Exponential Technology was a vendor of PowerPC microprocessor s. The company was founded by George Taylor and Jim Blomgren in 1993. The company s plan was to use BiCMOS technology to produce very fast processors for the Apple Computer market. Logic used 3 level ECL circuits single ended for control logic, and differential for datapaths while RAM structures used CMOS. The company was originally named Renaissance Microsystems . Rick Shriner was the CEO . Their chips were manufactured by Hitachi, Ltd. Hitachi . Their product, the Exponential X704 , was advertised to run at 533 MHz, but the first version of the device only ran at about 400 MHz. This lower frequency along with small level one CPU cache caches , produced systems which had good but not stellar performance. This allowed Motorola Apple s traditional processor vendor , to convince the computer maker that Motorola s future roadmap would produce processors with similar performance, hence making it less attractive for Apple to rely on the small startup company for critical technology. Due to Apple s financial problems at the time, Exponential starting marketing the device to Apple Macintosh clone makers such as Power Computing and UMAX . In order to diversify into other markets, a second design team was started under Paul Nixon engineer Paul Nixon in Austin, TX to build a BiCMOS Intel x86 processor. Due to Apple s decision to close off the Macintosh clone market, Exponential ran out of possible customers for their chips. The company closed in 1997, though the Texas design team run by Paul Nixon continued on as EVSX. EVSX changed its name to Intrinsity Intrinsity, Inc. in 2000. ref EVSX Announces Name Change And Technology Focus, http linuxpr.com releases 1885.html Linux PR , May 24, 2000 ref External links http www.cs.utexas.edu users karu papers exponential.html Fast Company article on the company http ieeexplore.ieee.org iel3 4 13972 00641683.pdf?arnumber 641683 JSSC paper on the processor http www.intrinsity.com ... more details
Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. Binary exponential backoff truncated exponential backoff In a variety of computer networks , binary exponential backoff or truncated binary exponential backoff refers to an algorithm used to space out repeated retransmission data networks retransmissions of the same block of data , often as part of network congestion avoidance . Examples are the retransmission of data frame frames in carrier sense multiple access with collision avoidance CSMA CA and carrier sense multiple access with collision detection CSMA CD networks, where this algorithm is part of the Media access control channel access method used to send data on these network. In Ethernet networks, the algorithm is commonly used to schedule retransmissions after collisions. The retransmission is delayed by an amount of time derived from the slot time and the number of attempts to retransmit. After c collisions, a random number of slot times between 0 and 2 sup c sup 1 is chosen. For the first collision, each sender will wait 0 or 1 slot times. After the second collision, the senders will wait anywhere from 0 to 3 slot times Interval mathematics inclusive . After the third collision, the senders will wait anywhere from 0 to 7 slot times inclusive , and so forth. As the number of retransmission attempts increases, the number of possibilities for delay exponential growth increases exponentially . The truncated simply means that after a certain number of increases, the exponentiation .... Citation needed date September 2010 An example of an exponential backoff algorithm This example ... value within an acceptable range to ensure that this situation doesn t happen. An exponential ... also Control theory References Reflist FS1037C Use dmy dates date September 2010 DEFAULTSORT Exponential Backoff Category Networking algorithms Category Ethernet de Binary Exponential Backoff hu Exponenci lis ... more details
Infobox data structure name Exponential tree type tree invented by Arne Andersson invented year 1995 space avg O n log n space worst O n log n search avg O min log n , log n log w , log log n , log w log log n search worst O min log n , log n log w , log log n , log w log log n insert avg O min log n , log n log w , log log n , log w log log n insert worst O min log n , log n log w , log log n , log w log log n delete avg O min log n , log n log w , log log n , log w log log n delete worst O min log n , log n log w , log log n , log w log log n An exponential tree is almost identical to a binary search tree , with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimension d of 1, and has 2 sup d sup children. In an exponential tree, the dimension equals the depth of the node, with the root node having a d 1. So the second level can hold two nodes, the third can hold eight nodes, the fourth 64 nodes, and