| Tropical apricot | |
|---|---|
Scientific classification  | |
| Kingdom: | Plantae |
| Clade: | Tracheophytes |
| Clade: | Angiosperms |
| Clade: | Eudicots |
| Clade: | Rosids |
| Order: | Malpighiales |
| Family: | Salicaceae |
| Tribe: | Saliceae |
| Genus: | Dovyalis |
| Species: | |
The tropical apricot or ketcot is a hybrid thorny shrub cultivated for its fruit. It arose naturally in Florida, and in 1953 selected plants were propagated. [1]
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable is denoted or , with the two notations used interchangeably. It is called exponential because its argument can be seen as an exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent although being of very different nature.
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.
In physics, the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors, dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix.
The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann.
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or and is measured in W·m−1·K−1.
The molar gas constant is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return. The equation and model are named after economists Fischer Black and Myron Scholes. Robert C. Merton, who first wrote an academic paper on the subject, is sometimes also credited.
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relative to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis. It plays the same role in rotational motion as mass does in linear motion. A body's moment of inertia about a particular axis depends both on the mass and its distribution relative to the axis, increasing with mass & distance from the axis.
Some Buddhist terms and concepts lack direct translations into English that cover the breadth of the original term. Below are given a number of important Buddhist terms, short definitions, and the languages in which they appear. In this list, an attempt has been made to organize terms by their original form and give translations and synonyms in other languages along with the definition.
In mathematics, the exterior algebra or Grassmann algebra of a vector space is an associative algebra that contains which has a product, called exterior product or wedge product and denoted with , such that for every vector in The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol and the fact that the product of two elements of is "outside"
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where:
In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions of one substrate and one product. It takes the form of a differential equation describing the reaction rate to , the concentration of the substrate A. Its formula is given by the Michaelis–Menten equation:
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system.
In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation. More precisely, an eigenvector, , of a linear transformation, , is scaled by a constant factor, , when the linear transformation is applied to it: . The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor .
Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier might affect the rate.
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. It can also be used for the number of events in other types of intervals than time, and in dimension greater than 1.
A transformer is a deep learning architecture that was developed by researchers at Google and is based on the multi-head attention mechanism, which was proposed in the 2017 paper "Attention Is All You Need". Text is converted to numerical representations called tokens, and each token is converted into a vector via lookup from a word embedding table. At each layer, each token is then contextualized within the scope of the context window with other (unmasked) tokens via a parallel multi-head attention mechanism, allowing the signal for key tokens to be amplified and less important tokens to be diminished.
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