In mathematics an asymptoticexpansion , asymptotic series or Poincar expansion after Henri Poincar ... an asymptotic scale if for every n , math varphi n 1 x o varphi n x x rightarrow L math . If f is a continuous function on the domain of the asymptotic scale, then f has an asymptoticexpansion of order ... x sim sum n 0 infty a n varphi n x x rightarrow L . math See asymptotic analysis and big O notation for the notation. The most common type of asymptoticexpansion is a power series in either positive .... Repeated integration by parts will often lead to an asymptoticexpansion. Since a convergent Taylor series fits the definition of asymptoticexpansion as well, the phrase asymptotic series usually implies a non convergent series. Despite non convergence, the asymptoticexpansion is useful when ... at the smallest term. This way of optimally truncating an asymptoticexpansion is known as superasymptotics. ref cite journal first John P. last Boyd title The Devil s Invention Asymptotic ... be recognized as the gamma function . Evaluating both, one obtains the asymptoticexpansion math e ... Ei x E 1 x math results in the asymptoticexpansion given earlier in this article. References references Bleistein, N. and Handlesman, R., Asymptotic Expansions of Integrals , Dover, New York, 1975 Arthur Erd lyi A. Erd lyi , Asymptotic Expansions , Dover, New York, 1955 G. H. Hardy Hardy, G ... exp left frac c epsilon right math where &epsilon is the expansion parameter. The error is thus beyond all orders in the expansion parameter. It is possible to improve on the superasymptotic error ... are often referred to as hyperasymptotic approximations. Examples of asymptotic expansions Gamma function ... s overline 2m 1 math is a rising factorial . This expansion is valid for all complex s and is often ... example Asymptotic expansions often occur when an ordinary series is used in a formal expression ... Mathematical analysis Category Asymptotic analysis Category Mathematical series de Asymptotische Folge ... more details
. It is often used in time series analysis. In mathematics an asymptoticexpansion , asymptotic series or Poincar expansion after Henri Poincar is a formal series of functions which has the property ... of the domain, then the sequence constitutes an asymptotic scale if for every n , math varphi n 1 x o varphi n x x rightarrow L math . If f is a continuous function on the domain of the asymptotic scale, then an asymptoticexpansion of f with respect to the scale is a formal series math sum n 0 infty ... by parts will often lead to an asymptoticexpansion. Examples of asymptotic expansions Gamma function ... that math operatorname Ei x E 1 x math results in the asymptoticexpansion given earlier in this article ...Asymptotic theory or large sample theory is the branch of mathematics which studies properties of asymptotic ... deviance in statistics , results that are used daily by applied statisticians. Asymptotic distribution In mathematics and statistics , an asymptotic distribution is a hypothetical distribution that is in a sense ... of random variables Z sub i sub for i 1 to n for some positive integer n . An asymptotic distribution allows i to range without bound, that is, n is infinite. A special case of an asymptotic distribution ... instances of asymptotic distribution refer only to this special case. This is based on the notion of an asymptotic function which cleanly approaches a constant value the asymptote as the independent ... L math . See asymptotic analysis and big O notation for the notation. The most common type of asymptoticexpansion is a power series in either positive or negative terms. While a convergent Taylor ... 2m 1 math is a rising factorial . This expansion is valid for all complex s and is often used ... Asymptotic expansions often occur when an ordinary series is used in a formal expression that forces ... math u w t math , may be recognized as the gamma function . Evaluating both, one obtains the asymptoticexpansion math e 1 t operatorname Ei left frac 1 t right sum n 0 infty n t n 1 math Here, the right ... more details
sense, in the limit. Asymptoticexpansion An asymptoticexpansion of a function f x is in practice ... the g sub k sub form an asymptotic scale . The requirement that the successive sums improve the approximation may then be expressed as math f g 1 cdots g k o g k . math In case the asymptoticexpansion .... In many cases, the asymptoticexpansion is in power of a small parameter, math epsilon math in the boundary ..., to obtain as many terms in the asymptoticexpansion as desired. The process is as follows 1. Assume that the asymptotic behavior has the form math y x sim e S x , math . 