Meshfree methodsIn the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.
Galerkin methodIn mathematics, in the area of numerical analysis, Galerkin methods are named after the Soviet mathematician Boris Galerkin. They convert a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.
Restriction enzymeA restriction enzyme, restriction endonuclease, REase, ENase or restrictase is an enzyme that cleaves DNA into fragments at or near specific recognition sites within molecules known as restriction sites. Restriction enzymes are one class of the broader endonuclease group of enzymes. Restriction enzymes are commonly classified into five types, which differ in their structure and whether they cut their DNA substrate at their recognition site, or if the recognition and cleavage sites are separate from one another.
Restriction digestA restriction digest is a procedure used in molecular biology to prepare DNA for analysis or other processing. It is sometimes termed DNA fragmentation, though this term is used for other procedures as well. In a restriction digest, DNA molecules are cleaved at specific restriction sites of 4-12 nucleotides in length by use of restriction enzymes which recognize these sequences. The resulting digested DNA is very often selectively amplified using polymerase chain reaction (PCR), making it more suitable for analytical techniques such as agarose gel electrophoresis, and chromatography.
Restriction siteRestriction sites, or restriction recognition sites, are located on a DNA molecule containing specific (4-8 base pairs in length) sequences of nucleotides, which are recognized by restriction enzymes. These are generally palindromic sequences (because restriction enzymes usually bind as homodimers), and a particular restriction enzyme may cut the sequence between two nucleotides within its recognition site, or somewhere nearby. For example, the common restriction enzyme EcoRI recognizes the palindromic sequence GAATTC and cuts between the G and the A on both the top and bottom strands.
Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
Σ-compact spaceIn mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces. A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact. That terminology can be somewhat confusing as it does not fit the usual pattern of σ-(property) meaning a countable union of spaces satisfying (property); that's why such spaces are more commonly referred to explicitly as σ-compact (weakly) locally compact, which is also equivalent to being exhaustible by compact sets.
Countably compact spaceIn mathematics a topological space is called countably compact if every countable open cover has a finite subcover. A topological space X is called countably compact if it satisfies any of the following equivalent conditions: (1) Every countable open cover of X has a finite subcover. (2) Every infinite set A in X has an ω-accumulation point in X. (3) Every sequence in X has an accumulation point in X. (4) Every countable family of closed subsets of X with an empty intersection has a finite subfamily with an empty intersection.
Locally compact spaceIn topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; they are abbreviated as LCH spaces. Let X be a topological space. Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.
