Tilings whose members have finitely many neighbors

Let ? be a tiling of the plane such that each tile of ? meets at most finitely many other tiles. Then exactly one of the following must occur:

1. Uncountably many boundary points of ? belong to no nondegenerate edge of ?, hence ? has uncountably many singular points; or
2. Every boundary point of ? belongs to a nondegenerate edge of ?, moreover, ? has no singular points.

Furthermore, ifS is the set of singular points of ? andW={t:t∈bdry ? andt belongs to no nondegenerate edge of ?}, thenS=clW.     

Hybrid polyoxovanadates: anion-influenced formation of nanoscopic cages and supramolecular assemblies of asymmetric clusters

Two novel hybrid polyoxovanadates that are functionalized by (4-aminophenyl)arsonic acid ligands form upon the reduction of vanadates(V) in aqueous systems, whereby the underlying condensation reactions are influenced by the nature of the employed acid. In the presence of Cl(-) ions that derive from hydrochloric acid, a tetradecanuclear cage structure [V(IV)(14)O(16)(OH)(8)-(O(3)AsC(6)H(4)-4-NH(2))(10)](4-), whose cavity contains stabilizing halide ions and water molecules, is obtained. When nitric acid is used, a decanuclear [V(10)O(18)(O(3)AsC(6)H(4)-4-NH(2))(7)(DMF)(2)](5-) cluster can be isolated. The latter organizes into a hexagonal packing arrangement in the solid state.     

Separation of proteins from human plasma by sample displacement chromatography in hydrophobic interaction mode

Sample displacement chromatography (SDC) in reversed-phase and ion-exchange modes was introduced approximately 20 years ago. This method was first used for the preparative purification of peptides and proteins. Recently, SDC in ion-exchange mode was also successfully used for enrichment of low-abundance proteins from human plasma. In this paper, the use of SDC for the separation of plasma proteins in hydrophobic interaction mode is demonstrated. By use of two or more columns coupled in series during sample application, and subsequent elution of detached columns in parallel, additional separation of bound proteins was achieved. Further low-abundance, physiologically active proteins could be highly enriched and detected by ESI-MS/MS.     

Suitable families of boxes and kernels of staircase starshaped sets in {\mathbb{R}^d}

Let S be an orthogonal polytope in ${\mathbb{R}^d}$ . There exists a suitable family ${\mathcal{C}}$ of boxes with ${S = \cup \{C : C {\rm in} \mathcal{C}\}}$ such that the following properties hold:

The staircase kernel Ker S is a union of boxes in ${\mathcal{C}}$ . Let ${\mathcal{V}}$ be the family of vertices of boxes in ${\mathcal{C}}$ , and let ${v_o\, \epsilon \mathcal{V}}$ . Point v _o belongs to Ker S if and only if v _o sees via staircase paths in S every point w in ${\mathcal{V}}$ . Moreover, these staircase paths may be selected to consist of edges of boxes in ${\mathcal{C}}$ . Let B be a box in ${\mathcal{C}}$ with vertices of B in Ker S. Box B lies in Ker S if and only if, for some b in rel int B and for every translate H of a coordinate hyperplane at ${b, b \epsilon}$ Ker (H ∩ S). For point p in S, p belongs to Ker S if and only if, for every x in S, there exist some p ? x geodesic λ (p, x) and some corresponding ${\mathcal{C}}$ - chain D containing λ (p, x) such that D is staircase starshaped at p.

     

Helly-type theorems for intersections of sets starshaped via orthogonally convex paths

Let ${\mathcal{K}}$ be a family of simply connected sets in the plane. If every countable subfamily of ${\mathcal{K}}$ has an intersection that is starshaped via orthogonally convex paths, then ${\mathcal{K}}$ itself has such an intersection. For the d-dimensional case, let ${\mathcal{K}}$ be a family of compact sets in ${\mathbb{R}^d}$ . If every finite subfamily of ${\mathcal{K}}$ has an intersection that is starshaped via orthogonally convex paths, again ${\mathcal{K}}$ itself has such an intersection.     

On the Cardinalities of Row Spaces of Boolean Matrices

No Abstract. February 8, 1999     

Substrate Activity Screening with Kinases: Discovery of Small‐Molecule Substrate‐Competitive c‐Src Inhibitors

Substrate‐competitive kinase inhibitors represent a promising class of kinase inhibitors, however, there is no methodology to selectively identify this type of inhibitor. Substrate activity screening was applied to tyrosine kinases. By using this methodology, the first small‐molecule substrates for any protein kinase were discovered, as well as the first substrate‐competitive inhibitors of c‐Src with activity in both biochemical and cellular assays. Characterization of the lead inhibitor demonstrates that substrate‐competitive kinase inhibitors possess unique properties, including cellular efficacy that matches biochemical potency and synergy with ATP‐competitive inhibitors.     

Intersections of Sets Starshaped Via Paths of Bounded Length

 Let S be a nonempty closed, simply connected set in the plane. For α > 0, let ℳ denote the family of all maximal subsets of S which are starshaped via paths of length at most α. Then ⋂{M : M in ℳ} is either starshaped via α-paths or empty. The result fails without the simple connectedness condition. However, even with a simple connectedness requirement, there is no Helly theorem for intersections of sets which are starshaped via α-paths. Received November 19, 2001; in revised form April 25, 2002 Published online November 18, 2002     

Influence of Gas Type on the Thermal Efficiency of Microwave Plasmas for the Sintering of Metal Powders

Microwave plasmas have enormous potential as a rapid and energy efficient sintering technology. This paper evaluates the influence of both plasma atmosphere and metal powder type on the sintering temperatures achieved and the properties of the sintered powder metal compacts. The sintering is carried out using a 2.45 GHz microwave-plasma process called rapid discharge sintering (RDS). The sintering of three types of metal powder are evaluated in this study: nickel (Ni), copper (Cu) and 316L stainless steel (SS). An in-depth study of the effects of the plasma processing parameters on the sintered powder compacts are investigated. These parameters are correlated with the mechanical performance of the sintered compacts to help understand the effect of the plasma heating process. The substrate materials are sintered in four different gas discharges, namely hydrogen, nitrogen oxygen and argon. Thermocouple, pyrometer and emission spectroscopy measurements were taken to determine the substrate and the discharge temperatures. The morphology and structure were examined using scanning electron microscopy and X-ray diffraction. The density and hardness of the sintered compacts were correlated with the plasma processing conditions. As expected higher densities were obtained with powders with lower sintering temperatures i.e. nickel and copper when compared with stainless steel. Under the power input and pressure conditions used, the highest substrate temperature attained was 1,100°C for Cu powder sintered in a nitrogen atmosphere. In contrast under the same processing conditions but in an argon plasma, the temperature achieved with SS was only 500°C. The effect of the plasma gas type on the sintered powder compact chemistry was also monitored, both hydrogen and nitrogen yielded a reducing effect for the metal in contrast with the oxidising effect observed in an oxygen plasma.