so on. Layout Exponential Tree can also refer to a method of laying out the nodes of a tree structure in n typically 2 dimensional space. Nodes are placed closer to a baseline than their parent node, by a factor equal to the number of child nodes of that parent node or by some sort of weighting , and scaled according to how close they are. Thus, no matter how deep the tree may be, there is always room for more nodes, and the geometry of a subtree is unrelated to its position in the whole tree. The whole has a fractal structure. In fact, this method of laying out a tree can be viewed as an application of the upper half plane model of hyperbolic ... number3 pxc3873876.pdf Implementation and Performance Analysis of Exponential Tree Sorting CS Trees ... more details
orphan date April 2012 In mathematics , the Carlitz exponential is a characteristic p analogue to the usual exponential function studied in real analysis real and complex analysis . It is used in the definition of the Carlitz module an example of a Drinfel d module . Definition We work over the polynomial ring F sub q sub T of one variable over a finite field F sub q sub with q elements. The Completion metric space completion C sub sub of an algebraic closure of the field F sub q sub T sup &minus 1 sup of formal Laurent series in T sup &minus 1 sup will be needed. It is a complete and algebraically closed field. First we need analogues to the factorials , which appear in the definition of the usual exponential function. For i 0 we define math i T q i T, , math math D i prod 1 le j le i j q i j math and D sub 0 sub 1. Note that that the usual factorial is inappropriate here, since n vanishes in F sub q sub T unless n is smaller than the Characteristic algebra characteristic of F sub q sub T . Using this we define the Carlitz exponential e sub C sub C sub sub C sub sub by the convergent sum math e C x sum j 0 infty frac x q j D i . math Relation to the Carlitz module The Calitz exponential satisfies the functional equation math e C Tx Te C x left e C x right q T tau e C x , , math where we may view as the power of q map or as an element of the ring F sub q sub T of noncommutative polynomials . By the universal property of polynomial rings in one variable this extends to a ringhomomorphism F sub q sub T C sub sub , defining a Drinfel d F sub q sub T module over C sub sub . It is called the Carlitz module. References reflist Citation last1 Goss first1 D. authorlink David Goss title Basic structures of function field arithmetic publisher Springer Verlag location Berlin, New York series Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Results in Mathematics and Related Areas 3 isbn 978 3 540 61087 8 mr 1423131 year 1996 volume 35 Citation ... more details
In combinatorics combinatorial mathematics , the exponential formula called the polymer expansion in physics states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures. The exponential formula is a power series version of a special case of Fa di Bruno s formula . Definition For any formal power series of the form math f x a 1 x a 2 over 2 x 2 a 3 over 6 x 3 cdots a n over n x n cdots , math we have math exp f x e f x sum n 0 infty b n over n x n, , math where math b n sum pi left ,S 1, , dots, ,S k , right a left S 1 right cdots a left S k right , math and the index runs through the list of all partition of a set partitions S sub 1 sub , ..., S sub k sub of the set 1, ..., n . When k 0, the product is Empty product empty and by definition equals 1. One can write the formula in the following form math b n B n a 1,a 2, dots,a n , math and thus math exp left sum n 1 infty a n over n x n right sum n 0 infty B n a 1, dots,a n over n x n, math where B sub n sub a sub 1 sub , ..., a sub n sub is the n th complete Bell polynomial . Examples math b 3 B 3 a 1,a 2,a 3 a 3 3a 2 a 1 a 1 3, math because there is one partition of the set 1, 2, 3 that has a single block of size 3, there are three partitions of 1, 2, 3 that split it into a block of size 2 and a block of size 1, and there is one partition of 1, 2, 3 that splits it into three blocks of size 1. If b sub n sub 2 sup n n &minus 1 2 sup is the number of graphs whose vertices are a given n point set, then a sub n sub is the number of connected graphs whose vertices are a given n point set. There are numerous variations of the previous example where the graph has certain properties for example, if b sub n sub counts graphs without cycles, then a sub n sub counts trees connected grphs without cycles . If b sub n ... by a formal sum over Feynman diagram s. The exponential formula shows that log Z can be given as a sum ... more details
