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  • Pi (mathematical constant)/Proofs/Student level proof that 22 over 7 exceeds π
    We work out the following integral: The latter integral is easily evaluated by making the substitution
    1 KB (220 words) - 15:08, 8 December 2009
  • Normalisation (ring theory)/Definition
    The integral closure of a ring in its field of fractions.
    93 bytes (14 words) - 13:30, 2 January 2009
  • Ion pump/Definition
    General class of integral membrane proteins that transport ions across a membrane against an electroc
    188 bytes (22 words) - 16:50, 14 May 2010
  • Boson/Definition
    elementary particle with integral spin; composite system consisting of an even number of [[Matter#Fermion_def
    164 bytes (21 words) - 11:56, 18 January 2011
  • Science and Health with Key to the Scriptures/Definition
    ...en by [[Mary Baker Eddy]] which, together with the Christian [[Bible]], is integral to Christian Science worship and practice.
    138 bytes (21 words) - 09:56, 25 March 2021
  • Heavy Brigade Combat Team/Definition
    ...de Combat Team with tanks, armored fighting vehicles for its infantry, and integral self-propelled [[M109 howitzer]]s; most powerful but hardest to deploy
    209 bytes (29 words) - 10:33, 22 May 2024
  • Integral domain
    In [[ring theory]], an '''integral domain''' is a [[commutativity|commutative]] [[ring (mathematics)|ring]] in * A commutative ring is an integral domain if and only if the zero [[ideal]] is [[prime ideal|prime]].
    1,021 bytes (145 words) - 15:11, 30 October 2008
  • Integral Fast Reactor/Bibliography
    ...cecouncil.com/pdfs/PlentifulEnergy.pdf ''PLENTIFUL ENERGY The Story of the Integral Fast Reactor''], Charles Till and Yoon Il Chang, 2011.<br>
    311 bytes (47 words) - 02:42, 7 April 2024
  • Ampere's law/Definition
    The integral of a magnetic field over a closed path is equal to the conduction current t
    163 bytes (26 words) - 08:19, 20 June 2008
  • Matthew Dallman
    ...plores ideas within the realm of [[art]]. These include [[Integral thought|integral]] as "a living tradition of imaginative fullness through the ages", art as ...a director of [[Integral University]]'s Integral Art Center. His paper "An Integral Art Manifesto" was one of eleven used in the IU's first course ever offered
    2 KB (370 words) - 11:46, 2 February 2023
  • Gauss' law (electrostatics)/Definition
    Relates the surface integral of the electric displacement through a closed surface to the electric char
    176 bytes (24 words) - 08:37, 20 June 2008
  • Green's function/Definition
    Auxiliary function in the theory of linear differential equations; integral operator with Green function as kernel is the inverse of a linear different
    200 bytes (27 words) - 09:44, 9 January 2009
  • Word game/Definition
    ...words, letters, sentences or other parts of a language as the basis or an integral part of the game, such as [[Scrabble]].
    175 bytes (29 words) - 10:09, 3 November 2011
  • Electric charge/Definition
    A positive or negative property of matter that occurs as integral multiples of an elementary charge unit, and causes mutual repulsion of like
    250 bytes (34 words) - 14:08, 22 August 2011
  • Closure (disambiguation)
    {{rpl|Integral closure}}
    151 bytes (17 words) - 05:13, 26 September 2013
  • Convolution (mathematics)
    Convolution of real functions by means of an integral are found in [[probability]], [[signal processing]] and [[control theory]]. ==Integral convolutions==
    2 KB (338 words) - 17:41, 23 December 2008
  • Calculus (disambiguation)
    ** [[Integral calculus]]
    478 bytes (48 words) - 09:33, 31 December 2008
  • Pi (mathematical constant)/Proofs/An elementary proof that 22 over 7 exceeds π
    Evaluation of this [[integral]] requires only routine first-year calculus techniques, see [[Pi_(mathemati The problem of showing that this integral evaluates to 22/7&nbsp;&minus;&nbsp;&pi;, perhaps despite its elementary na
    2 KB (219 words) - 15:08, 8 December 2009
  • Shaker gene/Definition
    ...e which plays a part in the operation of potassium ion channels, which are integral membrane proteins and are essential to the correct functioning of the cell,
    293 bytes (44 words) - 08:44, 6 September 2009
  • Arithmetic
    ...n, multiplication, division, raising to integral powers, and extraction of integral roots. The term is derived from the Greek word άριθμητικη (arithm ...gral numbers is augmented with the [[rational number]]s (quotients of two integral numbers).
