Effect of partial fluorination on the Lewis sites of microcrystalline γ-alumina studied by adsorption of pyridine as a probe molecule: A quantum chemical cluster model study

The influence of fluorination of microcrystalline γ-alumina on the acidity of Lewis sites was studied by quantum chemical cluster model approach. B3LYP and HF/6-31++G(d,p) levels of theory were employed, considering the standard and counterpoise-corrected potential energy surfaces (PESs). Explicit inclusion of dynamical electron correlation effects along with the elimination of the basis set superposition effects in geometry optimization and harmonic vibrational analysis were found to be crucial to reproduce the experimental trends in the shifts of the pyridine ν_19b and ν_8a modes upon fluorination. The acidity of surface-exposed Al-sites was found to increase upon fluorination, which is manifested as a ~ 10% increase of the interaction energies, and also in the characteristics of the electronic density and density Laplacian at the intermolecular bond critical point. Bader analysis of the electronic density has shown that pyridine adsorption on pure and fluorinated γ-alumina can be classified as non-covalent interaction.     

The first one-pot ‘alkane-like’ reactions of carbonyl-containing adamantanes

A novel ‘alkane-like’ methodology for the direct and very simple one-pot functionalization of amides and an ester of 1-adamantanecarboxylic acid provides access to new and synthetically challenging 1,3-dicarbonyl-containing adamantanoid compounds with the same or different functional groups.     

The hydrogen‐bonding network in deacetyl­cephalothin

The structural analysis of deacetyl­cephalothin [systematic name: (6R,7R)‐3‐hydroxy­methyl‐8‐oxo‐7‐(2‐thio­phen‐2‐yl­acetyl­amino)‐5‐thia‐1‐aza­bicyclo­[4.2.0]oct‐2‐ene‐2‐carboxylic acid], C₁₄H₁₄N₂O₅S₂, shows that the geometry of the central bicyclic moiety is close to the geometry exhibited by other biologically active cephalosporin antibiotics. The mol­ecules are arranged in a helical chain running parallel to the 2₁ axis via a strong O—H⋯O hydrogen bond. The main helices are zipped together via N—H⋯O inter­actions, forming infinite layers. The supramolecular architecture is stabilized by O—H⋯S and C—H⋯O hydrogen bonds.     

Applications of mapping cones over Clements–Lindström rings

We prove that Gotzmann's Persistence Theorem holds over every Clements–Lindström ring. We also construct the infinite minimal free resolution of a square-free Borel ideal over such a ring.     

Asymptotic behavior of solutions to plate equations with nonlinear dissipation occurring through shear forces and bending moments

We consider the question of strong stability of solutions to plate equations with nonlinear dissipation in the boundary conditions. Two cases are discussed: (1) dissipation occurring through the nonlinear forces applied on the boundary and (2) dissipation acting through the nonlinear moments. Asymptotic stability results are presented for both cases. In the first case the results are established under the natural geometric conditions imposed on the domain, while in the second case certain restrictions on the curvature on the active portion of the boundary are required.Research partially supported by NSF Grant DMS-8301668 and by AFOSR Grant AFOSR-84-0365.     

Amalgams and χ‐Boundedness

A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class of graphs is χ‐bounded if there exists a function such that for all graphs , and all induced subgraphs H of G, we have that . We prove that proper homogeneous sets, clique‐cutsets, and amalgams together preserve χ‐boundedness. More precisely, we show that if and are hereditary classes of graphs such that is χ‐bounded, and such that every graph in either belongs to or admits a proper homogeneous set, a clique‐cutset, or an amalgam, then the class is χ‐bounded. This generalizes a result of [J Combin Theory Ser B 103(5) (2013), 567–586], which states that proper homogeneous sets and clique‐cutsets together preserve χ‐boundedness, as well as a result of [European J Combin 33(4) (2012), 679–683], which states that 1‐joins preserve χ‐boundedness. The house is the complement of the four‐edge path. As an application of our result and of the decomposition theorem for “cap‐free” graphs from [J Graph Theory 30(4) (1999), 289–308], we obtain that if G is a graph that does not contain any subdivision of the house as an induced subgraph, then .     

Graphs with No Induced Five‐Vertex Path or Antipath

We prove that a graph G contains no induced ‐vertex path and no induced complement of a ‐vertex path if and only if G is obtained from 5‐cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class‐preserving operation introduced here.     

Attractors for Second-Order Evolution Equations with a Nonlinear Damping

We study long-time dynamics of abstract nonlinear second-order evolution equations with a nonlinear damping. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the function describing the dissipation. If the damping is bounded below by a linear function, this rate is exponential. Our approach is based on far reaching generalizations of the Ceron–Lopes theorem on asymptotic compactness and Ladyzhenskayas theorem on the dimension of invariant sets. An application of our results to nonlinear damped wave and plate equations allow us to obtain new results pertaining to structure and properties of global attractors for nonlinear waves and plates.     

Functionalization of the benzobicyclo[3.2.1]octadiene skeleton via photocatalytic and thermal oxygenation of a furan derivative

A simple and efficient protocol is utilized for the synthesis of novel functionalized benzobicyclo[3.2.1]octadiene derivatives by photocatalytic oxygenation of a furan derivative using an anionic free-base porphyrin as well as cationic and anionic manganese(III) porphyrins under different reaction conditions. The course and yields of these reactions were compared to those of the thermal reaction using m-chloroperbenzoic acid as the oxidizing agent. The deviating reaction pathways with anionic and cationic metalloporphyrins may be attributed to simultaneous electronic and steric effects. Application of free-base and metalated water-soluble porphyrins for photocatalytic oxygenation of the furan ring fused to the rigid methano-bridged skeleton proved to be regioselective and flexible compared to the thermal reactions with mCPBA, giving at the same time novel potentially biologically active bicyclo[3.2.1]octenes with the basic skeleton of which is incorporated in many natural compounds.