1.668(5)?Å and unexpected exo-cyclic bond angles at the nitroxyl nitrogen atoms. In the crystal, the molecules of 1c are bound to each other by strong π-π stacking and CH?O hydrogen bonding interactions into a three-dimensional framework that results in a high crystal density of 1.833?gcm^?3.     

First platinum(ii)–alkaline-earth acetate-bridged complexes Ptii(m-OAc)4Mii(AcOH)4 (M = Ca,Sr, Ba)

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Dinuclear copper(ii) complex with novel N,N’,N”,O-tetradentate Schiff base ligand containing trifluoromethylpyrazole and hydrazone moieties

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The features of hydrogen ignition over Pt and Pd foils at low pressures

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Synthesis and crystal structure of a new hybrid methylammonium iodocuprate

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Site‐Specific Dual Labeling of Proteins on Cysteine Residues with Chlorotetrazines

Dual‐labeled biomolecules constitute a new generation of bioconjugates with promising applications in therapy and diagnosis. Unfortunately, the development of these new families of biologics is hampered by the technical difficulties associated with their construction. In particular, the site specificity of the conjugation is critical as the number and position of payloads can have a dramatic impact on the pharmacokinetics of the bioconjugate. Herein, we introduce dichlorotetrazine as a trivalent platform for the selective double modification of proteins on cysteine residues. This strategy is applied to the dual labeling of albumin with a macrocyclic chelator for nuclear imaging and a fluorescent probe for fluorescence imaging.     

Formal Nickelate(−I) Complexes Supported by Group 13 Ions

Formal nickelate(?I) complexes bearing Group 13 metalloligands (M=Al and Ga) were isolated. These 17 e^? complexes were synthesized by one‐electron reduction of the corresponding Ni⁰→M^III precursors, and were investigated by single‐crystal X‐ray diffraction, EPR spectroscopy, and quantum chemical calculations. Collectively, the experimental and computational data support: 1) the strengthening of the Ni?M bond upon one‐electron reduction, and 2) the delocalization of the unpaired spin across the Ni and M atoms. An intriguing electronic configuration is revealed where three valence electrons occupy two σ‐type bonding interactions: Ni(3d )²→M and σ‐(Ni?M)¹. The latter is an unusual Ni?M σ‐bonding molecular orbital that comprises primarily the Ni 4p_z and M np_z/ns atomic orbitals.