Packing and covering the plane with translates of a convex polygon

A covering of the Euclidean plane by a polygon P is a system of translated copies of P whose union is the plane, and a packing of P in the plane is a system of translated copies of P whose interiors are disjoint. A lattice covering is a covering in which the translates are defined by the points of a lattice, and a lattice packing is defined similarly. We show that, given a convex polygon P with n vertices, the densest lattice packing of P in the plane can be found in O(n) time. We also show that the sparsest lattice covering of the plane by a centrally symmetric convex polygon can be solved in O(n) time. Our approach utilizes results from classical geometry that reduce these packing and covering problems to the problems of finding certain extremal enclosed figures within the polygon.     

Entangled Porphyrins in Cyclodextrin Vesicles

The entanglement process between porphyrins and some amphiphiliccyclodextrins and the occurrence of different species have been proved by the combination of UV-Visabsorption, fluorescence anisotropy, resonance light scattering and ¹H NMR spectroscopy.     

Chemical stability at noble metal M/YBa2Cu3O6.8 interfaces (M = Pt, Ag, Au)

The chemical compatibility between YBa₂Cu₃O_6.8 (Y123) and Pt, Ag or Au was studied using quasi-infinite diffusion couples which were encapsulated and annealed at 650 to 800°C for 5 to 80 h. The phase formation at the interface was analyzed in cross sections of these couples using optical and scanning electron microscopy together with energy- and wavelength dispersive X-ray microanalysis. In addition, bulk powder mixtures of Y123 with Pt, Ag or Au were annealed at 800°C for 100 h and phase analysis was performed using X-ray diffraction.

At the Pt/Y123 interface a reaction zone grows slowly but decisively at 800°C. Its microstructure is multiphase with Y---Cu-oxides and a fine-grained dispersion of Y₂BaCuO₅ (Y211) with Ba---Cu-oxides. Additional Ba---Pt oxides and other phases are seen in powder mixtures annealed for longer times. Barium is suspected to diffuse out from the superconductor along grain boundaries from as deep as 1 mm, causing the decomposition of Y123 into Y---Cu-oxides in the depleted regions. Ag and Au form a stable contact at the interface to Y123 with no reaction zone or new phases. Interdiffusion at the Ag/Y123 interface at 800°C was too low to be clearly detected. In contrast, Au diffuses very fast into Y123 and at 800°C the solubility is 4.2 mass% Au. Yttrium and barium diffuse much slower into the (Au) phase, Cu diffusion was not detected. Weak traces of decomposition products, mostly Y211 and Ba---Cu-oxides, were observed in bulk powder mixtures of Y123 with Ag or Au annealed at 800°C for 100 h in closed capsules. These decomposition products are considered to be due to the high oxygen pressure in the closed capsule, exceeding the stability limit of Y123, and not due to the reduction of Y123. Both Ag and Au are virtually non-reactive with Y123.     

An Approximate Analytical Solution for Counter-Current Spontaneous Imbibition

An approximate analytical solution is provided for one-dimensional, counter- current, spontaneous imbibition of a wetting phase (water) into a semi-infinite porous medium. The solution is based on the assumption that a similarity solution exists for the displacement process. This assumption, in turn, rests on the assumption that the set of relative permeability and capillary pressures curves are unique functions of saturation and do not depend on the nature of the displacement. It further rests on the assumption that the saturation at the imbibition face does not vary with time. It is demonstrated that the solution is in agreement with results obtained from experiments and also numerical analyses of these experiments. The experiments utilize cylindrical samples with the radial surface and one end-face sealed, and with counter-current imbibition occurring at the open end-face. The stage of the experiment that is modeled by the present solution is the period before the imbibition front contacts the sealed end-face. An important finding of the present analysis is that the pressure upstream of the advancing invasion front is a constant. A second, improved solution is also presented; this solution is an iterative, series solution of an integral-differential equation. It converges to a stable solution in very few terms.     

Facile Hydrolysis and Alcoholysis of Palladium Acetate

Palladium(II) acetate is readily converted into [Pd₃(μ²‐OH)(OAc)₅] ( 1 ) in the presence of water in a range of organic solvents and is also slowly converted in the solid state. Complex 1 can also be formed in nominally anhydrous solvents. Similarly, the analogous alkoxide complexes [Pd₃(μ²‐OR)(OAc)₅] ( 3 ) are easily formed in solutions of palladium(II) acetate containing a range of alcohols. An examination of a representative Wacker‐type oxidation shows that the Pd‐OH complex 1 and a related Pd‐oxo complex 4 can be excluded as potential catalytic intermediates in the absence of exogenous water.     

