Skeletal editing involves making specific point-changes to the core of a molecule through selective insertion, deletion or exchange atoms. It thus represents potentially powerful strategy for step-economic modification complex substrates and is perfect complement methods such as C−H functionalization that target molecular periphery. Given their ubiquity in biologically active compounds, ability...

Applications of the Covering Property Axiom Andrés Millán Millán The purpose of this work is two-fold. First, we present some consequences of the Covering Property Axiom CPA of Ciesielski and Pawlikowski which captures the combinatorial core of the Sacks’ model of the set theory. Second, we discuss the assumptions in the formulation of different versions of CPA. As our first application of CPA ...

For c ∈ [0, 1] let Pn(c) denote the set of n-vertex perfect graphs with density c and Cn(c) the set of n-vertex graphs without induced C5 and with density c. We show that log2 |Pn(c)|/ (

Brualdi et al. introduced the concept of poset codes. In this paper, we consider the problem of classifying all perfect linear codes when the set of coordinate positions is endowed with crown poset structure. We derive a Ramanujan–Nagell type diophantine equation which is satis ed by parameters of perfect linear P-code. Solving this equation, we characterize parameters of one and two error corr...

The surface functionalization of diamonds has been extensively studied through a variety techniques, such as controlled oxidation. Several oxygen groups have detected on oxidized diamonds, C–O–C (ester), C=O (ketonic), and C–OH (hydroxyl). However, the composition relative concentration these diamond surfaces can be affected by type oxygenation treatment quality. To investigate stability oxygen...

|This paper describes an algorithm for nding all the perfect matchings in a bipartite graph. By using the binary partitioning method, our algorithm requires O(c(n+m) + n 2:5 ) computational e ort and O(nm) memory storage, (where n denotes the number of vertices, m denotes the number of edges, and c denotes the number of perfect matchings in the given bipartite graph). Keywords|bipartite graph, ...

Two plane graphs with the same vertex set are compatible if their union is again a plane graph. We consider bichromatic plane straight-line graphs with vertex set S consisting of the same number of red and blue points, and (perfect) matchings which are compatible to them. For several different classes C of graphs, we present lower and upper bounds such that any given graph G(S) ∈ C admits a com...

In this paper we deal with the following natural family of geometric matching problems. Given a class C of geometric objects and a point set P , a C-matching is a set M ⊆ C such that every C ∈ M contains exactly two elements of P . The matching is perfect if it covers every point, and strong if the objects do not intersect. We concentrate on matching points using axis-aligned squares and rectan...

TC = 203, TG = 379, HDL-C = 37, LDL-C = 90 and fasting insulin 26. NMR LipoProfile (lipoprotein concentrations) LDL-P = 1820 (desirable < 1300 perfect < 1000) Small LDL-P = 1556 (perfect < 600) However likely not a problem if total LDL-P is OK LDL particle size = 19.5 (quite small) Cutoff between Pattern A (normal) and Pattern B (small is 20.5) Large HDL-P 3.9 Quite low Small HDL-P not provided...