This study is a review of the properties of protein planes. The basis of the research is the covalent bonds along the backbone of the protein, since the plane is defined by these atoms. We will measure the values of the bond lengths and the angles between the bonds to determine the consistency of these values in the PDB. We will go further to measure the lengths of the planes and omega, the dih...

Given a complete graph Kn = (V, E), with edge weight ce on each edge, we consider the problem of partitioning the vertices of graph Kn into subcliques that each have at least S vertices, so as to minimize the total weight of the edges that have both endpoints in the same subclique. It is an extension of the classic Clique Partition Problem that can be well solved using triangle inequalities, bu...

OBJECTIVES To investigate the availability of correction of mandibular plane using software for vertical measurements in cone beam computed tomography (CBCT) according to the sites of the mandible. METHODS CBCT scans of six dry mandibles were performed at 0-, 5-, 10-, 15-, and 20-degree angles relative to CBCT scanning table. Using the imaging software, mandibular planes of the different angl...

The classical 1962 Benders decomposition scheme is a traditional approach for solving mixed-integer problems such as the uncapacitated facility location problem. Subsequent research has been focused on finding better cutting-plane generation schemes to reduce the solution process time. Pareto-optimal cuts are typically preferred because no other cut can dominate them. However, the Pareto-optim...

In the title compound, C(15)H(20)O(7), the benzene ring makes dihedral angles of 69.17 (5) and 80.81 (4)° with the two side chains of malonate. The two malonate side chains comprising C/C/O/C atoms are oriented at right angles [86.26 (6)°] with respect to each other. In the crystal structure, the crystal packing is stabilized by weak non-classical inter-molecular C-H⋯O hydrogen bonds, which lin...

The asymmetric unit of the title compound, C(34)H(28)S(8), contains two crystallographically independent half-mol-ecules. The mol-ecules lie on centers of inversion. The four benzene rings of each mol-ecule are substantially twisted from the planes of the 1,3-dithiole rings, forming dihedral angles of 43.6 (2) and 61.4 (1)° in one mol-ecule and 54.2 (1) and 65.2 (1)° in the other.

The N-H and C=O bonds of the SO(2)-NH-CO group in the title compound, C(11)H(15)NO(3)S, are anti to each other. The asymmetric unit contains two independent mol-ecules. The benzene rings form dihedral angles of 83.19 (8) and 76.01 (10)° with the mean planes of the C(2)NOS fragments. The mol-ecules are linked into chains parallel to the b axis by inter-molecular N-H⋯O hydrogen bonds.