Signature (topology)In the field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension divisible by four. This invariant of a manifold has been studied in detail, starting with Rokhlin's theorem for 4-manifolds, and Hirzebruch signature theorem. Given a connected and oriented manifold M of dimension 4k, the cup product gives rise to a quadratic form Q on the 'middle' real cohomology group The basic identity for the cup product shows that with p = q = 2k the product is symmetric.
Finding NemoFinding Nemo is a 2003 American computer-animated comedy-drama adventure film produced by Pixar Animation Studios for Walt Disney Pictures. Directed by Andrew Stanton with co-direction by Lee Unkrich, the screenplay was written by Stanton, Bob Peterson, and David Reynolds from a story by Stanton. The film stars the voices of Albert Brooks, Ellen DeGeneres, Alexander Gould, Willem Dafoe, and Geoffrey Rush. It tells the story of an overprotective clownfish named Marlin (Brooks) who, along with a forgetful regal blue tang named Dory (DeGeneres), searches for his missing son Nemo (Gould).
Hirzebruch signature theoremIn differential topology, an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing the signature of a smooth closed oriented manifold by a linear combination of Pontryagin numbers called the L-genus. It was used in the proof of the Hirzebruch–Riemann–Roch theorem. The L-genus is the genus for the multiplicative sequence of polynomials associated to the characteristic power series The first two of the resulting L-polynomials are: (for further L-polynomials see or ).
Simple columnar epitheliumSimple columnar epithelium is a single layer of columnar epithelial cells which are tall and slender with oval-shaped nuclei located in the basal region, attached to the basement membrane. In humans, simple columnar epithelium lines most organs of the digestive tract including the stomach, and intestines. Simple columnar epithelium also lines the uterus. Cilia and Mucociliary clearance Simple columnar epithelium is further divided into two categories: ciliated and non-ciliated (glandular).
Toxic megacolonToxic megacolon is an acute form of colonic distension. It is characterized by a very dilated colon (megacolon), accompanied by abdominal distension (bloating), and sometimes fever, abdominal pain, or shock. Toxic megacolon is usually a complication of inflammatory bowel disease, such as ulcerative colitis and, more rarely, Crohn's disease, and of some infections of the colon, including Clostridium difficile infections, which have led to pseudomembranous colitis.