    4 KB (562 words) - 18:28, 5 January 2010
  • Integral cryptanalysis
    ...nputs that differ in only one bit position, with all other bits identical. Integral analysis, for block size b, holds b-k bits constant and runs the other k th
    1 KB (171 words) - 05:48, 8 April 2024
  • Computer algebra system
    *some [[antidifferentiation|indefinite]] and [[integral|definite integration]] *integral transforms
    1 KB (164 words) - 14:01, 18 January 2008
  • Michael Ostrolenk/Definition
    ...erty Coalition]], Vice President of [[HSLEADER]]; a founding member of the Integral Institute (promoting new approaches to personal and professional relationsh
    391 bytes (47 words) - 22:52, 9 January 2010
  • F4ten.cin
    ...[[C++]] routine for evaluation of [[tetration]] to base 10 by the [[Cauchi integral]], using its values along the imaginary axis stored at [[f2048ten.inc]] (th // The integral is evaluated using the [[Gauss-Legendre]] quadrature formula; the nodes and
    2 KB (300 words) - 11:24, 2 March 2013
  • Gauss' law (magnetism)
    ...gnetic charges) do not exist. More technically, Gauss' law states that the integral vanishes of the [[magnetic induction]] '''B''' over any closed surface. Ex ...es a [[dot product]] between the vectors '''B''' and d'''S'''. The double integral is over a closed surface that may envelop one or more permanent magnets a
    3 KB (415 words) - 13:04, 29 March 2009
  • Measure theory
    ...ns converging to the function to be integrated, for details see [[Lebesque integral]]. As with almost everything in mathematics, these basic ideas were subsequ [[Lebesque integral]]
    4 KB (604 words) - 05:50, 12 May 2008
  • Magnetic flux
    ...B''' times the area of ''S''. If '''B''' varies across ''S'', &Phi; is the integral The integrand (expression under the integral) is an [[inner product]] of the vector '''B''' and the vector d'''S'''. The
    1 KB (217 words) - 05:55, 11 July 2008
  • Legendre-Gauss Quadrature formula/Definition
    the specific approximation of the integral with the sum of N terms, which becomes exact for the polynomial integrand o
    574 bytes (85 words) - 19:43, 30 January 2009
  • Monogenic field/Bibliography
    ...| first = István | authorlink = | title = Diophantine Equations and Power Integral Bases | publisher = [[Birkhäuser Verlag]] | date = 2002 | location = Bosto
    517 bytes (60 words) - 12:48, 3 January 2013
  • Fermion
    In physics, a '''fermion''' is a particle with half-integral spin, i.e., an odd multiple of one-half. Examples include the electron, the
    468 bytes (72 words) - 20:43, 12 November 2020
  • Kernel (mathematics)
    * A function determining an integral transform, such as a [[Green's function]]
    387 bytes (58 words) - 09:26, 30 September 2009
  • Parable of the two watchmakers
    The concept of the [[holon]] is also central to the theory of [[Integral Consciousness]] developed by [[Ken Wilber]]. <ref>Wilber, K. (1995). ''Sex, [[Category:Integral theory Catalogs]]
    2 KB (263 words) - 18:45, 22 September 2008
  • Special function/Catalogs/Catalog
    ==Exponential integral related== |[[Exponential integral]]
    8 KB (1,184 words) - 14:58, 8 December 2009
  • Dedekind domain
    ...K</math> is a finite extension of <math>K</math> and <math>O</math> is the integral closure of <math>o</math> in <math>L</math>, then <math>O</math> is again a
    2 KB (306 words) - 15:51, 10 December 2008
  • Scheme (mathematics)/Catalogs
    #Integral scheme
    399 bytes (49 words) - 10:23, 15 September 2009
  • Ito process
    ...Japanese mathematician Kiyoshi Ito, which can be written as the sum of the integral of a process over time and of another process over a [[Brownian Motion]].<b Those processes are the base of [[Stochastic Integral|Stochastic Integration]], and are therefore widely used in [[Financial Math
    5 KB (858 words) - 12:47, 29 December 2008
  • Ampere (disambiguation)
    * [[Ampere's law]] Integral relation between magnetic field and current (forerunner of Maxwell equation
    530 bytes (70 words) - 12:42, 31 May 2009
  • Signifier/Related Articles
    {{r|Integral theory}}
    430 bytes (55 words) - 20:23, 11 January 2010
  • Customer service
    ...s|publisher=Oxford University Press|accessdate=22 April 2014}}</ref> It is integral to a good business as good customer service will ensure that the customer r
    644 bytes (89 words) - 23:27, 21 April 2014
  • Differential equation/Related Articles
    {{r|Integral equation}}
    659 bytes (72 words) - 10:05, 12 June 2009
  • Howard Gardner/Related Articles
    {{r|Integral theory}}
    452 bytes (59 words) - 17:17, 11 January 2010
  • Helmholtz decomposition
    ...onent. This will now be proved directly, without making the detour via the integral expressions for '''A'''('''r''') and &Phi;('''r'''). ==Integral expressions for the transverse and longitudinal components ==
    11 KB (1,756 words) - 14:38, 12 April 2009
  • Calculus
    ...divided into two major branches: '''[[differential calculus]]''' and '''[[integral calculus]]''', concerned with the study of the derivatives and integrals of ...cs. The motivation for the derivative is rather different from that of the integral, yet it turns out that they are very closely related.
