Function spaceIn mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space. Vector space#Function spaces Let be a vector space over a field and let be any set.
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.
Green's functionIn mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if is the linear differential operator, then the Green's function is the solution of the equation , where is Dirac's delta function; the solution of the initial-value problem is the convolution ().
Gas chromatography–mass spectrometryGas chromatography–mass spectrometry (GC–MS) is an analytical method that combines the features of gas-chromatography and mass spectrometry to identify different substances within a test sample. Applications of GC–MS include drug detection, fire investigation, environmental analysis, explosives investigation, food and flavor analysis, and identification of unknown samples, including that of material samples obtained from planet Mars during probe missions as early as the 1970s.
Letter caseLetter case is the distinction between the letters that are in larger uppercase or capitals (or more formally majuscule) and smaller lowercase (or more formally minuscule) in the written representation of certain languages. The writing systems that distinguish between the upper- and lowercase have two parallel sets of letters: each in the majuscule set has a counterpart in the minuscule set. Some counterpart letters have the same shape, and differ only in size (e.g. {C,c} or {S,s}), but for others the shapes are different (e.
Arabic diacriticsArabic script has numerous diacritics, which include consonant pointing known as ALA (إِعْجَام), and supplementary diacritics known as ALA (تَشْكِيل). The latter include the vowel marks termed ALA (حَرَكَات; singular: حَرَكَة, ALA). The Arabic script is a modified abjad, where short consonants and long vowels are represented by letters but short vowels and consonant length are not generally indicated in writing. ALA is optional to represent missing vowels and consonant length.
Residue theoremIn complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. The residue theorem should not be confused with special cases of the generalized Stokes' theorem; however, the latter can be used as an ingredient of its proof.
ArabicArabic (اَلْعَرَبِيَّةُ, DIN al ʕaraˈbijːa; عَرَبِيّ, DIN ˈʕarabiː or ʕaraˈbij) is a Semitic language spoken primarily across the Arab world. Having emerged in the 1st century, it is named after the Arab people; the term "Arab" was initially used to describe those living in the Arabian Peninsula, as perceived by geographers from ancient Greece. Since the 7th century, Arabic has been characterized by diglossia, with an opposition between a standard prestige language—i.e.
Arabic verbsArabic verbs (فِعْل ALA; () أَفْعَال ALA), like the verbs in other Semitic languages, and the entire vocabulary in those languages, are based on a set of two to five (but usually three) consonants called a root (triliteral or quadriliteral according to the number of consonants). The root communicates the basic meaning of the verb, e.g. ك-ت-ب ALA 'write', ق-ر-ء ALA 'read', ء-ك-ل ALA 'eat'. Changes to the vowels in between the consonants, along with prefixes or suffixes, specify grammatical functions such as person, gender, number, tense, mood, and voice.
Residue (complex analysis)In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.) Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the residue theorem.
AlephAleph (or alef or alif, transliterated ʾ) is the first letter of the Semitic abjads, including Phoenician 𐤀, Hebrew א, Aramaic 𐡀, Syriac ܐ, Arabic ʾ ا, and North Arabian 𐪑. It also appears as South Arabian 𐩱 and Ge'ez አ. These letters are believed to have derived from an Egyptian hieroglyph depicting an ox's head to describe the initial sound of *ʾalp, the West Semitic word for ox (compare Biblical Hebrew ʾelef, "ox"). The Phoenician variant gave rise to the Greek alpha (Α), being re-interpreted to express not the glottal consonant but the accompanying vowel, and hence the Latin A and Cyrillic А.
Camel caseCamel case (sometimes stylized as camelCase or CamelCase, also known as camel caps or more formally as medial capitals) is the practice of writing phrases without spaces or punctuation and with capitalized words. The format indicates the first word starting with either case, then the following words having an initial uppercase letter. Common examples include "YouTube", "iPhone" and "eBay". Camel case is often used as a naming convention in computer programming.
