Singular perturbationIn mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion as . Here is the small parameter of the problem and are a sequence of functions of of increasing order, such as . This is in contrast to regular perturbation problems, for which a uniform approximation of this form can be obtained.
Macron (diacritic)A macron (ˈmækrɒn,_ˈmeɪ-) is a diacritical mark: it is a straight bar placed above a letter, usually a vowel. Its name derives from Ancient Greek μακρόν (makrón) 'long' because it was originally used to mark long or heavy syllables in Greco-Roman metrics. It now more often marks a long vowel. In the International Phonetic Alphabet, the macron is used to indicate a mid-tone; the sign for a long vowel is instead a modified triangular colon ː. The opposite is the breve , which marks a short or light syllable or a short vowel.
Series expansionIn mathematics, a series expansion is a technique that expresses a function as an infinite sum, or series, of simpler functions. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division). The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.
UU, or u, is the twenty-first and sixth-to-last letter and fifth vowel letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages, and others worldwide. Its name in English is u (pronounced 'juː), plural ues. U derives from the Semitic waw, as does F, and later, Y, W, and V. Its oldest ancestor goes to Egyptian hieroglyphics, and is probably from a hieroglyph of a mace or fowl, representing the sound v or the sound w.
Perturbation theory (quantum mechanics)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 (e.g.
Voice onset timeIn phonetics, voice onset time (VOT) is a feature of the production of stop consonants. It is defined as the length of time that passes between the release of a stop consonant and the onset of voicing, the vibration of the vocal folds, or, according to other authors, periodicity. Some authors allow negative values to mark voicing that begins during the period of articulatory closure for the consonant and continues in the release, for those unaspirated voiced stops in which there is no voicing present at the instant of articulatory closure.
Taylor seriesIn mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Aspirated consonantIn phonetics, aspiration is the strong burst of breath that accompanies either the release or, in the case of preaspiration, the closure of some obstruents. In English, aspirated consonants are allophones in complementary distribution with their unaspirated counterparts, but in some other languages, notably most South Asian languages (including Indian ones) and East Asian languages, the difference is contrastive.
Law of noncontradictionIn logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds.
UnicodeUnicode, formally The Unicode Standard, is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic scripts, as well as symbols, thousands of emoji (including in colours), and non-visual control and formatting codes.