Regiodivergent and Stereoselective Hydrosilylation of 1,3‐Disubstituted Allenes

Methods for the highly stereoselective and regiodivergent hydrosilylation of 1,3‐disubstituted allenes have been developed. The synthesis of E allylsilanes is accomplished with palladium NHC catalysts, and trisubstituted Z alkenylsilanes are accessed with nickel NHC catalysts. Unsymmetrically substituted allenes are well tolerated with nickel catalysis and afford Z alkenylsilanes. Evidence for a plausible mechanism was obtained through an isotopic double‐labeling crossover study.     

Stability and Conversion of Tin Zintl Anions in Liquid Ammonia Investigated by NMR Spectroscopy

Homoatomic polyanions of post‐transition main‐group metals, namely, Zintl anions, are precast in analogous Zintl phases and can react in solution to form new materials. Despite comprehensible reaction approaches, the formed products cannot be planned in advance, as hitherto undetected and therefore disregarded side reactions take place. The outcomes and interpretations of the reactions of Zintl anions are so far based mainly on crystal structures, which only allow characterization of the product that has the lowest solubility. Here we present the results of our investigation of the stability of highly charged tin Zintl anions in liquid ammonia, which is not exclusively based on solution effects but also on the oxidative influence of the solvent. This allows for a deeper understanding of the ongoing processes in solution and opens doors to the directed synthesis of transition metal complexes of Sn₄^4?, here shown by its reactivity towards MesCu.     

Genetics in primary care: a USA faculty development initiative

The Genetics in Primary Care (GPC) project is a USA national faculty development initiative with the goal of enhancing the training of medical students and primary care residents by developing primary care faculty expertise in genetics. Educational strategies were developed for the project by an executive committee with input from an advisory committee, comprising individuals with primary care, medical education and genetics expertise. These committees identified the key issues in genetics education for primary care as (1) considering inherited disease in the differential diagnosis of common disorders; (2) using appropriate counseling strategies for genetic testing and diagnosis, and (3) understanding the implications of a genetic diagnosis for family members. The group emphasized the importance of a primary care perspective, which suggests that the clinical utility of genetic information is greatest when it has the potential to improve health outcomes. The group also noted that clinical practice already incorporates the use of family history information, providing a basis for discussing the application of genetic concepts in primary care. Genetics and primary care experts agreed that educational efforts will be most successful if they are integrated into existing primary care teaching programs, and use a case-based teaching format that incorporates both clinical and social dimensions of genetic disorders. Three core clinical skills were identified: (1) interpreting family history; (2) recognizing the variable clinical utility of genetic information, and (3) acquiring cultural competency. Three areas of potential controversy were identified as well: (1) the role of nondirective counseling versus shared decision-making in discussions of genetic testing; (2) the intrinsic value of genetic information when it does not influence health outcomes, and (3) indications for a genetics referral. The project provides an opportunity for ongoing discussion about these important issues.     

Material properties of matrix lipids determine the conformation and intermolecular reactivity of diacetylenic phosphatidylcholine in the lipid bilayer

Photopolymerizable phospholipid DC(8,9)PC (1,2-bis-(tricosa-10,12-diynoyl)-sn-glycero-3-phosphocholine) exhibits unique assembly characteristics in the lipid bilayer. Because of the presence of the diacetylene groups, DC(8,9)PC undergoes polymerization upon UV (254 nm) exposure and assumes chromogenic properties. DC(8,9)PC photopolymerization in gel-phase matrix lipid 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) monitored by UV-vis absorption spectroscopy occurred within 2 min after UV treatment, whereas no spectral shifts were observed when DC(8,9)PC was incorporated into liquid-phase matrix 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). Liquid chromatography-tandem mass spectrometry analysis showed a decrease in the amount of DC(8,9)PC monomer in both DPPC and POPC environments without any change in the matrix lipids in UV-treated samples. Molecular dynamics (MD) simulations of DPPC/DC(8,9)PC and POPC/DC(8,9)PC bilayers indicate that the DC(8,9)PC molecules adjust to the thickness of the matrix lipid bilayer. Furthermore, the motions of DC(8,9)PC in the gel-phase bilayer are more restricted than in the fluid bilayer. The restricted motional flexibility of DC(8,9)PC (in the gel phase) enables the reactive diacetylenes in individual molecules to align and undergo polymerization, whereas the unrestricted motions in the fluid bilayer restrict polymerization because of the lack of appropriate alignment of the DC(8,9)PC fatty acyl chains. Fluorescence microscopy data indicates the homogeneous distribution of lipid probe 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-lissamine rhodamine B sulfonyl ammonium salt (N-Rh-PE) in POPC/DC(8,9)PC monolayers but domain formation in DPPC/DC(8,9)PC monolayers. These results show that the DC(8,9)PC molecules cluster and assume the preferred conformation in the gel-phase matrix for the UV-triggered polymerization reaction.