In economics and finance , exponential utility refers to a specific form of the utility function , used in some contexts because of its convenience when risk sometimes referred to as uncertainty is present, in which case Expected utility hypothesis expected utility is maximized. Formally, exponential utility is given by math u c 1 e a c math , where math c math is a variable that the economic decision maker is concerned with, such as consumption, and math a math is a positive constant that represents the degree of risk aversion . The variable c itself will be a function of the agent s choices of for example labor supply , etc., depending on the focus of the model and of Exogenous variable exogenous stochastic process stochastic variables. Note that the additive term 1 in the above function is mathematically irrelevant and is sometimes included only for the aesthetic feature that it keeps the range of the function between zero and one over the domain of non negative values for c . The reason for its irrelevance is that maximizing the expected value of utility math u c 1 e a c math gives the same result for the choice variable as does maximizing the expected value of math u c e a c math ... values are of no significance. The exponential utility function is a special case of the hyperbolic absolute risk aversion utility functions. Risk aversion characteristic Exponential utility implies ... be allocated totally to additional holdings of the risk free asset. This feature explains why the exponential ... as are other utility functions exhibiting decreasing absolute risk aversion , exponential utility is particularly ... . Then under exponential utility, expected utility is given by math text E u c text E 1 e a c x epsilon ... expected exponential utility math text E e aW math of final wealth W subject to math W x r W 0 x ... shows the two key features of exponential utility tractability under joint normality, and lack of realism ... utility Isoelastic power utility function References reflist DEFAULTSORT Exponential Utility Category ... more details
See Lyapunov stability , which gives a definition of asymptotic stability for more general dynamical systems . All exponentially stable systems are also asymptotically stable. In control theory , a continuous LTI system theory linear time invariant system is exponentially stable if and only if the system has eigenvalue s i.e., the pole complex analysis pole s of input to output systems with strictly negative real parts. i.e., in the left half of the complex plane . ref David N. Cheban 2004 , Global Attractors Of Non autonomous Dissipative Dynamical Systems . p. 47 ref A discrete time input to output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. Exponential stability is a form of asymptotic stability . Systems that are not LTI are exponentially stable if their convergence is bounded function bounded by exponential growth exponential decay . Practical consequences An exponentially stable LTI system is one that will not blow up i.e., give an unbounded output when given a finite input or non zero initial condition. Moreover, if the system is given a fixed, finite input i.e., a Heaviside step function step , then any resulting oscillations in the output will decay at an exponential growth exponential rate , and the output will tend asymptote asymptotically to a new final, steady state value. If the system is instead given a Dirac delta function Dirac delta impulse as input, then induced oscillations will die away and the system will return to its previous value. If oscillations do not die away, or the system does not return to its original output when an impulse is applied, the system is instead marginal stability marginally stable . Example exponentially stable LTI systems Image AsymptoticStabilityImpulseScilab.png thumb 320px The impulse responses of two exponentially stable systems The graph on the right shows the impulse response of two similar ... more details
This is a list of exponential topics , by Wikipedia page. See also list of logarithm topics . Accelerating change Artin Hasse exponential Talk Artin Hasse exponential Bacterial growth Talk Bacterial growth ... formula Beer Lambert law Talk Beer Lambert law Characterizations of the exponential function Talk Characterizations of the exponential function Catenary Talk Catenary Compound interest Talk Compound interest De Moivre s formula Talk de Moivre s formula Dol ans Dade exponential Talk Dol ans Dade exponential Elimination half life Talk Elimination half life Error exponent Talk Error exponent Exponential factorial Talk Exponential factorial Euler s formula Talk Euler s formula Euler s identity Talk ... bias Talk Exponent bias Exponential disambiguation Talk ExponentialExponential backoff Talk Exponential backoff Exponential decay Talk Exponential decay Exponential dichotomy Talk Exponential dichotomy Exponential discounting Talk Exponential discounting Exponential diophantine equation Talk Exponential diophantine equation Exponential dispersion model Talk Exponential dispersion model Exponential