Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Regeneration (biology)In biology, regeneration is the process of renewal, restoration, and tissue growth that makes genomes, cells, organisms, and ecosystems resilient to natural fluctuations or events that cause disturbance or damage. Every species is capable of regeneration, from bacteria to humans. Regeneration can either be complete where the new tissue is the same as the lost tissue, or incomplete after which the necrotic tissue becomes fibrosis.
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Cell biologyCell biology (also cellular biology or cytology) is a branch of biology that studies the structure, function, and behavior of cells. All living organisms are made of cells. A cell is the basic unit of life that is responsible for the living and functioning of organisms. Cell biology is the study of the structural and functional units of cells. Cell biology encompasses both prokaryotic and eukaryotic cells and has many subtopics which may include the study of cell metabolism, cell communication, cell cycle, biochemistry, and cell composition.
Glossary of genetics (0–L)This glossary of genetics is a list of definitions of terms and concepts commonly used in the study of genetics and related disciplines in biology, including molecular biology, cell biology, and evolutionary biology. It is split across two articles: This page, Glossary of genetics (0–L), lists terms beginning with numbers and those beginning with the letters A through L. Glossary of genetics (M–Z) lists terms beginning with the letters M through Z.
Cellular differentiationCellular differentiation is the process in which a stem cell changes from one type to a differentiated one. Usually, the cell changes to a more specialized type. Differentiation happens multiple times during the development of a multicellular organism as it changes from a simple zygote to a complex system of tissues and cell types. Differentiation continues in adulthood as adult stem cells divide and create fully differentiated daughter cells during tissue repair and during normal cell turnover.
Developmental biologyDevelopmental biology is the study of the process by which animals and plants grow and develop. Developmental biology also encompasses the biology of regeneration, asexual reproduction, metamorphosis, and the growth and differentiation of stem cells in the adult organism. The main processes involved in the embryonic development of animals are: tissue patterning (via regional specification and patterned cell differentiation); tissue growth; and tissue morphogenesis.
Hydra (genus)Hydra (ˈhaɪdrə ) is a genus of small freshwater hydrozoans of the phylum Cnidaria. They are native to the temperate and tropical regions. The genus was named by Linnaeus in 1758 after the Hydra, which was the many-headed beast defeated by Heracles, as when the animal had a part severed, it would regenerate much like the hydra’s heads. Biologists are especially interested in Hydra because of their regenerative ability; they do not appear to die of old age, or to age at all.
PhraseIn grammar, a phrasecalled expression in some contextsis a group of words or singular word acting as a grammatical unit. For instance, the English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". Phrases can consist of a single word or a complete sentence. In theoretical linguistics, phrases are often analyzed as units of syntactic structure such as a constituent. There is a difference between the common use of the term phrase and its technical use in linguistics.
Nerve netA nerve net consists of interconnected neurons lacking a brain or any form of cephalization. While organisms with bilateral body symmetry are normally associated with a condensation of neurons or, in more advanced forms, a central nervous system, organisms with radial symmetry are associated with nerve nets, and are found in members of the Ctenophora, Cnidaria, and Echinodermata phyla, all of which are found in marine environments. In the Xenacoelomorpha, a phylum of bilaterally symmetrical animals, members of the subphylum Xenoturbellida also possess a nerve net.
Verb phraseIn linguistics, a verb phrase (VP) is a syntactic unit composed of a verb and its arguments except the subject of an independent clause or coordinate clause. Thus, in the sentence A fat man quickly put the money into the box, the words quickly put the money into the box constitute a verb phrase; it consists of the verb put and its arguments, but not the subject a fat man. A verb phrase is similar to what is considered a predicate in traditional grammars.
Noun phraseA noun phrase, or nominal (phrase), is a phrase that has a noun or pronoun as its head or performs the same grammatical function as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently occurring phrase type. Noun phrases often function as verb subjects and objects, as predicative expressions and as the complements of prepositions. Noun phrases can be embedded inside each other; for instance, the noun phrase some of his constituents contains the shorter noun phrase his constituents.
Adpositional phraseAn adpositional phrase is a that includes prepositional phrases, postpositional phrases, and circumpositional phrases. Adpositional phrases contain an adposition (preposition, postposition, or circumposition) as head and usually a complement such as a noun phrase. Language syntax treats adpositional phrases as units that act as arguments or adjuncts. Prepositional and postpositional phrases differ by the order of the words used.
Adjective phraseAn adjective phrase (or adjectival phrase) is a phrase whose head is an adjective. Almost any grammar or syntax textbook or dictionary of linguistics terminology defines the adjective phrase in a similar way, e.g. Kesner Bland (1996:499), Crystal (1996:9), Greenbaum (1996:288ff.), Haegeman and Guéron (1999:70f.), Brinton (2000:172f.), Jurafsky and Martin (2000:362). The adjective can initiate the phrase (e.g. fond of steak), conclude the phrase (e.g. very happy), or appear in a medial position (e.g.
Python (programming language)Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library.