2. Make a clever guess as to which ...about the comparison of functions as inputs approach infinite asymptotes in geometry asymptotic curve In mathematical analysis , asymptotic analysis is a method of describing Limit mathematics limiting ... do not necessarily converge, but such that taking any initial partial sum provides an asymptotic .... Asymptotic expansions typically arise in the approximation of certain integrals Laplace s method ... Edgeworth series . The famous Feynman graphs in quantum field theory are another example of asymptotic expansions which often do not converge. Use in applied mathematics Asymptotic analysis is a key ... thickness to a typical lengthscale of the problem. Indeed, applications of asymptotic analysis in mathematical ... of dominant balance The method of dominant balance is used to determine the asymptotic behavior of solutions ..., then we have the controlling factor of the asymptotic behavior. Otherwise, we need to try dropping ... S , frac c x S , frac a x o S 2 ,o S , math as math x to infty math We get the dominant asymptotic behaviour by setting math S 0 2 S 0 , math If math S 0 math satisfies the above asymptotic conditions ... asymptotic behaviour, which is what we are interested in. Let us check that this choice for math S 0 ... asymptotic behaviour of a solution to our ODE math S 0 x , math math y sim e x , math By convention, the asymptotic series is written as math y sim Ax p e lambda x r left 1 frac u 1 x frac u ... more details
In mathematics and statistics , an asymptotic distribution is a hypothetical distribution that is in a sense the limiting distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution function ... variables Z sub i sub for i 1, 2, ... In the simplest case, an asymptotic distribution exists if the probability distribution of Z sub i sub converges to a probability distribution the asymptotic ... in distribution . A special case of an asymptotic distribution is when the sequence of random variables always approaches zero that is, the Z sub i sub go to 0 as i goes to infinity. Here the asymptotic ... usual sense in which the term asymptotic distribution is used arises where the random variables Z ... i sub then Z sub i sub is said to have that distribution as its asymptotic distribution. If the distribution function of the asymptotic distribution is F then, for large n , the following approximations ... If an asymptotic distribution exists, it is not necessarily true that any one outcome of the sequence ... that converges. Asymptotic normality seealso local asymptotic normality Perhaps the most common distribution to arise as an asymptotic distribution is the normal distribution . In particular, the central limit theorem provides an example where the asymptotic distribution is the normal distribution . Barndorff Nielson & Cox ref Barndorff Nielson, O.E., Cox, D.R. 1989 Asymptotic Techniques for Use in Statistics. Chapman and Hall. ISBN 0 412 31400 2 ref provide a direct definition of asymptotic normality. The Binomial distribution seems to be the first asymptotic approximation by a normal ... to the normal is especially rapid. cn date March 2011 Asymptotic normality of the Binomial distribution is proven by the de Moivre Laplace theorem . cn date March 2011 See also Asymptotic theory ... Category Theory of probability distributions Category Asymptotic statistical theory eo Asimptota ... more details
In the differential geometry of surfaces , an asymptotic curve is a curve always tangent to an asymptotic direction of the surface where they exist . It is sometimes called an asymptotic line , although it need not be a line mathematics line . An asymptotic direction is one in which the normal curvature is zero. Which is to say for a point on an asymptotic curve, take the plane mathematics plane which bears both the curve s tangent and the surface s surface normal normal at that point. The curve of intersection of the plane and the surface will have zero curvature at that point. Asymptotic directions can only occur when the Gaussian curvature is negative or zero . There will be two asymptotic directions through every point with negative Gaussian curvature, these directions are bisected by the principal curvature principal directions . The direction of the asymptotic direction are the same as the asymptote s of the hyperbola of the Dupin indicatrix . ref cite book title Geometry and Imagination author David Hilbert authorlink David Hilbert coauthors Stephan Cohn Vossen Cohn Vossen, S. year 1999 publisher American Mathematical Society isbn 0 8218 1998 4 ref A related notion is a Monstar curvature line , which is a curve always tangent to a principal direction. References MathWorld urlname AsymptoticCurve title Asymptotic Curve http www.seas.upenn.edu cis70005 cis700sl10pdf.pdf Lines of Curvature, Geodesic Torsion, Asymptotic Lines http www.mathcurve.com surfaces asymptotic asymptotic.shtml Asymptotic line of a surface at Encyclop die des Formes Math matiques Remarquables in French language French references Category Curves Category Differential geometry of surfaces Category Surfaces differential geometry stub ar cs Asymptotick k ivka eo Asimptota kurbo fr Branche parabolique ru ... more details
