Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds

Let X be a strongly pseudoconvex compact 3-dimensional CR manifolds which bounds a complex variety with isolated singularities in some C^N. The weighted dual graph of the exceptional set of the minimal good resolution of V is a CR invariant of X; in case X has a tranversal holomorphic S¹ action, we show that it is a complete topological invariant of except for two special cases. When X is a rational CR manifolds, we give explicit algebraic algorithms to compute the graph invariant in terms of the ring structure of _k=0 m^k/m^k+1, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.     

Crystal and molecular structures of three trimethylamine-boron halide adducts: (CH3)3NBCl3, (CH3)3NBBr3, and (CH3)3NBI3

X-ray diffraction data from single crystals of the trimethylamine complexes of the three boron halides, BCl₃, BBr₃, and BI₃, lead to aP2₁/m monoclinic cell containing two molecules for each complex. The unit cell dimensions area = 6·68(1),b = 10·247(3),c = 6·502(6) Å, =116·2(1)° (chloro);a = 6·86(1),b = 10·612(4),c = 6·737(6) Å, = 115·8(1)° (bromo);a = 6·92(2),b = 10·86(1),c = 7·147(6) Å, = 93·9(1)° (iodo). The structures were solved by three-dimensional sharpened Patterson functions and show only the chloro and bromo compounds to be isomorphous. Refinement of 662,718 and 954 observed reflexions for the chloro, bromo and iodo complexes, respectively, using anisotropic thermal parameters yielded conventionalR factors of 0·045, 0·087 and 0·054.The molecules are shown to possess a B—N dative bond, a staggered conformation, and effective 3m (C _3v) symmetry. Average C—N bond lengths are 1·52(1) Å for all three complexes. Boronhalogen bond lengths average 1·864(4), 2·04(2) and 2·28(2) Å, while B—N bond distances are 1·609(6), 1·60(2) and 1·58(3) Å, respectively, for the chloro through iodo compounds. Bond angles are approximately tetrahedral with the C—N—C angle decreasing by several degrees in the Cl Br I series.Based in part on a dissertation submitted by Patty H. Clippard to the Rackham School of Graduate Studies of the University of Michigan, January 1969 in partial fulfillment of the requirements of the Ph.D. Degree.     

Studies toward frondosin A and its analogues. Formal total synthesis of (+/-)-frondosin A

Two reaction sequences commencing with different starting materials were successfully employed for the synthesis of frondosin A analogues, including (+/-)-frondosin A dimethyl ether. Construction of the bicyclo[5.4.0]undecane core in each case was achieved through an expedient microwave-assisted tandem 5-exo cyclization--Claisen rearrangement process.     

The benzil rearrangement reaction: trapping of a hitherto minor product and its application to the development of a selective cyanide anion indicator

The isolation and characterization of an intermediate from the benzil-cyanide reaction is reported. The use of this trapping chemistry to produce a chemical indicator for the cyanide anion is described. It relies on the synthesis and reaction of a pi-extended analogue of benzil. Addition of tetrabutylammonium cyanide to organic solutions of this species, referred to as compound 3 in the text, gives rise to a dramatic change in both color and fluorescence properties.     

Biomaterials and biofunctionality in layered macromolecular assemblies

Recent research in the field of LbL assembly is summarized and categorized as fabrication, sensing, drug release/delivery, and cell technology. Special emphasis is given to topics such as cell-membrane-mimic assembly, fabrication of free-standing biomolecular structures including protein microtubes, detection of DNA adducts and reactive metabolites, DNA hybridization analysis, sensing of toxic and bio-active chemicals, entrapment of proteins and DNA, biocomponent carriers with barcode encoding, release and delivery of DNA plasmids, multiagent delivery, smart defense capsules and oxidation-resistant films, vector introduction to cells, patterned cell culturing and microfluidic microreactors, stem cell differentiation, cellular uptake and degradation, and control of cellular apoptosis.     

