A coccus is any bacterium or archaeon that has a spherical, ovoid, or round shape. Bacteria are categorized based on their shapes into three classes: cocci and spirochetes cells. Coccus refers to the shape of the bacteria, can contain multiple genera, such as staphylococci or streptococci. Cocci can grow in pairs, chains, or clusters, depending on their orientation and attachment during cell division. Contrast to many bacilli-shaped bacteria, most cocci bacteria do not have flagella and are non-motile. Cocci is an English loanword of a modern or neo-Latin noun, which in turn stems from the Greek masculine noun cóccos meaning "berry". Cocci Structure Structure for cocci may vary between gram positive and gram negative bacterial wall types; the cell wall structure for cocci may vary between gram positive and gram negative. While living in their host organism, cocci can be commensal, or symbiotic. Gram-Positive Cocci The Gram-Positive Cocci are a large group of loosely bacteria with similar morphology.

All are spherical or nearly so, but they vary in size. Members of some genera are identifiable by the way cells are attached to one another: in pockets, in chains, or grapes like clusters; these arrangements reflect patterns of cell fact that cell stick together. Sarcina cells, for example, are arranged in cubical pockets because cell division alternates among the three perpendicular planes. Streptococcus spp. resemble a string of beads. Some of these strings, for example, S. pneumoniae, are only two cells long. They are called diplococci. Species of Staphylococcus have no regular plane of division, they form grape-like structures. The various Gram-positive cocci differ physiologically and by habitat. Micrococcus spp. are obligate aerobes. Staphylococcus spp. inhabit human skin, but they are facultative anaerobes. They ferment sugars. Many of these species produce carotenoid pigments, which color their colonies orange. Staphylococcus aureus is a major human pathogen, it can infect any tissue in the body the skin.

It causes nosocomial infections. Cocci may remain attached following cell division; those that remain attached can be classified based on cellular arrangement: Diplococci are pairs of cocci Streptococci are chains of cocci. Staphylococci are irregular clusters of cocci. Tetrads are clusters of four cocci arranged within the same plane. Sarcina is a genus of bacteria that are found in cuboidal arrangements of eight cocci

Roman Catholic Diocese of Kimbe

The Roman Catholic Diocese of Goroka is a suffragan diocese of the Roman Catholic Archdiocese of Rabaul. It was erected in 2003; the new coat of arms of the Diocese was adopted in 2016. The proposal of coat of arms created Marek Sobola, a heraldic specialist from Slovakia, who made a redesign of coat of arms for the bishop William Fey, O. F. M. Cap. Alphonse Liguori Chaupa William Fey, O. F. M. Cap. John Bosco Auram "Diocese of Kimbe". Catholic-Hierarchy. Retrieved 2007-01-10. Papal bull - papal bull of 12 June 2003 establishing the diocese of Kimbe, accessed from

Carathéodory's existence theorem

In mathematics, Carathéodory's existence theorem says that an ordinary differential equation has a solution under mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence of solutions for some discontinuous equations; the theorem is named after Constantin Carathéodory. Consider the differential equation y ′ = f with initial condition y = y 0, where the function ƒ is defined on a rectangular domain of the form R =. Peano's existence theorem states that if ƒ is continuous the differential equation has at least one solution in a neighbourhood of the initial condition. However, it is possible to consider differential equations with a discontinuous right-hand side, like the equation y ′ = H, y = 0, where H denotes the Heaviside function defined by H = { 0, if t ≤ 0, it makes sense to consider the ramp function y = ∫ 0 t H d s = { 0, if t ≤ 0. Speaking though, it does not satisfy the differential equation at t = 0, because the function is not differentiable there.

This suggests that the idea of a solution be extended to allow for solutions that are not everywhere differentiable, thus motivating the following definition. A function y is called a solution in the extended sense of the differential equation y ′ = f with initial condition y = y 0 if y is continuous, y satisfies the differential equation everywhere and y satisfies the initial condition; the absolute continuity of y implies that its derivative exists everywhere. Consider the differential equation y ′ = f, y = y 0, with f defined on the rectangular domain R =. If the function f satisfies the following three conditions: f is continuous in y for each fixed t, f is measurable in t for each fixed y, there is a Lebesgue-integrable function m: → [ 0, ∞ ) such that | f | ≤ m for all ∈ R,then the differential equation has a solution in the extended sense in a neighborhood of the initial condition. A mapping f: R