In mathematics, an asymptotic formula for a quantity function or expression depending on natural numbers, or on a variable taking real numbers as values, is a function of natural numbers, or of a real variable, whose values are nearly equal to the values of the former when both are evaluated for the same large values of the variable. An asymptotic formula for a quantity is a function which is asymptotically equivalent to the former. More generally, an asymptotic formula is a statement of equality between two functions which is not a true equality but which means the ratio of the two functions approaches 1 as the variable approaches some value, usually infinity . ref Cite web url http www.answers.com topic asymptotic formula title Sci Tech Dictionary asymptotic formula accessdate 13 May 2010 ref Definition Let P n be a quantity or function depending on n which is a natural number. A function F n of n is an asymptotic formula for P n if P n is asymptotically equivalent to F n , that is, if math lim n rightarrow infty frac P n F n 1. math This is symbolically denoted by math P n sim F n , math Examples Prime number theorem For a real number x , let &pi x denote the number of prime numbers less than or equal to x . The classical prime number theorem gives an asymptotic formula for &pi ... formula is a well known asymptotic formula for the following quantity math n 1 times 2 times ldots times n math . The asymptotic formula is math n sim sqrt 2 pi n left frac n e right n. math Asymptotic ... Ramanujan in 1918 obtained the following asymptotic formula for P n ref name Wolfram math P n sim frac 1 4n sqrt 3 e pi sqrt 2n 3 . math Asymptotic formula for Airy function The Airy function Ai x ... in physics, has the following asymptotic formula math mathrm Ai x sim frac e frac 2 3 x 3 2 2 sqrt pi x 1 4 . math See also Asymptotic analysis References Reflist Use dmy dates date September 2010 DEFAULTSORT Asymptotic Formula Category Asymptotic analysis sq Formula asimptotike ... more details
unreferenced date March 2009 Orphan date February 2009 In theoretical physics and especially general theory of relativity , asymptotic flatness is the property of a geometry or a configuration in general relativity which means that in appropriate coordinates, the limit of the metric at infinity approaches the metric of the flat space. For spacetimes satisfying asymptotic flatness, it is often possible to calculate the ADM energy . It is also possible to consider asymptotically locally flat ALF spaces that can include additional discrete identifications of points at infinity asymptotically, they are orbifold s . Category General relativity relativity stub ... more details
inline date September 2011 In Scientific Visualization the Asymptotic Decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurface isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some bad topology, but should better not be seen as an addition to marching cubes, but as an algorithm of its own. Principle In general, the algorithm divides the scalar field first in regular cubes. Then it draws topologically correct contours on the sides interface of the cubes. These contours will then be connected to polygones and triangulated. The triangles of all cubes form the isosurfaces and are thus the output of the algorithm References reflist http dl.acm.org citation.cfm?id 949621 The asymptotic decider resolving the ambiguity in marching cubes Category Visualization graphic ... more details
In physics , asymptotic freedom is a property of some gauge theory gauge theories that causes interactions between particles to become arbitrarily weak at energy scale s that become arbitrarily large, or, equivalently, at length scale s that become arbitrarily small at the shortest distances . Asymptotic freedom is a feature of quantum chromodynamics QCD , the quantum field theory of the strong nuclear force nuclear interaction between quarks and gluon s, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing perturbative calculations by DGLAP of cross sections in deep inelastic processes of particle physics and strongly at low energies, preventing the unbinding of baryons like protons or neutrons with three quarks or mesons like pions with two quarks , the composite particles of nuclear matter. Asymptotic freedom was discovered by Frank Wilczek , David Gross , and David Politzer who in 2004 shared the Nobel Prize in physics. Discovery Asymptotic freedom was discovered in 1973 by David Gross and Frank Wilczek , and by David Politzer . Although these authors were the first to understand the physical relevance to the strong