distribution Talk Exponential distribution Exponential error Talk Exponential error Exponential family Talk Exponential family Exponential field Talk Exponential field Exponential formula Talk Exponential formula Exponential function Talk Exponential function Exponential generating function Talk Exponential generating function Exponential Golomb coding Talk Exponential Golomb coding Exponential growth Talk Exponential growth Exponential hierarchy Talk Exponential hierarchy Exponentialintegral Talk ExponentialintegralExponential map Talk Exponential map Exponential notation Talk Exponential notation Exponential object Talk Exponential object category theory Exponential polynomials &mdash see also Touchard polynomials Talk Touchard polynomials combinatorics Exponential sheaf sequence Talk Exponential sheaf sequence Exponential smoothing Talk Exponential smoothing Exponential stability ... more details
In nonlinear optics , B Integral is a measure of the nonlinear phase shift of light. It calculates the exponential growth of the least stable spatial frequency in a laser beam , and is the numerical equivalent of the nonlinear phase shift along the laser system s optical axis. In a multipass laser system as a cumulative measure of the nonlinear interaction, ref Cite web url http www.rp photonics.com b integral.html title B Integral publisher Encyclopedia of Laser Physics and Technology ref this integral is given by math B frac 2 pi lambda int n 2I z ,dz , math where math I z math is the optical intensity along the beam axis, math z math the position in beam direction, and math n 2 math the nonlinear index quantifying the Kerr nonlinearity. As math n 2I z math is the nonlinear change in the refractive index, one easily recognizes the B integral to be the total on axis nonlinear phase shift accumulated in a passage through the device. The B integral is frequently used in the context of ultrafast amplifiers, e.g. for optical components such as the Pockels cell of a regenerative amplifier. See also Kerr effect References reflist Category Laser science Category Photonics optics stub ... more details
will converge slowly initially, requiring many terms for high precisions. Relation with the exponentialintegral of imaginary argument Function math rm E 1 z int 1 infty frac exp zt t rm d t qquad rm Re z ge 0 math is called exponentialintegral . It is closely related with Si and Ci math rm ... n 1 n 2 . math See also Exponentialintegral Logarithmic integral Signal processing Gibbs phenomenon ... , the trigonometric integrals are a indexed family family of integral s which involve trigonometric ... of trigonometric functions . Sine integral Image Sine integral.svg thumb right Plot of Si x for 0 x 8 . The different sine integral definitions are math rm Si x int 0 x frac ... . When math x infty math , this is known as the Dirichlet integral . In signal processing , the oscillations of the Sine integral cause overshoot signal overshoot and ringing artifacts when using the sinc ... the Fourier series , which causes the Gibbs phenomenon. Cosine integral Image Cosine integral.svg thumb right Plot of Ci x for 0 x 8 . The different cosine integral ... rm Cin x gamma ln x rm Ci x , math Hyperbolic sine integral The hyperbolic sine integral math rm Shi ... x 3 3 cdot3 frac x 5 5 cdot5 frac x 7 7 cdot7 cdots. math Hyperbolic cosine integral The hyperbolic cosine integral math rm Chi x gamma ln x int 0 x frac cosh t 1 t ,dt rm chi x math where math gamma ... integral s. This spiral has applications in vision processing, road and track construction and other ... integro exponential function are math int 1 infty cos ax frac ln x x dx frac pi 2 24 gamma frac ... empanel index.html pg 300 dlmf id 6 title Exponential, Logarithmic, Sine, and Cosine Integrals ... of the oscillatory integral over exp i pi x x 1 x between 1 and infinity year 2009 , Appendix B. http de2de.synechism.org c5 sec58.pdf Sine Integral Taylor series proof. DEFAULTSORT Trigonometric Integral Category Trigonometry Category Special functions Category Special hypergeometric functions ... more details
. For example, the first example s integral is expressible using Elliptic integral Incomplete elliptic integral of the first kind incomplete elliptic integrals of the first kind , the second and third use the logarithmic integral , the fourth the exponentialintegral , and the fifth the error ... indefinite integral s, but definite integral s can be evaluated numerically, for instance by Simpson ... DEFAULTSORT Nonelementary Integral Category Integral calculus Category Integrals ca Integral no elemental es Integral no elemental ... more details
