Let P be an H-polytope in R with vertex set V . The vertex centroid is defined as the average of the vertices in V . We first prove that computing the vertex centroid of an H-polytope, or even just checking whether it lies in a given halfspace, are #P-hard. We also consider the problem of approximating the vertex centroid by finding a point within an ǫ distance from it and prove this problem to...

In the crystal structure of the title compound, C(12)H(12)N(2) (2+)·2C(15)H(9)O(5) (-), the cation has site symmetry with the mid-point of C=C bond located on an inversion center. The two benzene rings of the anion are oriented at a dihedral angle 85.87 (6)°. In the crystal, inter-molecular O-H⋯O and N-H⋯O hydrogen bonds link the cations and anions into supra-molecular double chains, which are ...

3-Fluoro-salicylaldoxime, C(7)H(6)FNO(2), unlike many salicylaldoxime derivatives, forms a crystal structure containing hydrogen-bonded chains rather than centrosymmetric hydrogen-bonded ring motifs. Each chain inter-acts with two chains above and two chains below via π-π stacking contacts [shortest centroid-centroid distance = 3.295 (1) Å]. This structure at 6.5 GPa represents the final point ...

Extended source size effects have been detected in photometric monitoring of gravitational microlensing events. We study similar effects in the centroid motion of an extended source lensed by a point mass. We show that the centroid motion of a source with uniform surface brightness can be obtained analytically. For a source with circularly symmetric limb-darkening profile, the centroid motion c...

Content description has become a topic of interest for many researchers in the audiovisual field [1][2]. While manual annotation has been used for many years in different applications, the focus now is on finding automatic contentextraction and content-navigation tools. An increasing number of projects, in some of which we are actively involved, focus on the extraction of meaningful features fr...

In the title compound, C(7)H(7)Cl(2)N, a halogenated derivative of 2,6-lutidine, the C-Cl vectors of the chloro-methyl groups point at opposite sides of the aromatic plane to each other. A weak dispersive Cl⋯Cl contact [3.4342 (3) Å] connects the mol-ecules into a chain along the [101] direction. A π-π inter-action with a centroid-centroid distance of 3.7481 (5) Å is also observed.

— A method for solving the problem of minimizing the work expended in sliding blocks along an inclined plane to a central location is considered. Significant improvement in the itérative procedure is offered in cases where the centroid does not coïncide with a demand point. Also, an alternative to the itérative procedure is suggested for cases of such coïncidence. This approach adds an insight ...

The title mol-ecule, C(25)H(21)N, situated on the crystallographic twofold axis has a symmetry point group 2. The inter-planar angles between the central pyridyl ring and the phenyl and the methyl-phenyl rings are 32.8 (2) and 23.7 (2)°, respectively. In the crystal packing, the central pyridyl rings of adjacent mol-ecules are involved in π-π inter-actions, forming one-dimensional arrays along ...

b a c k g r o u n d  & aim: it is very helpful to classify and predict the clinical  category  of a sample based  on  its  gene  expression  profile.  this  study  was  conducted  to predict  tissues  of colorectal adenoma,  adenocarcinoma,  and  paired  normal  in  colon  based  on  microarray  data  using  nearest shrunken centroid method. methods   &  materials:    in  this  study,   the  co...

This study investigates acoustic characteristics of Aymara ejectives. Acoustic measurements of the Aymara ejectives were conducted in terms of the durations of the release burst, the vowel, and the intervening gap (VOT), the intensity and spectral centroid of the release burst, and H1-H2 of the initial part of the vowel. Results showed that ejectives vary with place of articulation in the durat...