    5 KB (912 words) - 09:26, 29 May 2009
  • Derivative/Related Articles
    {{r|Integral}}
    572 bytes (72 words) - 02:47, 8 November 2008
  • Integral closure/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Integral closure]]. Needs checking by a human.
    497 bytes (63 words) - 17:28, 11 January 2010
  • Rectangle/Related Articles
    {{r|Integral}}
    548 bytes (69 words) - 19:56, 11 January 2010
  • Divergence theorem
    ...ard flux of a vector field through a closed surface is equal to the triple integral of the [[divergence]] of the vector field inside the surface. ...orem is that several physical laws can be written in both differential and integral form, see, for instance, [[Gauss' law (electrostatics)|Gauss' law]] for an
    4 KB (639 words) - 10:31, 19 June 2009
  • Lambert W function/Related Articles
    {{r|Integral}}
    522 bytes (67 words) - 17:58, 11 January 2010
  • APP/Function
    ...rch_constraint=terms&depth=0&query=GO:0016021 {{#if: integral to membrane |integral to membrane|GO:0016021 }}]</span><br> ...straint=terms&depth=0&query=GO:0005887 {{#if: integral to plasma membrane |integral to plasma membrane|GO:0005887 }}]</span><br>
    11 KB (1,519 words) - 11:17, 11 May 2009
  • Cystine
    Such disulfide bonds are integral to the structural stability of many proteins.
    632 bytes (96 words) - 07:51, 8 June 2009
  • Divisor (ring theory)/Related Articles
    {{r|Integral domain}}
    516 bytes (65 words) - 16:01, 11 January 2010
  • Bessel functions
    ===Integral representations===
    3 KB (459 words) - 07:58, 13 July 2012
  • Localisation (ring theory)
    ...ns''' of ''R''. A ring can be embedded in a field if and only if it is an integral domain.
    2 KB (312 words) - 09:18, 21 October 2009
  • Sigma algebra
    ...) integration]] can be developed which is much more general than [[Riemann integral|Riemann integration]].
    2 KB (314 words) - 16:35, 27 November 2008
  • Fourier transform
    A '''Fourier transform''' is an integral transform,<ref>To transform is to change the form of a figure, expression, ...math> has been transformed into <math>\scriptstyle F</math> with the above integral.
    3 KB (547 words) - 07:21, 24 December 2008
  • Ken Wilber
    ...er and thinker whose primary focus is the development and exposition of an integral theory of consciousness. His first book, ''[[The Spectrum of Consciousness ...is a consequence of the meta-disciplinary and meta-theoretical nature of [[Integral Theory]], which the highly specialized orientation of academic journals and
    3 KB (420 words) - 18:16, 26 February 2010
  • Pi (mathematical constant)/Proofs/Proof that π is irrational
    ...century, proofs were found that require no prerequisite knowledge beyond [[integral calculus]]. One of those is due to [[Ivan Niven]], another to [[Mary Cartw is a positive integer. But by the inequality (*), the integral approaches 0 as ''n'' approaches infinity, and that is impossible for a seq
    2 KB (325 words) - 06:31, 15 September 2009
  • Jacobian/Related Articles
    {{r|Integral}}
    629 bytes (80 words) - 17:36, 11 January 2010
  • Square (cipher)
    [[Lars Knudsen]] invented a new attack, called [[integral cryptanalysis]] or the '''square attack''', to break Square. It was publish
    659 bytes (101 words) - 05:48, 8 April 2024
  • Equation (mathematics)/Related Articles
    {{R|Integral equation}}
    572 bytes (67 words) - 07:18, 2 October 2008
  • Green's Theorem
    ...l around a simple closed curve <math>\partial\Omega</math> with the double integral over the plane region <math>\Omega\,</math>. This formula gives a relationship between the area of a region and the line integral around its boundary.
