Harmonic series (music)A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves.
Quasi-arithmetic meanIn mathematics and statistics, the quasi-arithmetic mean or generalised f-mean or Kolmogorov-Nagumo-de Finetti mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function . It is also called Kolmogorov mean after Soviet mathematician Andrey Kolmogorov. It is a broader generalization than the regular generalized mean. If f is a function which maps an interval of the real line to the real numbers, and is both continuous and injective, the f-mean of numbers is defined as , which can also be written We require f to be injective in order for the inverse function to exist.
ThyroidThe thyroid, or thyroid gland, is an endocrine gland in vertebrates. In humans, it is in the neck and consists of two connected lobes. The lower two thirds of the lobes are connected by a thin band of tissue called the isthmus (: isthmi). The thyroid gland is a butterfly-shaped gland located in the neck below the Adam's apple. Microscopically, the functional unit of the thyroid gland is the spherical thyroid follicle, lined with follicular cells (thyrocytes), and occasional parafollicular cells that surround a lumen containing colloid.
Dirichlet distributionIn probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted , is a family of continuous multivariate probability distributions parameterized by a vector of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.
Fermat's Last TheoremIn number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. Fermat added that he had a proof that was too large to fit in the margin.
Gödel's incompleteness theoremsGödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.
Differential operatorIn mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative.
IP addressAn Internet Protocol address (IP address) is a numerical label such as 192.0.2.1 that is connected to a computer network that uses the Internet Protocol for communication. An IP address serves two main functions: network interface identification, and location addressing. Internet Protocol version 4 (IPv4) defines an IP address as a 32-bit number. However, because of the growth of the Internet and the depletion of available IPv4 addresses, a new version of IP (IPv6), using 128 bits for the IP address, was standardized in 1998.
Regional Internet registryA regional Internet registry (RIR) is an organization that manages the allocation and registration of Internet number resources within a region of the world. Internet number resources include IP addresses and autonomous system (AS) numbers. The regional Internet registry system evolved, eventually dividing the responsibility for management to a registry for each of five regions of the world. The regional Internet registries are informally liaised through the unincorporated Number Resource Organization (NRO), which is a coordinating body to act on matters of global importance.
IPv4 address exhaustionIPv4 address exhaustion is the depletion of the pool of unallocated IPv4 addresses. Because the original Internet architecture had fewer than 4.3 billion addresses available, depletion has been anticipated since the late 1980s, when the Internet started experiencing dramatic growth. This depletion is one of the reasons for the development and deployment of its successor protocol, IPv6. IPv4 and IPv6 coexist on the Internet.
Thyroid hormonesFile:Thyroid_system.svg|thumb|upright=1.5|The [[thyroid]] system of the thyroid hormones [[triiodothyronine|T3]] and T4References used in image are found in image article in Commons:[[Commons:File:Thyroid system.png#References]].
Frenet–Serret formulasIn differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space , or the geometric properties of the curve itself irrespective of any motion. More specifically, the formulas describe the derivatives of the so-called tangent, normal, and binormal unit vectors in terms of each other. The formulas are named after the two French mathematicians who independently discovered them: Jean Frédéric Frenet, in his thesis of 1847, and Joseph Alfred Serret, in 1851.
