Rigorous Solution of the Gardner Problem

 We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of p random patterns. The Gardner formula for this volume in the limit N, p→∞, p/N→α is proven for all values of α. Besides, we prove a useful criterion for the factorisation of all correlation functions for a class of models of classical statistical mechanics. Received: 2 December 2001 / Accepted: 12 June 2002 Published online: 31 January 2003 Communicated by A. Kupiainen     

Synthesis, crystal structure and physico-chemical properties of the new quaternary oxide Sr5BiNi2O9.6

A new black quaternary oxide Sr₅BiNi₂O_9.6 was synthesized by solid state reaction at 1200 °C. Its structure was solved by electron crystallography and X-ray powder refinement, yielding a tetragonal structure with space group I4/mmm, a=5.3637 (2) Å, c=17.5541(5) Å, Z=4. The structure can be described as a stacking of (Bi,Sr)-O rocksalt slabs and SrNiO_3−δ perovskite slabs. The initial nickel valence is close to +3.1. Thermogravimetry and high-temperature oxygen coulometry showed that this compound has variable oxygen content as a function of temperature and oxygen pressure, and ultimately decomposes when heated in low oxygen pressure above 800 °C. It is a metallic conductor with n-type conduction. Its thermoelectric power was determined and found to be −20 and −38 μV/K at 300 and 650 °C, respectively. Magnetic measurements confirm the nickel valence close to +3 and show evidence of magnetic ordering at 20 K.     

Zipper and layer-by-layer assemblies of artificial photosystems analyzed by combining optical and piezoelectric surface techniques

Quartz crystal microbalance (QCM) and surface plasmon resonance (SPR) were used to study zipper and layer-by-layer multilayer assemblies of artificial photosystems based on naphthalenediimides (NDIs) attached to an oligophenylethynyl (OPE-NDI) or p-oligophenyl (POP-NDI) backbone in dry and wet state. For the most interesting OPE-NDI zipper, one obtains for the dry film a monolayer thickness of 1.85 nm and a density of 1.58 g/cm(3), while the wet film has a larger monolayer thickness of 3.6 nm with a water content of 36%. The dry thickness of a monolayer in OPE-NDI zippers corresponds to about one-half of the length of the OPE scaffold in agreement with the proposed structure of the zipper. The low water content of the OPE-NDI films confirms their compact structure. The dry monolayer thickness of the POP-NDI films of 1.45 nm is smaller than that for the OPE-NDI films, which is probably related to a tilt of the POP scaffolds within the adsorbed layer. The POP-NDI films swell in water much more substantially, suggesting a much more open structure. These features are in excellent agreement with the better photophysical performance of the OPE-NDI assemblies when compared to the POP-NDI films.     

Four-Center Nodes: Supramolecular Synthons Based on Cyclic Halogen Bonding

The isocyanide trans-[PdBr₂(CNC₆H₄-4-X′)₂] (X′=Br, I) and nitrile trans-[PtX₂(NCC₆H₄-4-X′)₂] (X/X′=Cl/Cl, Cl/Br, Br/Cl, Br/Br) complexes exhibit similar structural motif in the solid state, which is determined by hitherto unreported four-center nodes formed by cyclic halogen bonding. Each node is built up by four Type II C−X′⋅⋅⋅X−M halogen-bonding contacts and include one Type I M−X⋅⋅⋅X−M interaction, thus giving the rhombic-like structure. These nodes serve as supramolecular synthons to form 2D layers or double chains of molecules linked by a halogen bond. Results of DFT calculations indicate that all contacts within the nodes are typical noncovalent interactions with the estimated strengths in the range 0.6–2.9 kcal mol⁻¹.     

Marie Curie: Pioneering Discoveries and Humanitarianism

Marie Sk?odowska‐Curie, the first woman to win a Nobel Prize and the only person to be awarded the Nobel Prize twice in different scientific disciplines, is an inspiring figure. She discovered two new elements, polonium and radium, and was appointed as the first female professor at the University of Paris, when in most countries women did not yet have the right to vote. She serves as a role model for scholarly and humanitarian endeavors through what she attained in science, and through the hardships she had to overcome and the gender discrimination barriers faced by women scientists of that period, which she had to break. This article is a tribute to Marie Sk?odowska‐Curie's achievements.     

A non-splitting theorem in the enumeration degrees

We complete a study of the splitting/non-splitting properties of the enumeration degrees below by proving an analog of Harrington’s non-splitting theorem for the enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees.     

Reverse Arene Sandwich Structures Based upon π‐Hole⋅⋅⋅[MII] (d8 M=Pt,Pd) Interactions,where Positively Charged Metal Centers Play the Role of a Nucleophile

The complexes [Pt(tpp)] (H₂tpp=tetraphenylporphyrin), [M(acac)₂] (M=Pd, Pt, Hacac=acetylacetone), and [Pd(ba)₂] (Hba=benzoylacetone) were co‐crystallized with highly electron‐deficient arene systems to form reverse arene sandwich structures built by π‐hole???[M^II] (d⁸M=Pt, Pd) interactions. The adduct [Pt(tpp)]?2 C₆F₆ is monomeric, whereas the diketonate 1:1 adducts form columnar infinity 1D‐stack assembled by simultaneous action of both π‐hole???[M^II] and C???F interactions. The reverse sandwiches are based on noncovalent interactions and calculated ESP distributions indicate that in π‐hole???[M^II] contacts, [M^II] plays the role of a nucleophile.     

Reverse Arene Sandwich Structures Based upon π‐Hole⋅⋅⋅[MII] (d8 M=Pt,Pd) Interactions,where Positively Charged Metal Centers Play the Role of a Nucleophile

The complexes [Pt(tpp)] (H₂tpp=tetraphenylporphyrin), [M(acac)₂] (M=Pd, Pt, Hacac=acetylacetone), and [Pd(ba)₂] (Hba=benzoylacetone) were co‐crystallized with highly electron‐deficient arene systems to form reverse arene sandwich structures built by π‐hole???[M^II] (d⁸M=Pt, Pd) interactions. The adduct [Pt(tpp)]?2 C₆F₆ is monomeric, whereas the diketonate 1:1 adducts form columnar infinity 1D‐stack assembled by simultaneous action of both π‐hole???[M^II] and C???F interactions. The reverse sandwiches are based on noncovalent interactions and calculated ESP distributions indicate that in π‐hole???[M^II] contacts, [M^II] plays the role of a nucleophile.     

Functional optical coherence tomography for detecting neural activity through scattering changes

We have demonstrated functional optical coherence tomography (fOCT) for neural imaging by detecting scattering changes during the propagation of action potentials through neural tissue. OCT images of nerve fibers from the abdominal ganglion of the sea slug Aplysia californica were taken before, during, and after electrical stimulation. Images acquired during stimulation showed localized reversible increases in scattering compared with those acquired before stimulation. Motion-mode OCT images of nerve fibers showed transient scattering changes from spontaneous action potentials. These results demonstrate that OCT is sensitive to the optical changes in electrically active nerve fibers.     

Methods of Synthesis and Antiviral Activity of New 4-Alkyl-3-Nitro-1,4-Dihydroazolo[5,1-c][1,2,4]Triazin-4-ols

Chemistry of Heterocyclic Compounds - An azo coupling reaction of α-nitro ketones with 5-diazoazoles was used to obtain 4-alkyl-3-nitro-1,4-dihydroazolo[5,1-с][1,2,4]triazines, which...