as a new precursor, [tris(2-hydroxyacetophenato) triaqua(iii)], [y(hap)3(h2o)3]; complex was used in thermal decomposition process for the synthesis of rod-like high-temperature ceramic ybco with length of about 320-350 nm and diameters 60–90 nm. the as-synthesized products were characterized by xrd, ft-ir, tem, sem and edx analyses. the results showed that by using fine raw materials, the calc...

In this paper, we investigate the L1 geodesic farthest neighbors in a simple polygon P , and address several fundamental problems related to farthest neighbors. Given a subset S ⊆ P , an L1 geodesic farthest neighbor of p ∈ P from S is one that maximizes the length of L1 shortest path from p in P . Our list of problems include: computing the diameter, radius, center, farthestneighbor Voronoi di...

Problem B1 (20 pts). A ray , R, of E is any subset of the form R = {a+ tu | t ∈ R, t ≥ 0}, for some point, a ∈ E and some nonzero vector, u ∈ R. A subset, A ⊆ E, is unbounded iff it is not contained in any ball. Prove that every closed and unbounded convex set, A ⊆ E, contains a ray. Hint : Pick some point, c ∈ A, as the origin and consider the sphere, S(c, r) ⊆ E, of center c and radius r > 0....

In this paper, we show that the center of every Coxeter group is finite and isomorphic to (Z2) n for some n ≥ 0. Moreover, for a Coxeter system (W, S), we prove that Z(W ) = Z(W S\S̃) and Z(W S̃ ) = 1, where Z(W ) is the center of the Coxeter group W and S̃ is the subset of S such that the parabolic subgroup W S̃ is the essential parabolic subgroup of (W, S) (i.e. W S̃ is the minimum parabolic subgr...

a 50-year-old male underwent a check-up for an insurance company. chest x-ray revealed a large ball-like lesion in the posterior mediastinum. the finding was confirmed by computed tomography (ct) scan (figure 1). the patient was referred to our center, where he had a successful mass removal surgery (figure 2). pathology identified the mass as neurinoma.

With Gaia’s first data release comes a large amount of new data on stars in the Milky Way. We were interested in a subset of these that were cross referenced with the Tycho-2 catalogue. In this project, we look at two ways of analyzing the data spatial correlation functions and velocity profiles. To find a velocity profile, we looked at a subset of stars along the sun to galactic center line to...

Let D be a set of disks of arbitrary radii in the plane, and let P be a set of points. We study the following three problems: (i) Assuming P contains the set of center points of disks in D, find a minimum-cardinality subset P∗ of P (if exists), such that each disk in D is pierced by at least h points of P∗, where h is a given constant. We call this problem minimum h-piercing. (ii) Assuming P is...