The dependence of critical temperature on oxygen concentration in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+<Emphasis Type="Italic">x</Emphasis></Subscript> in terms of the fragmented chain model

An extended ASYNNNI model, that beside nearest-neighbour and next-nearest neighbour O-O interactions in the basal plane also includes interactions between the three nearest oxygen atoms, is used to describe the statistics of CuO chain fragmentation and to calculate doping and T _c in YBa₂Cu₃O_6+x . Calculations were made by the Monte Carlo method employing the recently proposed charge transfer model that assumes only chains whose length is equal to, or exceeds, a characteristic (critical) length, l _cr , can provide holes to the layers and contribute to doping p. The obtained p(x) is then combined with a universal T _c versus p relation to yield T _c (x) characteristics that correlate remarkably with those reported in recent experiments. The best coordination between theoretical and experimental T _c (x) characteristics has been achieved for l _cr = 2, implying that only isolated basal plane oxygen atoms (trivial chains) do not contribute holes to CuO₂ layers.     

Two measures for proving Gentzen's Hauptsatz without mix

 This paper presents a cut-elimination procedure for classical and intuitionistic logic, in which cut is eliminated directly, without introducing the mix rule. The well-known problem of cut eliminations, when in the derivation the contractions of the cut-formulae are above the premisses of the cut, will be solved by new transformations of the derivation. Received: 1 June 2001 / Published online: 5 November 2002 Mathematics Subject Classification (2000): 03F05 Key words or phrases: Systems of sequents – Cut-elimination theorem     

Reversible interconversion of thiazolidine-tetrahydrothiazine in the thiadiazabicyclooctanone system

Summary The interconversion of thiazolidine-tetrahydrothiazine in some derivatives of thiadiazabicyclooctanone in aqueous HCl has been studied. In the case of 6- and 7-substituted hydroxy or methoxy thiadiazabicyclooctanone a reversible rearrangement was found. The sulfoxide of thiadiazabicyclooctanone under the same reaction conditions undergoes epimerisation, while reaction with PCl₅ — via a corresponding sulfenyl chloride — affords a mixture of 6-and 7-substituted hydroxy or methoxy derivatives of thiadiazabicyclooctanone.The authors dedicate this paper to Dr. B. Gapert for his 60th birthday     

Coordination behaviour and two‐dimensional‐network formation in poly[[μ‐aqua‐diaqua(μ5‐propane‐1,3‐diyldinitrilotetraacetato)dilithium(I)cobalt(II)] dihydrate]: the first example of an MII–1,3‐pdta complex with a monovalent metal counter‐ion

The title compound, {[CoLi₂(C₁₁H₁₄N₂O₈)(H₂O)₃]·2H₂O}_n, constitutes the first example of a salt of the [M^II(1,3‐pdta)]²⁻ complex (1,3‐pdta is propane‐1,3‐diyldinitrilotetraacetate) with a monopositive cation as counter‐ion. Insertion of the Li⁺ cation could only be achieved through application of the ion‐exchange column technique which, however, appeared unsuccessful with other alkali metals and the ammonium cation. The structure contains two tetrahedrally coordinated Li⁺ cations, an octahedral [Co(1,3‐pdta)]²⁻ anion and five water molecules, two of which are uncoordinated, and is built of two‐dimensional layers extending parallel to the (010) lattice plane, the constituents of which are connected by the coordinate bonds. O—H_water...O hydrogen bonds operate both within and between these layers. The crystal investigated belongs to the enantiomeric space group P2₁ with only one (Λ) of two possible optical isomers of the [Co(1,3‐pdta)]²⁻ complex. A possible cause of enantiomer separation during crystallization might be the rigidification and polarization of the [M(1,3‐pdta)]²⁻ core, resulting from direct coordination of Li⁺ cations to three out of four carboxylate groups constituting the 1,3‐pdta ligand. The structure of (I) differs considerably from those of the other [M^II(1,3‐pdta)]²⁻ complexes, in which the charge compensation is realized by means of divalent hexaaqua complex cations. This finding demonstrates a significant structure‐determining role of the counter‐ions.     