easily be solved using series. For example the solution to the integral of the exponential of a quartic ... distribution List of integrals of exponential functions Error function integral Category Integrals Category ... and the x axis, which is equal to math scriptstyle sqrt pi math . The Gaussian integral , also known as the Euler Poisson integral ref http slovari.yandex.ru dict bse article 00063 81000.htm ref is the integral of the Gaussian function e sup x sup 2 sup sup over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss . The integral is math int infty infty e x 2 ,dx sqrt pi . math This integral has wide applications. For example ... . The same integral with finite limits is closely related both to the error function and the cumulative ... for the error function, as can be proven by the Risch algorithm , the Gaussian integral can be solved analytically through the tools of calculus . That is, there is no elementary indefinite integral for math scriptstyle int e x 2 ,dx math , but the definite integral math scriptstyle int infty infty e x 2 ,dx math can be evaluated. The Gaussian integral is encountered very often in physics and numerous generalizations of the integral are encountered in quantum field theory . Computation By polar coordinates A standard way to compute the Gaussian integral, whose idea goes back to Poisson ref ... its integral two ways on the one hand, by double integration in the Cartesian coordinate system , its integral is a square math left int e x 2 ,dx right 2 math on the other hand, by shell integration a case of double integration in polar coordinates , its integral is computed to be math pi math . Comparing these two computations yields the integral, though one should take care about the improper ... function math I a int a a e x 2 dx. math If the integral math int infty infty e x 2 ,dx ... , the above double integral can be seen as an area integral math int e x 2 y 2 ,d x,y , math ... more details
Product integrals are counterparts of the usual integral of calculus classical calculus . The first product integral was developed by the mathematician Vito Volterra in 1887 to solve systems of linear ..., 2007. ref Please see Type II below. Other examples of product integrals are the geometric integral Type I below , the bigeometric integral, and some other integrals of non Newtonian calculus. ref ... integration instead of the integral math int math usually modified by a superimposed times symbol ... some order in the field. Basic definitions The classical Riemann integral of a function math ... f x i Delta x exp left int a b ln f x , dx right math , which is called the geometric integral and is a multiplicative operator. This definition of the product integral is the continuous equivalent ... equivalent to the normal standard additive integral math int a b dx math with math x in a,b ... where the log likelihood i.e. the logarithm of a product integral of independent random variables equals the integral of the log of the these infinitesimally many random variables math ln prod a b p ... integrable. There are other more general definitions such as the Lebesgue product integral, Riemann Stieltjes product integral, or Henstock&ndash Kurzweil product integral. The Type II product integral ... is not a multiplicative operator. So the concepts of product integral and multiplicative integral are not the same . However, this type of product integral is most useful when applied to matrix valued ... see the references below . Results The geometric integral Type I above plays a central role in the geometric ... calculi Ordered exponential A. E. Bashirov, E. M. Kurp nar, A. zyap c . http linkinghub.elsevier.com ... Product Integration Richard Gill, http wiki.contextgarden.net Product integral Product Integral ... product integration DEFAULTSORT Product Integral Category Integrals Category Multiplication Category Non Newtonian calculus ca Integral multiplicativa pt Integral produto ... more details
Path integral may refer to Line integral , the integral of a function along a curve Functional integration , the integral of a functional over a space of curves Path integral formulation of quantum mechanics using functional integration, due to Richard Feynman mathdab ... more details
In mathematical analysis an oscillatory integral is a type of distribution mathematics distribution . Oscillatory integrals make rigorous many arguments that, on a naive level, appear to use divergent integrals. It is possible to represent approximate solution operators for many differential equations as oscillatory integrals. Definition An oscillatory integral math f x math is written formally as math f x int e i phi x, xi , a x, xi , mathrm d xi math where math phi x, xi math and math a x, xi math are functions defined on math mathbb R x n times mathrm R N xi math with the following properties. 