Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is constrained to lie on a query line segment. Our algorithm preprocesses a given set of n points P = {p1, p2, . . . , pn} such that for any query line or line segment L, it efficiently locates a point c′ on L that minimizes the maximum distance among the points in P from c′. Roy et al. [11] has prop...

We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).

We obtain some simple criteria for the boundedness and compactness of the product of differentiation and composition operator CφD on Bloch type spaces.

Public libraries have been associated with a Habermasian public sphere, but articulations between public libraries and the public sphere remain undefined. To make fuller sense of the public sphere as it relates to public libraries, we used qualitative content analysis as a research methodology to study 12 Carnegie Library of Pittsburgh annual reports from 1900 to 2010. We identified 6 dimension...

A finite element model is developed to study the transient thermo-mechanical contact between a rigid sphere and an elastic–plastic sphere. Interference and tangential displacement are applied to the rigid sphere while the elastic–plastic sphere is stationary. The radius of the rigid sphere is larger than that of the elastic–plastic sphere to model flattening. Universal solutions are obtained fo...

introduction: the limited resolution of the imaging system causes partial volume effects (pves). these results in spreading of image counts to the neighboring pixels. this phenomenon is called spill-out effect. this study aimed at quantifying pves using imagej. methods:technetium-99m solution of concentration of 74 kbq/ml was filled into spheres a, b and c of diameters: 26 mm, 20 mm and 16 mm r...

This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V -cell ...

We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d − 1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that A ∩B = H and A ∪B = G and such that the complementary graphs A,B are both d-balls. The graph theoretic definitions are due to Evako: the unit sphere of a vertex x of a graph G = (V,E) is the graph generated by ...

We derive an exact, analytic expression for the fourth virial coefficient of a system of polydisperse spheres under the constraint that the smallest sphere has a radius smaller than a given function of the radii of the three remaining particles.