Chromatographic Behavior of Fosinopril Sodium and Fosinoprilat Using Neural Networks

In this paper, the chromatographic characterization of fosinopril sodium and fosinoprilat is presented. The first stept was pK _a determination for the active substance and its degradation product using RP-LC. It was followed by optimization employing the combination of experimental design and artificial neural networks. For the definition of input and output variables, the central composite design for three factors was built. Back propagation algorithm was applied to model the system, and then the optimization of the experimental conditions was carried out in the neural network with 3-8-2 structure, which confirmed to be able to provide the maximum performance. From the method optimization, the most appropriate experimental conditions for fosinopril sodium and fosinoprilat analysis were extracted. The optimized method was validated and applied in the quality control of tablets and for forced degradation studies.     

Intermolecular reactions of foiled carbenes with N-H bonds: evidence for an ylidic pathway

The chemistry of endo-tricyclo[6.2.1.0 (2.7)]undec-9-en-11-ylidene (10), an archetypal foiled carbene, has been investigated. The intermolecular reactions of 10 are most conveniently performed with oxadiazoline 6 because the corresponding diazirine can be obtained only in very low yield. Furthermore, the aziridinyl imine is difficult to decompose and the tosylhydrazone sodium salt poorly soluble in common organic solvents. Photolysis of 6 in diethylamine leads merely to a reduction of the diazo group and regeneration of acetyl hydrazone 5, whereas thermolysis cleanly affords tertiary amine 12(anti) in 77% yield. Calculations show that even stabilized-nucleophilic carbenes react with amines through an ylidic pathway and not by a concerted insertion into the N-H bond. Nevertheless, in the gas phase, norbornen-7-ylidene (13) is predicted to be stabilized by one molecule of NH3 more efficiently through a hydrogen bond than by ylide formation.     

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis‐ and trans‐2‐Butene

Noncovalent interactions of cis‐ and trans‐2‐butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2‐butene dimers, in butane dimers, and between 2‐butene and saturated butane. The results show the trend that interactions of 2‐butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2‐butene dimers are the weakest. The strongest calculated interaction energy is between trans‐2‐butene and butane, with a CCSD(T)/CBS energy of ?2.80 kcal mol^?1. Interactions in cis‐2‐butene dimers are stronger than interactions in trans‐2‐butene dimers. Interestingly, some of the interactions involving 2‐butene are as strong as interactions in a benzene dimer. These insights into interactions of cis‐ and trans‐2‐butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.     

Symmetry properties of resolving sets and metric bases in hypercubes

In this paper we consider some special characteristics of distances between vertices in the \(n\)-dimensional hypercube graph \(Q_n\) and, as a consequence, the corresponding symmetry properties of its resolving sets. It is illustrated how these properties can be implemented within a simple greedy heuristic in order to find efficiently an upper bound of the so called metric dimension \(\beta (Q_n)\) of \(Q_n\), i.e. the minimal cardinality of a resolving set in \(Q_n\). This heuristic was applied to generate upper bounds of \(\beta (Q_n)\) for \(n\) up to \(22\), which are for \(n\ge 19\) better than the existing ones. Starting from these new bounds, some existing upper bounds for \(23\le n\le 90\) are improved by a dynamic programming procedure.     

A metaheuristic approach to the dominating tree problem

This paper considers a recently introduced NP-hard problem on graphs, called the dominating tree problem. In order to solve this problem, we develop a variable neighborhood search (VNS) based heuristic. Feasible solutions are obtained by using the set of vertex permutations that allow us to implement standard neighborhood structures and the appropriate local search procedure. Computational experiments include two classes of randomly generated test instances and benchmark test instances from the literature. Optimality of VNS solutions on small size instances is verified with CPLEX.