1 The function math phi math is real valued, homogeneous function Positive homogeneity positive homogeneous of degree 1, and infinitely differentiable away from math xi 0 math . Also, we assume that math phi math does not have any critical point mathematics Several variables critical points on the support ... math m n 1 math the formal integral defining math f x math converges for all math x math and there is no need ... n 1 math the oscillatory integral is still defined as a distribution on math mathbb R n math even though the integral may not converge. In this case the distribution math f x math is defined by using ... that have exponential decay in math xi math . One possible way to do this is by setting ..., psi rangle int e i phi x, xi L left a x, xi , psi x right , mathrm d x , mathrm d xi math where this integral ... i x cdot xi , mathrm d xi. math If we apply the first method of defining this oscillatory integral from ... R n e i x cdot xi L psi x, xi , mathrm d xi , mathrm d x, math and this integral converges absolutely ... integral. Indeed if math L sum limits alpha leq m p alpha x D alpha math where math ... integrals see harvtxt H rmander 1983 . Conversely any oscillatory integral is a Lagrangian distribution ... first Lars last Lars H rmander H rmander title Fourier integral operators I journal Acta Math. year 1971 volume 127 pages 79 183 Category Mathematical analysis de Oszillierendes Integral ... more details
wiktionarypar integralIntegral is a mathematical concept Integral may also refer to in mathematics integer , a number Integral symbol Lebesgue integration Integral measure theory , or Lebesgue integration Integrally closed Integral ring theory or Integral element Integral domain , a commutative ring with 0 1 in which the product of any two non zero elements is always non zero Integral imaging , 3D imaging in philosophy and spirituality Integral humanism India , political philosophy in Hindu nationalism Integral spirituality , inclusive philosophy, spirituality, or practice, inspired by the writings of Sri Aurobindo, Jean Gebser, Ken Wilber, and or others Integral Theory , an area of discourse emanating from Ken Wilber s thought on spiritual evolution, methodology and ontology Traditionalist School Integral traditionalism , Perennialist esotericism taught by Ren Gu non, Frithjof Schuon and others Cultural Creatives Use of the term integralIntegral Culture , transmodern subculture referred to by sociologist Paul H. Ray as a proper name INTEGRAL , the International Gamma Ray Astrophysics Laboratory Integral Systems , a human resource and accounting systems company Int gral The Journal of Applied Musical Thought , a music theory journal Integral song , a Pet Shop Boys song from Fundamental The Integral , a glass spaceship in Yevgeny Zamyatin s novel We novel We See also lookfrom Integral Integralism , ideology according to which a nation is an organic unity Integrality , in commutative algebra, the notions of an element integral over a ring Integration disambiguation Completeness disambig de Integral es Integral desambiguaci n fr Int gral hr Integral razdvojba lt Integralas nl Integral ru ... more details
Integral expression may refer to Integral equation More generally, a mathematical expression involving one or more integral s Integer polynomial An algebraic expression which is not in fractional form, see algebraic fraction mathdab zh ... more details
Integral Autonomy may refer to Integral Autonomy 1980s , regionalist Italian political party Autonomia Integrale , 1982 1988 Integral Autonomy 1990s , regionalist Italian political party Autonomia Integrale FAR , 1996 2000 disambig ... more details
Integral politics is an endeavor to develop a balanced and comprehensive politics around the principles of integral studies. Theorists including Don Beck management consultant Don Beck , Lawrence Chickering, Jack Crittenden, David Sprecher, and Ken Wilber have applied concepts such as the AQAL methodology of Integral Theory to issues in political philosophy and applications in government . ref name wilber atoe1 Ken Wilber 2000 . A Theory of Everything An Integral Vision for Business, Politics, Science and Spirituality, p. 153. Boston Shambhala Publications. ISBN 1570628556 ref An example of an application of integral politics is a proposal for a world federal constitution informed by integral philosophy such as that proposed by Steve McIntosh in Integral Consciousness and the Future of Evolution . According to McIntosh, an integral world federation would provide democratic oversight of the international economy, protect the global environment, defend human rights, and preserve multicultural diversity. Its ultimate aim is described as an end to war, disease, and poverty. ref name mctinsoh1 Steve McIntosh 2007 . Integral Consciousness and the Future of Evolution, p. 311. St. Paul, Minn. Paragon House. ISBN 2007021976 ref See also Integral Theory Integral spirituality References reflist 2 External links http www.integralinstitute.com Integral Institute a non profit academic think tank that studies integral politics. http www.integralworld.net Integral World website and online resource which has published articles on topics in integral politics. http www.jfku.edu integraltheory John F. Kennedy University, MA in Integral Theory offers courses on integral politics. DEFAULTSORT Integral Studies Category Integral studies Category Political theories poli stub ar bg da Integralteori de Integrale Theorie es Enfoque integral pt Movimento Integral ru th tr ntegral d nce ... more details
