Cis–trans isomerismCis–trans isomerism, also known as geometric isomerism or configurational isomerism, is a term used in chemistry that concerns the spatial arrangement of atoms within molecules. The prefixes "cis" and "trans" are from Latin: "this side of" and "the other side of", respectively. In the context of chemistry, cis indicates that the functional groups (substituents) are on the same side of some plane, while trans conveys that they are on opposing (transverse) sides.
Coupling reactionIn organic chemistry, a coupling reaction is a type of reaction in which two reactant molecules are bonded together. Such reactions often require the aid of a metal catalyst. In one important reaction type, a main group organometallic compound of the type R-M (where R = organic group, M = main group centre metal atom) reacts with an organic halide of the type R'-X with formation of a new carbon-carbon bond in the product R-R'. The most common type of coupling reaction is the cross coupling reaction. Richard F.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Cross-coupling reactionIn organic chemistry, a cross-coupling reaction is a reaction where two different fragments are joined. Cross-couplings are a subset of the more general coupling reactions. Often cross-coupling reactions require metal catalysts. One important reaction type is this: (R, R' = organic fragments, usually aryle; M = main group center such as Li or MgX; X = halide) These reactions are used to form carbon–carbon bonds but also carbon-heteroatom bonds. Cross-coupling reaction are a subset of coupling reactions.
Hiyama couplingThe Hiyama coupling is a palladium-catalyzed cross-coupling reaction of organosilanes with organic halides used in organic chemistry to form carbon–carbon bonds (C-C bonds). This reaction was discovered in 1988 by Tamejiro Hiyama and Yasuo Hatanaka as a method to form carbon-carbon bonds synthetically with chemo- and regioselectivity. The Hiyama coupling has been applied to the synthesis of various natural products.
Kumada couplingIn organic chemistry, the Kumada coupling is a type of cross coupling reaction, useful for generating carbon–carbon bonds by the reaction of a Grignard reagent and an organic halide. The procedure uses transition metal catalysts, typically nickel or palladium, to couple a combination of two alkyl, aryl or vinyl groups. The groups of Robert Corriu and Makoto Kumada reported the reaction independently in 1972. The reaction is notable for being among the first reported catalytic cross-coupling methods.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Structural isomerIn chemistry, a structural isomer (or constitutional isomer in the IUPAC nomenclature) of a compound is another compound whose molecule has the same number of atoms of each element, but with logically distinct bonds between them. The term metamer was formerly used for the same concept. For example, butanol , methyl propyl ether , and diethyl ether have the same molecular formula but are three distinct structural isomers. The concept applies also to polyatomic ions with the same total charge.
IsomerIn chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism refers to the existence or possibility of isomers. Isomers do not necessarily share similar chemical or physical properties. Two main forms of isomerism are structural or constitutional isomerism, in which bonds between the atoms differ; and stereoisomerism or spatial isomerism, in which the bonds are the same but the relative positions of the atoms differ.
StereoisomerismIn stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, but the bond connections or their order differs. By definition, molecules that are stereoisomers of each other represent the same structural isomer.
SignalIn signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.
Newton's methodIn numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then is a better approximation of the root than x0.
Decomposition of spectrum (functional analysis)The spectrum of a linear operator that operates on a Banach space is a fundamental concept of functional analysis. The spectrum consists of all scalars such that the operator does not have a bounded inverse on . The spectrum has a standard decomposition into three parts: a point spectrum, consisting of the eigenvalues of ; a continuous spectrum, consisting of the scalars that are not eigenvalues but make the range of a proper dense subset of the space; a residual spectrum, consisting of all other scalars in the spectrum.
Applied scienceApplied science is the use of the scientific method and knowledge obtained via conclusions from the method to attain practical goals. It includes a broad range of disciplines such as engineering and medicine. Applied science is often contrasted with basic science, which is focused on advancing scientific theories and laws that explain and predict natural or other phenomena. Applied science can also apply formal science, such as statistics and probability theory, as in epidemiology.
Passive managementPassive management (also called passive investing) is an investing strategy that tracks a market-weighted index or portfolio. Passive management is most common on the equity market, where index funds track a stock market index, but it is becoming more common in other investment types, including bonds, commodities and hedge funds. The most popular method is to mimic the performance of an externally specified index by buying an index fund.
Spectrum (functional analysis)In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator if either has no set-theoretic inverse; or the set-theoretic inverse is either unbounded or defined on a non-dense subset. Here, is the identity operator. By the closed graph theorem, is in the spectrum if and only if the bounded operator is non-bijective on .
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
Applied physicsApplied physics is the application of physics to solve scientific or engineering problems. It is usually considered a bridge or a connection between physics and engineering. "Applied" is distinguished from "pure" by a subtle combination of factors, such as the motivation and attitude of researchers and the nature of the relationship to the technology or science that may be affected by the work.