Two‐ and three‐dimensional hydrogen‐bonded structures in the 1:1 proton‐transfer compounds of 4,5‐dichlorophthalic acid with the isomeric monoaminobenzoic acids

The crystal structures of the 1:1 proton‐transfer compounds of 4,5‐dichlorophthalic acid with the three isomeric monoaminobenzoic acids, namely the hydrate 2‐carboxyanilinium 2‐carboxy‐4,5‐dichlorobenzoate dihydrate, C₇H₈NO₂⁺·C₈H₃Cl₂O₄⁻·2H₂O, (I), and the anhydrous salts 3‐carboxyanilinium 2‐carboxy‐4,5‐dichlorobenzoate, C₇H₈NO₂⁺·C₈H₃Cl₂O₄⁻, (II), and 4‐carboxyanilinium 2‐carboxy‐4,5‐dichlorobenzoate, C₇H₈NO₂⁺·C₈H₃Cl₂O₄⁻, (III), have been determined at 130 K. Compound (I) has a two‐dimensional hydrogen‐bonded sheet structure, while (II) and (III) are three‐dimensional. All three compounds feature sheet substructures formed through anilinium N⁺—H...O_carboxyl and anion carboxylic acid O—H...O_carboxyl interactions and, in the case of (I), additionally linked through the donor and acceptor associations of the solvent water molecules. However, (II) and (III) have additional lateral extensions of these substructures though cyclic R²₂(8) associations involving the carboxylic acid groups of the cations. Also, (II) and (III) have cation–anion π–π aromatic ring interactions. This work provides further examples illustrating the regular formation of network substructures in the 1:1 proton‐transfer salts of 4,5‐dichlorophthalic acid with the bifunctional aromatic amines.     

Force microscopy analysis using chemometric tools

In this paper we report the first application of multivariate data analysis techniques to force spectrometry measurement sets to enable the physicochemical assignment of spatially ordered multi-component systems. Principal component analysis (PCA) and hierarchical clustering techniques were used to reveal hidden chemical information within force-distance curves generated by high spatial resolution force microscopy. Two experimental samples were analyzed: (i) a two-component system of cytochrome c proteins on a mica surface, and (ii) a three-component system of avidin protein islands positioned on a gold and glass surface. PCA and hierarchical clustering techniques were used to discriminate the different components of the two-component system, whereas hierarchical clustering was found to be superior for the three-component system. Results were in good agreement with the topography and prior knowledge of the surface patterns. This research represents a formative step towards the combination of force spectrometry with chemometric tools for the high resolution physicochemical investigation of complex biochemical systems.     

Unavoidable subgraphs of colored graphs

A natural generalization of graph Ramsey theory is the study of unavoidable sub-graphs in large colored graphs. In this paper, we find a minimal family of unavoidable graphs in two-edge-colored graphs. Namely, for a positive even integer k, let S_k be the family of two-edge-colored graphs on k vertices such that one of the colors forms either two disjoint K_k/2's or simply one K_k/2. Bollobás conjectured that for all k and ε>0, there exists an n(k,ε) such that if n?n(k,ε) then every two-edge-coloring of K_n, in which the density of each color is at least ε, contains a member of this family. We solve this conjecture and present a series of results bounding n(k,ε) for different ranges of ε. In particular, if ε is sufficiently close to , the gap between our upper and lower bounds for n(k,ε) is smaller than those for the classical Ramsey number R(k,k).     

Exploring the relationship between cocrystal stability and symmetry: is Wallach's rule applicable to multi-component solids?

Comparison of structure and hydration stability of pairs of chiral and racemic binary cocrystals indicates that the racemic solid is more stable than the chiral one; we illustrate that this difference might arise from intermolecular (crystal packing) factors in one case, while intramolecular (molecular conformation) factors are more significant in the other.     

Highly diastereoselective self-assembly of chiral tris(m-ureidobenzyl)amino capsules

The self-assembly of chiral tris(m-ureidobenzyl)amines to give dimeric capsules is a highly diastereoselective process in solution, while in the solid state, the formation of the corresponding capsules is not only diastereoselective but also regioselective.