Unreferenced date December 2006 Integral thought Integral art can be variously defined as art that reaches ..., or perspectives, as the belief that every human being is creative and that art is integral to all human endeavours, or simply as art that was created by someone who thinks or acts in an integral way. A problem of definition There is no one form of integral art, and although the term is most .... Integral art may equally derive from integral teachers like Sri Aurobindo and Mirra Alfassa the Mother , or other integral thought integral thinkers , or simply developed integral art independently. Integral artists As with Integral thought in general, any list of Integral artists will be controversial. Integral artists influenced by Ken Wilber Alex Grey b. 1953 is a psychedelic visual ... whose works include the concept album Bright Apocalypse . Mystical and integral themes feature prominently ... Williams b. 1972 is a Hip hop music hip hop artist associated with the Integral Institute . Wilber ... poet artist author of Suicide Dictionary associated with Integral Institute . Adam Scott Miller .... His work is strongly informed by integral aesthetics to embody characteristics of mystery, awe, and inspiration. Adam is a featured artist at Integral Naked . Michael Garfield b. 1984 is a songwriter, painter, and essayist once associated with Integral Institute as a member of Ken Wilber s editorial team and as a featured performer at Integral Naked . Multi perspectivism characterizes his work in all media. He has interviewed Ken at length about integral art. Joe Perez b. 1969 is a writer poet ... focuses on Integral Archetypes. David Titterington b. 1983 is a Kansas based painter and featured artist at Integral Naked . Other Integral artists H. Johannes Wallmann b. 1952 is a composer and integral ... Integral Art Johannes Wallmann http www.ellenicolai.com Alchemies of the TransVisible Elle Nicolai http www.sofia.net.au School of Integral Art http www.adamscottmiller.com Integrally inspired paintings ... more details
In mathematics, the Pfeffer integral is an integration technique created by Washek Pfeffer as an attempt to extend the Henstock integral to a multidimensional domain. This was to be done in such a way that the fundamental theorem of calculus would apply analogously to the theorem in one dimension, with as few preconditions on the function under consideration as possible. The integral also permits analogues of the chain rule and other theorems of the integral calculus for higher dimensions. Definition The construction is based on the Henstock or gauge integral, however Pfeffer proved that the integral, at least in the one dimensional case, is less general than the Henstock integral. It relies on what Pfeffer refers to as a set of bounded variation , this is equivalent to a Caccioppoli set . The Riemann sums of the Pfeffer integral are taken over partitions made up of such sets, rather than intervals as in the Riemann or Henstock integrals. A gauge is used, exactly as in the Henstock integral, except that the gauge function may be zero on a negligible set. Properties Pfeffer defined a notion of generalized absolute continuity math ACG math , close to but not equal to the definition of a function being math ACG math , and proved that a function is Pfeffer integrable iff it is the derivative of an math ACG math function. He also proved a chain rule for the Pfeffer integral. In one dimension his work as well as similarities between the Pfeffer integral and the McShane integral indicate that the integral is more general than the Lebesgue integral and yet less general than the Henstock integral . Bibliography Citation surname1 Bongiorno given1 Benedetto surname2 Pfeffer given2 Washek title A concept of absolute continuity and a Riemann type integral journal Comment. Math. Univ ... A Riemann type definition of a variational integral journal Proc. American Math. Soc. volume 114 year 1992 page 99&ndash 106 integral Category Definitions of mathematical integration ... more details