interactions, in 1969 Iosif Khriplovich discovered asymptotic freedom in the SU 2 gauge theory as a mathematical curiosity, and Gerardus t Hooft in 1972 also noted the effect but did not publish. For their discovery, Gross, Wilczek and Politzer were awarded the Nobel Prize in Physics in 2004. The discovery was instrumental in rehabilitating quantum field theory. Prior to 1973, many theorists suspected that field theory ... free. In fact, there are only 6 known quark flavors. Calculating asymptotic freedom Asymptotic ..., the existence of asymptotic freedom depends on the gauge group and number of flavor particle ... N 3, math and math beta 1 0 math gives math n f 33 over 2 . math See also Asymptotic safety Quantum ... author D.J. Gross year 1998 title Twenty Five Years of Asymptotic Freedom doi 10.1016 S0920 5632 99 ... more details
wiktionary expand expansionExpansion may refer to tocright Physics Metric expansion of space Thermal expansion Prandtl Meyer expansion fan Computer programming Expand Unix Inline expansion Mathematics Expansion geometry Polynomial expansion Taylor expansion Expander graph expansion of a graph The converse of a reduct , in model theory or universal algebra Economics Economic expansion Expansionary policies Other uses Expansion card , in computer hardware Expansion pack , in gaming Expansion team , in sports Trinucleotide repeat disorder Trinucleotide repeat expansion disorder , in medicine, the result of expansion during DNA translation Expansion album Expansion album , by Dave Burrell Expansions album , an album by jazz pianist McCoy Tyner Expansion joint , in engineering Audio level expansion, in audio engineering disambig Expansion life ,in nature cs Expanze da Ekspansion de Expansion fr Expansion hr Ekspanzija it Espansione nl Expansie ru sk Expanzia sv Expansion ... more details
In computational complexity theory , asymptotic computational complexity is the usage of the asymptotic analysis for the estimation of computational complexity of algorithm s and computational problem s, commonly associated with the usage of the big O notation . In terms of the most commonly estimated computational resource s, it is spoken about the asymptotic time complexity and asymptotic space complexity . Other asymptotically estimated resources include circuit complexity and various measures of parallel computation , such as the number of parallel processors. Since the groundlaying 1965 paper of Juris Hartmanis Hartmanis and Richard Stearns computer scientist Stearns ref J. Hartmanis, R. Stearns. On the computational complexity of algorithms, Transactions of the American Mathematical Society , 1965 vol. 117, pp. 285 306 ref and the 1979 book by Garey and Johnson on NP completeness , ref Michael Garey , and David S. Johnson Computers and Intractability A Guide to the Theory of NP Completeness. New York W. H. Freeman & Co., 1979. ref the term computational complexity of algorithms most commonly refers to the asymptotic computational complexity. Further, unless specified otherwise, the term computational complexity usually refers to the upper bound for the asymptotic computational complexity of an algorithm or a problem, which is usually written in terms of the Big O notation , e.g.. math O n 3 . math Other types of asymptotic computational complexity estimates are lower bound s Big Omega notation e.g., n and asymptotically tight estimates, when the asymptotic upper and lower bounds coincide written using the Big Theta e.g., n log n . A further tacit assumption is that the worst case analysis of computational complexity is in question unless stated otherwise. An alternative approach is probabilistic analysis of algorithms . In most practical cases deterministic algorithm s or randomized algorithm s are discussed, although theoretical computer science also considers ... more details
right y y 0, , math which implies, due to the uniqueness of the solution, that the matched asymptotic ... is the first term in a binomial expansion of the exact solution in powers of math y 1 e 1 1 epsilon ... Asymptotic analysis ... more details
In statistics , asymptotic theory , or large sample theory , is a generic framework for assessment of properties of estimator s and statistical test s. Within this framework it is typically assumed that the sample size n grows indefinitely, and the properties of statistical procedures are evaluated in the limit as nowrap n . In practical applications, asymptotic theory is applied by treating the asymptotic results as approximately valid for finite sample sizes as well. Such approach is often criticized for not having any mathematical grounds behind it, yet it is used ubiquitously anyway. The importance of the asymptotic theory is that it often makes possible to carry out the analysis and state ... problems begin with a dataset of sample size size n . The