Today, we will use an algebraic approach to solve the matching problem. Our goal is to derive an algebraic test for deciding if a graph G = (V, E) has a perfect matching. We may assume that the number of vertices is even since this is a necessary condition for having a perfect matching. First, we will define a few basic needed notations.

The title compound, C(12)H(17)NO(4), features an almost planar mol-ecule (r.m.s. deviation for all non-H atoms = 0.070 Å). All methyl-ene C-C bonds adopt an anti-periplanar conformation. In the crystal structure the mol-ecules lie in planes parallel to (12) and the packing is stabilized by O-H⋯O hydrogen bonds.

Background and Purpose. Physiotherapists use a variety of techniques aimed at improving lung volumes and secretion clearance in patients after surgery. Periodic continuous positive airway pressure (PCPAP) is used to treat patients following elective upper abdominal surgery. However, the optimal method of application has not been identified, more specifically, the dosage of application of PCPAP....

In the title mol-ecule, C(16)H(13)Cl O(3), the two aromatic rings form a dihedral angle of 65.3 (1)°. In the crystal structure, weak inter-molecular C-H⋯O hydrogen bonds link the mol-ecules into centrosymmetric dimers, which are further packed into columns propagating in [100] by weak C-H⋯π inter-actions.