In mathematics, the Kolmogorov integral or Kolmogoroff integral is a general integral introduced by harvs txt last Kolmogoroff authorlink Andrey Kolmogorov year 1930 including the Lebesgue Stieltjes integral , the Burkill integral , and the Hellinger integral as special cases. References Citation last1 Kolmogoroff first1 A. authorlink Andrey Kolmogorov title Untersuchungen ber den Integralbegriff url http dx.doi.org 10.1007 BF01455714 publisher Springer Berlin Heidelberg doi 10.1007 BF01455714 year 1930 journal Mathematische Annalen issn 0025 5831 volume 103 issue 1 pages 654 696 eom id k k055720 first V. A. last Skvortsov integral Category Definitions of mathematical integration ... more details
An integral lighthouse is a lighthouse in which the tower and keeper s dwelling are united in one structure. Generally, the term is not used to refer to a caisson lighthouse caisson or screw pile lighthouse . References http www.unc.edu rowlett lighthouse types earlyintegral.htm The Oldest Integral Lighthouses DEFAULTSORT Integral Lighthouse Category Lighthouses Pharology stub ... more details
lead too long date September 2011 primarysources date March 2010 Integral thought The Integral Institute .... ref http www.fielding.edu programs hod isC Integral Studies at Fielding Graduate University ref For example, the Integral Institute currently has a number of branches including Integral psychology , Integral business , Integral politics , Integral medicine , Integral education , Integral ecology ... health promotion into the 21 st century the integral idea whose time has come. Global Health Promotion , 17 3 , September 2010, 44 53. doi 10.1177 1757975910375169 ref Integral law and criminal justice, Integral art , and Integral spirituality . This attempt to integrate the knowledge base of a particular ... take all competitors, are seen as unique but partial contributors to a more realistic or Integral ..., one feels the ears, the trunk, etc. Integral theory , in a nutshell, says that these viewpoints can be integrated to create a more complete and accurate version of reality. Integral Institute outreach is occurring through a variety of projects. These include the Integral Institute Workshop Series, Integral Naked, Integral Life Practice , Integral University, and the Integral Spiritual Center . Notable ... Kabat Zinn , Ed Kowalczyk from the band Live band Live , and others. Integral Research Center Integral Research Center provides support, including student grants, in the field of Integral Research IR . The methodologies supported use the post metaphysical position of Integral Theory and its practice ... who successfully apply Integral principles. The group s senior researcher is Sean Esbj rn Hargens, Ph.D., an associate professor in the Integral Studies Department and Program Director of two Master ... IRC Vision, IntegralResearchCenter.org, accessed 2010 1 10. ref Integral Spiritual Center Integral ... of Integral spirituality and share it with thousands of practitioners around the world. ref Editors ... Integral Institute Category Integral theory Category Ken Wilber Category Postmodernism ... more details
In theory of oscillation vibration s, Duhamel s integral is a way of calculating the response of linear system s and structures to arbitrary time varying external excitation s. Introduction Background The response of a linear, viscously damped single degree of freedom SDOF system to a time varying mechanical excitation p t is given by the following second order ordinary differential equation math m frac d 2 x t dt 2 c frac dx t dt kx t p t math where m is the equivalent mass, x stands for the amplitude of vibration, t for time, c for the viscous damping coefficient, and k for the stiffness of the system or structure. If a system is initially rest at its Mechanical equilibrium equilibrium position, from where it is acted upon by a unit impulse at the instance t 0, i.e., p t in the equation above is a delta function t , math x 0 left. frac dx dt right t 0 0 math , then by solving the differential equation one can get a fundamental solution known as a unit impulse response function math h t begin cases frac 1 m omega d e varsigma omega n t sin omega d t, & t 0 0, & t 0 end cases math where math varsigma frac c 2m omega n math is called the damping ratio of the system, math omega n sqrt frac k m math is the natural angular frequency of the undamped system when c 0 and math omega d omega n sqrt 1 varsigma 2 math is the circular frequency when damping effect is taken into account when ... tau cdot h t tau math Letting math Delta tau to 0 math , and replacing the summation by Integral integration ... the expression of h t into the above equation leads to the general expression of Duhamel s integral ... primitive of x t computed at t z , in the case z t this integral is the primitive itself ... 0 math the difference between the primitives at t t and t 0 with integral definite integrals by another ... s exponential formula will lead to canceling out the imaginary terms and reveals the Duhamel s solution ... Category Structural analysis Category Integrals ca Integral de Duhamel zh ... more details
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