For every dimension d ≥ 1 there exists a constant c = c(d) such that for all n ≥ 1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.

The aim of the present work is to explore crystal and electronic structure of N,N-di[(5-chloro-2-oxo-2,3-dihydrobenzo[d]oxazole-3-yl) methyl]ethanamine. In the title compound, C18H15Cl2N3O4, the two 2, 3-dihydro-1, 3-benzoxazole ring systems are almost planar and make a dihedral angle of 96.12(7) with each other. The ethyl group is disordered over two set of sites with a site-occupancy ratio of...

In the title compound, C(16)H(14)N(4)OS, the three fused rings of the benzothieno[3,2-d]pyrimidinone unit are essentially coplanar, the maximum deviation from the mean plane being 0.067 (3) Å. The dihedral angle between the mean plane of the fused rings and the imidazole ring is 72.00 (3)°. Offset π-π stacking inter-actions involving the fused rings are effective in the stabilization of the cry...

In the title compound, C(31)H(37)ClN(4)O(3), the fused rings of the pyrrolo-[3,2-d]pyrimidine system form a dihedral angle of 5.80 (11)°. The phenyl and benzene rings are twisted with respect to the mean plane of the pyrrolo-[3,2-d]pyrimidine system [maximum deviation = 0.077 (2) Å], making dihedral angles of 61.05 (12) and 75.39 (10)°, respectively. The eth-oxy group is disordered over two pos...

in this paper, by considering a squint angle for synthetic aperture radar in the strip-map mode, a method is proposed for estimating parameters of a fixed acceleration moving target. non-zero doppler centroid and range-azimuth coupling in the squint mode add complexity to estimation equations of moving target parameters and cause doppler ambiguity. this, in turn, causes to lose the efficiency o...

The aim of the study was to report postoperative corneal and surgically induced astigmatism (SIA) in patients with preoperative against-the-rule (ATR) astigmatism who underwent superior approach manual small incision cataract surgery (MSICS). 58 eyes of 58 cataract patients with preoperative ATR astigmatism were involved in this study. All patients had operable cataracts and underwent superior ...

following the 1994 northridge and 1995 kobe earthquakes, most of modern structures damaged seriously or devastated totally despite the seismic codes of these countries that had been expected to bear advanced criteria for seismic design of structures. after extensive research, the most probable reason of those destructions was attributed to special specifications of near-field earthquakes. in th...