Basis set (chemistry)In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals are expanded within the basis set as a linear combination of the basis functions , where the expansion coefficients are given by .
Lower limit topologyIn mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set of real numbers; it is different from the standard topology on (generated by the open intervals) and has a number of interesting properties. It is the topology generated by the basis of all half-open intervals [a,b), where a and b are real numbers. The resulting topological space is called the Sorgenfrey line after Robert Sorgenfrey or the arrow and is sometimes written .
ScalabilityScalability is the property of a system to handle a growing amount of work. One definition for software systems specifies that this may be done by adding resources to the system. In an economic context, a scalable business model implies that a company can increase sales given increased resources. For example, a package delivery system is scalable because more packages can be delivered by adding more delivery vehicles.
PrototypeA prototype is an early sample, model, or release of a product built to test a concept or process. It is a term used in a variety of contexts, including semantics, design, electronics, and software programming. A prototype is generally used to evaluate a new design to enhance precision by system analysts and users. Prototyping serves to provide specifications for a real, working system rather than a theoretical one. In some design workflow models, creating a prototype (a process sometimes called materialization) is the step between the formalization and the evaluation of an idea.
PleiadesThe Pleiades (ˈpliː.ədiːz,_ˈpleɪ-,_ˈplaɪ-), also known as the Seven Sisters, Messier 45, and other names by different cultures, is an asterism and an open star cluster containing middle-aged, hot B-type stars in the north-west of the constellation Taurus. At a distance of about 444 light years, it is among the nearest star clusters to Earth. It is the nearest Messier object to Earth, and is the most obvious cluster to the naked eye in the night sky. It is also observed to house the reflection nebula NGC 1432, an HII region.
Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883. Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments.
Site-directed mutagenesisSite-directed mutagenesis is a molecular biology method that is used to make specific and intentional mutating changes to the DNA sequence of a gene and any gene products. Also called site-specific mutagenesis or oligonucleotide-directed mutagenesis, it is used for investigating the structure and biological activity of DNA, RNA, and protein molecules, and for protein engineering. Site-directed mutagenesis is one of the most important laboratory techniques for creating DNA libraries by introducing mutations into DNA sequences.