    3 KB (549 words) - 20:34, 19 February 2009
  • Elementary function/Related Articles
    {{r|Integral}}
    682 bytes (88 words) - 10:48, 4 October 2013
  • Gamma function/Related Articles
    {{r|Integral}}
    684 bytes (86 words) - 16:46, 11 January 2010
  • Special function
    ...ction is defined as a solution of a simple [[differential equation]] or an integral of an [[elementary function]], or an [[inverse function]] of some [[element
    716 bytes (101 words) - 16:51, 8 December 2009
  • Integral/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Integral]]. Needs checking by a human.
    763 bytes (99 words) - 17:28, 11 January 2010
  • Integral domain/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Integral domain]]. Needs checking by a human.
    675 bytes (89 words) - 17:28, 11 January 2010
  • Holomorphic function/Proofs
    The argument, first given by Cauchy, hinges on [[Cauchy's integral formula]] and the power series development of the expression ...at open disk but farther from ''a'' than ''z'' is. Starting with Cauchy's integral formula, we have
    4 KB (730 words) - 15:17, 8 December 2009
  • Complex analysis/Related Articles
    {{r|Cauchy's integral formula}}
    670 bytes (80 words) - 08:52, 7 August 2008
  • Polynomial ring/Related Articles
    {{r|Integral domain}}
    770 bytes (96 words) - 19:39, 11 January 2010
  • Simeon Denis Poisson
    ...pril 25, 1840) was a French mathematician known for his work on [[definite integral]]s, [[electromagnetism | electromagnetic theory]] and [[probability theory] [[Poisson's integral]], [[Poisson's equation]] in [[potential theory ]], [[Poisson's brackets]]
    2 KB (317 words) - 11:12, 5 October 2009
  • Enthalpy/Related Articles
    {{r|Integral}}
    856 bytes (107 words) - 16:19, 11 January 2010
  • Commutativity/Related Articles
    {{r|Integral domain}}
    858 bytes (112 words) - 15:35, 11 January 2010
  • Heaviside step function
    ...tion ''f''(''x'') that vanishes for plus/minus infinity, the result of the integral is minus the function value for ''x'' = 0, ...hy principal value of the integral, i.e., exclude the singularity from the integral; we make the replacement
    5 KB (796 words) - 13:09, 24 December 2008
  • Limit (mathematics)/Related Articles
    {{r|Integral}}
    774 bytes (100 words) - 18:05, 11 January 2010
  • Curl
    ...integrand of the integral on the left-hand side may be taken constant, the integral becomes ...is a unit vector perpendicular to &Delta;''S''. The right-hand side is an integral over a small contour, say a small circle, and in total the curl may be writ
    7 KB (1,067 words) - 07:27, 23 October 2021
  • Integral
    ...on which is varying as the rocket's mass decreases from fuel usage, and an integral can take this complication into account. Finally, within calculus ''integra ...um of their individual areas. This is the basic meaning of integration: an integral is simply a sum of smaller parts that together add up to the whole.
    13 KB (2,303 words) - 16:28, 23 January 2011
  • Well-posed problem
    [[integral equation|integral]] and [[functional equation|functional]] equations.
    3 KB (414 words) - 19:32, 16 March 2010
  • Green's function
    The integral operator that has the Green function as kernel may be seen as the inverse o ...'x''''', ''j'' &harr; '''''y''''', and compare the sum over ''j'' with the integral over '''''y''''', and the correspondence is evident.
