In recent years there have been a number of surveys and comparison of techniques for estimating global discretization error in numerical solutions of differential equations [25, 29, 35, 36, 37, 39]. These have been an important stimulus to research in this area. In this paper we attempt to give an updated, organized, comprehensive survey of global error estimation techniques. For most of these ...

The “thirteen spheres problem,” also known as the “Gregory-Newton problem” is to determine the maximum number of three-dimensional spheres that can simultaneously touch a given sphere, where all the spheres have the same radius. The history of the problem goes back to a disagreement between Isaac Newton and David Gregory in 1694. Using a combination of harmonic analysis and linear programming i...

T use of alternative medicine (AM)—treatments such as herbs or massage therapy—has long been a part of healthcare in many regions of the world “to complement mainstream medicine by contributing to a common whole, by satisfying a demand not met by orthodoxy or by diversifying the conceptual frameworks of medicine” [1]. What AM cannot do is replace conventional treatment, particularly when it com...

Thirteen fern species are reported for the first time for Brazil. Among the new records, eight are from Acre state (Cyatheasubincisa, Cyclodiumtrianae, Elaphoglossumstenophyllum, Hypoderrisbrauniana, Pleopeltisstolzei, Thelypterisarcana, Thelypteriscomosa, Thelypterisvaldepilosa), two are from Pará state (Polypodiumflagellare, Tectariaheracleifolia), one from Minas Gerais state (Alsophilasalvin...

excised ganglion resemble that of synovial membrane. However, it is generally accepted that if a synovial herniation becomes loculated as in a Baker’s cyst, the lining membrane can undergo a metaplastic change to mesothelium. \Vhile the predisposing factors responsible for the formation of ganglia are by no means certain, accumulated evidence suggests that trauma to the joint ma\’ be important,...