On-Line Encyclopedia of Integer SequencesThe On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Sloane is the chairman of the OEIS Foundation. OEIS records information on integer sequences of interest to both professional and amateur mathematicians, and is widely cited. , it contains over 360,000 sequences, making it the largest database of its kind.
PresentThe present is the period of time that is occurring now. The present is contrasted with the past, the period of time that has already occurred, and the future, the period of time that has yet to occur. It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration.
Sequence alignmentIn bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Aligned sequences of nucleotide or amino acid residues are typically represented as rows within a matrix. Gaps are inserted between the residues so that identical or similar characters are aligned in successive columns.
Arc lengthArc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) , then the curve is rectifiable (i.
Sequence analysisIn bioinformatics, sequence analysis is the process of subjecting a DNA, RNA or peptide sequence to any of a wide range of analytical methods to understand its features, function, structure, or evolution. Methodologies used include sequence alignment, searches against biological databases, and others. Since the development of methods of high-throughput production of gene and protein sequences, the rate of addition of new sequences to the databases increased very rapidly.
Product of ringsIn mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the . Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings.
Length of a moduleIn algebra, the length of a module is a generalization of the dimension of a vector space which measures its size. page 153 It is defined to be the length of the longest chain of submodules. The modules of finite length are finitely generated modules, but as opposite to vector spaces, many finitely generated modules have an infinite length. Finitely generated modules of finite length are also called Artinian modules and are at the basis of the theory of Artinian rings. For vector spaces, the length equals the dimension.
Category of ringsIn mathematics, the category of rings, denoted by Ring, is the whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is , meaning that the class of all rings is proper. The category Ring is a meaning that the objects are sets with additional structure (addition and multiplication) and the morphisms are functions that preserve this structure.
Rings of SaturnThe rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entirely of water ice, with a trace component of rocky material. There is still no consensus as to their mechanism of formation. Although theoretical models indicated that the rings were likely to have formed early in the Solar System's history, newer data from Cassini suggested they formed relatively late.
Philosophical presentismPhilosophical presentism is the view that only present entities exist (or, equivalently, that everything is present). According to presentism, there are no past or future entities. In a sense, the past and the future do not exist for presentists—past events have happened (have existed) and future events will happen (will exist), but neither exist at all since they do not exist now.