asymptotic theory proceeds by assuming ... . In this case the asymptotic is again taken as the number of observations usually denoted ... these standard approaches, various other alternative asymptotic approaches exist Within the local asymptotic normality framework, it is assumed that the value of the true parameter in the model varies ... s asymptotic. In kernel density estimation and kernel regression additional parameter the bandwidth ... see Convergence of random variables Asymptotic properties Estimators ul li Consistent estimator Consistency ... in practice. li Asymptotic distribution if it is possible to find sequences of non random constants ... math style vertical align .1em scriptstyle hat theta n math is said to have the asymptotic distribution ... N 0, V math sqrt n hat theta n theta 0 xrightarrow d mathcal N 0, V . math li Asymptotic confidence region s . li Regular estimator Regularity . ul Asymptotic theorems Law of large numbers Central ... ref CITEREFLe CamYang2000 cite book last van der Vaart first A.W. title Asymptotic statistics year 1998 ... DEFAULTSORT Asymptotic Theory Statistics Category Statistical theory Category Econometrics Category Asymptotic statistical theory ... more details
In statistics , local asymptotic normality is a property of a sequence of statistical model s, which allows this sequence to be asymptotic distribution asymptotically approximated by a normal distribution normal location model , after a rescaling of the parameter. An important example when the local asymptotic normality holds is in the case of iid sampling from a regular parametric model . The notion of local asymptotic normality was introduced by harvtxt Le Cam 1960 . Definition Technical reason notation should be explained for example, what is here? date September 2010 A sequence of parametric statistical model s nowrap &thinsp P sub n, sub &thinsp is said to be locally asymptotically normal LAN at if there exist matrix mathematics matrices r sub n sub and I sub sub and a random Coordinate vector vector nowrap sub n, sub N 0, I sub sub such that, for every converging sequence math h sub n sub h , ref name V harvtxt van der Vaart 1998 pp 103 104 ref math ln frac dP n, theta r n 1 h n dP n, theta h Delta n, theta frac12 h I theta ,h o P n, theta 1 , math where the derivative here is a Radon Nikodym theorem Radon Nikodym derivative Radon Nikodym derivative , which is a formalised version of the likelihood ratio , and where o is a type of big O in probability notation . In other words, the local likelihood ratio must convergence in distribution converge in distribution to a normal random variable whose mean is equal to minus one half the variance math ln frac dP n ... bigg , bigg . math Thus, the definition of the local asymptotic normality is satisfied, and we have ... likelihood has the LAN property. See also Asymptotic distribution Notes Reflist 3 References Refbegin Cite book last1 Ibragimov first1 I.A. last2 Has minski first2 R.Z. title Statistical estimation asymptotic ... Vaart first A.W. title Asymptotic statistics year 1998 publisher Cambridge University Press isbn 978 0 521 78450 4 ref harv Refend DEFAULTSORT Local Asymptotic Normality Category Asymptotic statistical ... more details
The asymptotic gain model ref Middlebrook, RD Design oriented analysis of feedback amplifiers Proc. of National ... of negative feedback amplifier s given by the asymptotic gain relation math G G infty left frac T T 1 ... amplifier Unilateral or bilateral unilateral blocks , G sub sub is the asymptotic gain and math ... thumb 300px right Figure 1 Block diagram for asymptotic gain model ref name Gray Meyer cite book ... diagram that leads to the asymptotic gain expression. The asymptotic gain relation also can be expressed as a Signal flow graph Example 3 Asymptotic gain formula signal flow graph . See Figure 2. The asymptotic ... amplifier.PNG thumbnail 300px Figure 2 Possible signal flow graph for the asymptotic gain model Definition of terms As follows directly from limiting cases of the gain expression, the asymptotic gain ... math G math of the system is approximately equal to the asymptotic gain G sub sub . The asymptotic ... to T 0. Substitute the values for T, G sub sub and G sub 0 sub into the asymptotic gain formula. These steps ... the asymptotic gain model becomes math G G infin frac T 1 T math math frac G infin T 1 frac 1 G infin ... in deriving the gain using the asymptotic gain formula are outlined below for two negative feedback ... gain of this circuit G v sub out sub i sub in sub using the asymptotic gain model. Image Transresistance ... only the dependent source. ref Asymptotic gain Finding the asymptotic gain G sub sub provides insight ... the asymptotic gain, which makes the gain insensitive to amplifier parameters g sub m sub and R sub ... 7 Schematics for using asymptotic gain model parameter 1 resistor R sub C sub R sub C1 sub ..., and the asymptotic gain approach has the advantage disadvantage that it works whether or not you ... later. To implement the asymptotic gain model, the dependent source associated with either transistor ... into the asymptotic gain model equation to find the overall gain G. The resulting gain is the current ... 2004 L290 ReturnRatio 2UP.pdf Lecture notes on the asymptotic gain model Category Electronic feedback ... more details
