Natural logarithmThe natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.
Nonelementary integralIn mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field operations). A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives.
DysprosiumDysprosium is the chemical element with the symbol Dy and atomic number 66. It is a rare-earth element in the lanthanide series with a metallic silver luster. Dysprosium is never found in nature as a free element, though, like other lanthanides, it is found in various minerals, such as xenotime. Naturally occurring dysprosium is composed of seven isotopes, the most abundant of which is 164Dy. Dysprosium was first identified in 1886 by Paul Émile Lecoq de Boisbaudran, but it was not isolated in pure form until the development of ion-exchange techniques in the 1950s.
Closed-form expressionIn mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, −, ×, ÷, and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions . However, the set of basic functions depends on the context.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Transcription (biology)Transcription is the process of copying a segment of DNA into RNA. The segments of DNA transcribed into RNA molecules that can encode proteins are said to produce messenger RNA (mRNA). Other segments of DNA are copied into RNA molecules called non-coding RNAs (ncRNAs). mRNA comprises only 1–3% of total RNA samples. Less than 2% of the human genome can be transcribed into mRNA (Human genome#Coding vs. noncoding DNA), while at least 80% of mammalian genomic DNA can be actively transcribed (in one or more types of cells), with the majority of this 80% considered to be ncRNA.
.comThe domain com is a top-level domain (TLD) in the Domain Name System (DNS) of the Internet. Created in the first group of Internet domains at the beginning of 1985, its name is derived from the word commercial, indicating its original intended purpose for subdomains registered by commercial organizations. Later, the domain opened for general purposes. The domain was originally administered by the United States Department of Defense, but is today operated by Verisign, and remains under ultimate jurisdiction of U.
Elimination reactionAn elimination reaction is a type of organic reaction in which two substituents are removed from a molecule in either a one- or two-step mechanism. The one-step mechanism is known as the E2 reaction, and the two-step mechanism is known as the E1 reaction. The numbers refer not to the number of steps in the mechanism, but rather to the kinetics of the reaction: E2 is bimolecular (second-order) while E1 is unimolecular (first-order). In cases where the molecule is able to stabilize an anion but possesses a poor leaving group, a third type of reaction, E1CB, exists.
