3-manifoldIn mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below. A topological space is a 3-manifold if it is a second-countable Hausdorff space and if every point in has a neighbourhood that is homeomorphic to Euclidean 3-space.
Homology sphereIn algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer . That is, and for all other i. Therefore X is a connected space, with one non-zero higher Betti number, namely, . It does not follow that X is simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but using homology with rational coefficients.
Spherical 3-manifoldIn mathematics, a spherical 3-manifold M is a 3-manifold of the form where is a finite subgroup of SO(4) acting freely by rotations on the 3-sphere . All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds or Clifford-Klein manifolds. A spherical 3-manifold has a finite fundamental group isomorphic to Γ itself. The elliptization conjecture, proved by Grigori Perelman, states that conversely all compact 3-manifolds with finite fundamental group are spherical manifolds.
Digital NegativeDigital Negative (DNG) is a open, lossless developed by Adobe and used for digital photography. It was launched on September 27, 2004. The launch was accompanied by the first version of the DNG specification, plus various products, including a free-of-charge DNG converter utility. All Adobe photo manipulation software (such as Adobe Photoshop and Adobe Lightroom) released since the launch supports DNG. DNG is based on the standard format, and mandates significant use of metadata.
Chinese mathematicsMathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry. Since the Han dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like continued fractions are widely used and have been well-documented ever since.
Alexanderson alternatorAn Alexanderson alternator is a rotating machine invented by Ernst Alexanderson in 1904 for the generation of high-frequency alternating current for use as a radio transmitter. It was one of the first devices capable of generating the continuous radio waves needed for transmission of amplitude modulated signals by radio. It was used from about 1910 in a few "superpower" longwave radiotelegraphy stations to transmit transoceanic message traffic by Morse code to similar stations all over the world.