    10 KB (1,681 words) - 12:22, 11 June 2009
  • Black-body radiation
    ...itance]] of an ideal black body. The study of black-body radiation was an integral step in the formulation of quantum mechanics. ...]] equation. In general, there is no closed-form solution for the definite integral of the Planck blackbody equation; numerical integration techniques must be
    4 KB (537 words) - 09:19, 11 September 2022
  • Entire function
    ...ral]]s of entire functions, for example the [[error function]] erf, [[sine integral]] Si and the [[Bessel function]] ''J''<sub>0</sub> are also entire function ===Cauchy integral===
    6 KB (827 words) - 14:44, 19 December 2008
  • Legendre-Gauss Quadrature formula
    ...formula''' or '''Gauss-Legendre quadrature''' is the approximation of the integral ...decimal logarithm]] of the modulus of the residual of the appdoximation of integral with Gaussian quadrature is shown versus number of terms in the sum, for fo
    4 KB (630 words) - 12:32, 11 June 2009
  • Calculus/Related Articles
    {{r|Integral}}
    1 KB (136 words) - 11:36, 11 January 2010
  • Algebraic number field/Related Articles
    {{r|Integral closure}}
    843 bytes (113 words) - 10:49, 11 January 2010
  • Local ring
    ...lisation (ring theory)|localisation]] of a [[commutativity|commutative]] [[integral domain]] at a non-zero [[prime ideal]] is a local ring.
    844 bytes (130 words) - 12:09, 2 January 2009
  • Equation (mathematics)
    ==[[Differential equation]]s and [[integral equation]]s== In these cases, the equation is called a [[differential equation]] or an [[integral equation]].
    6 KB (951 words) - 05:01, 8 December 2009
  • Gauss' law (electrostatics)
    ...ically in [[electrostatics]], Gauss' law is a theorem concerning a surface integral of an [[electric field]] '''E'''. In [[Vacuum (science)|vacuum]] Gauss' law ...e distribution. If the closed surface does not envelop any charge then the integral is zero. The constant &epsilon;<sub>0</sub> is the [[electric constant]].
    6 KB (988 words) - 17:21, 2 November 2021
  • Namghar
    ...the religious values and culture of the Assamese people, and has become an integral part of the Assamese Hindu community.
    1 KB (164 words) - 07:03, 14 September 2013
  • I.G. Farben
    ...German synthetic dye companies a major WWII industrial conglomerate was an integral part of Nazi war production. Executives, 24 of which were indicted in the [
    1 KB (160 words) - 09:02, 4 May 2024
  • Rational number/Related Articles
    {{r|Integral domain}}
    1 KB (169 words) - 19:54, 11 January 2010
  • Ring (mathematics)/Related Articles
    {{r|Integral domain}}
    1 KB (174 words) - 20:03, 11 January 2010
  • Maps of tetration
    [[Cauchi integral]] is used for evaluation. It is described in [[Mathematics of Computation]] The evaluation uses almost the same algorithm of the Cauchi integral <ref name=analuxp>
    6 KB (929 words) - 05:34, 2 September 2014
  • Schrödinger equation/Bibliography
    ...exts and provides an introduction to other approaches, like [[Feynman path integral]]s.
    2 KB (197 words) - 09:40, 28 March 2011
  • Augustin-Louis Cauchy/Related Articles
    {{r|Cauchy's integral formula}}
    1 KB (162 words) - 07:35, 9 January 2011
  • Ion pump
    '''Ion pumps''' are a "general class of integral membrane proteins that transport ions across a membrane against an electroc
    956 bytes (129 words) - 23:02, 18 June 2008
  • Norbert Wiener
    -Wiener, Norbert. (1989) Fourier Integral and Certain of Its Applications
    1 KB (153 words) - 04:43, 24 February 2009
  • Natrium reactor
    ...as the fuel and molten sodium as the coolant.<ref name=NatriumSite/> See [[Integral Fast Reactor]] for more discussion of the technology behind this design. ''PLENTIFUL ENERGY The Story of the Integral Fast Reactor'', CHARLES E. TILL and YOON IL CHANG, 2011.
    3 KB (532 words) - 14:13, 12 November 2023
  • Stokes' theorem
    is a vector normal to the surface element d''S'', the contour integral is over a closed, non-intersecting path ''C'' bounding the open, two-sided
    1 KB (176 words) - 10:16, 19 July 2008
  • Tetration/Bibliography
    M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and M.H.Hooshmand. ”Ultra power and ultra exponential functions”. [[Integral Transforms and Special Functions]] <b>17</b> (8), 549-558 (2006)
    5 KB (668 words) - 21:17, 2 November 2013
  • Finite and infinite
    finite [[interval]], finite value, finite [[integral]],
    1 KB (191 words) - 17:30, 15 July 2009
  • Superfunction/Bibliography
    |journal=Integral Transforms and Special Functions M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and
    4 KB (444 words) - 02:34, 14 August 2009
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