aligned with its previous red giant branch red giant track , hence the name asymptotic giant branch ... publisher Springer isbn 1402051786 ref References H. J. Habing, Hans Olofsson Asymptotic Giant Branch ..., E. S. Dufton, P. L. Keenan, F. P. Hot post asymptotic giant branch stars at high galactic latitudes ... Planetary nebula e Red giant Star Category Asymptotic Giant Branch stars Category Hertzsprung Russell ... more details
In information theory the asymptotic equipartition property AEP is a general property of the output samples of a stochastic process stochastic source . It is fundamental to the concept of typical set used in theories of data compression compression . Roughly speaking, the theorem states that although there are many series of results that may be produced by a random process, the one actually produced is most probably from a loosely defined set of outcomes that all have approximately the same chance of being the one actually realized. This is a consequence of the law of large numbers and ergodic theory . Although there are individual outcomes which have a higher probability than any outcome in this set, the vast number of outcomes in the set almost guarantees that the outcome will come from the set. In the field of Pseudorandom number generator Pseudorandom number generation , a candidate generator of undetermined quality whose output sequence lies too far outside the typical set by some statistical criteria is rejected as insufficiently random. Thus, although the typical set is loosely defined, practical notions arise concerning sufficient typicality. Definition Given a discrete time stationary ergodic stochastic process math X math on the probability space math Omega,B,p math , AEP is an assertion that math frac 1 n log p X 1 n to H X math where math X 1 n math denotes the process limited to duration math 1, dots,n math , and math H X math or simply math H math denotes the entropy rate of math X math , which must exist for all discrete time stationary process es including the ergodic ones. AEP is proved for finite valued i.e. math Omega infty math stationary ergodic stochastic processes in the AEP for discrete time finite valued stationary ergodic sources Shannon McMillan Breiman theorem using the ergodic theory and for any independent identically distributed random variables ... of the Asymptotic Equipartition Property in Noiseless Source Coding. IEEE Transactions on Information ... more details
An expansion draft , in professional sports , occurs when a sports league decides to create one or more new expansion team s or sports franchising franchise s. This occurs mainly in North American sports. One of the ways of stocking the new team or teams is an expansion draft. Although how each league ... by furnishing their names to the league office on or before a certain date. The expansion team ... they truly need on the protected list. This means that the expansion franchise is usually left to choose ... so highly compensated that a team wishes to remove them from the payroll. For this reason, expansion ... teams this process is referred to as a dispersal draft . Expansion Drafts Baseball Baseball expansion was initially hastened by the threat of a competing league, known as the Continental League . 1960 Major League Baseball expansion draft 1961 Major League Baseball expansion draft 1968 Major League Baseball expansion draft 1976 Major League Baseball expansion draft 1992 Major League Baseball expansion draft 1997 Major League Baseball expansion draft Basketball 1961 NBA Expansion Draft 1966 NBA Expansion Draft 1967 NBA Expansion Draft 1968 NBA Expansion Draft 1970 NBA Expansion Draft 1974 NBA Expansion Draft 1980 NBA Expansion Draft 1988 NBA Expansion Draft 1989 NBA Expansion Draft 1995 NBA Expansion Draft 2004 NBA Expansion Draft 2006 NBA Development League Expansion Draft 2007 NBA Development League Expansion Draft 2008 NBA Development League Expansion Draft 2009 NBA Development League Expansion Draft 2010 NBA Development League Expansion Draft Football 1960 NFL Expansion Draft 1961 NFL Expansion Draft 1966 NFL Expansion Draft 1967 NFL Expansion Draft 1976 NFL Expansion Draft 1995 NFL Expansion Draft 1999 NFL Expansion Draft 2002 NFL Expansion Draft 2012 CFL Expansion Draft Hockey 1967 NHL Expansion Draft 1970 NHL Expansion Draft 1972 NHL Expansion Draft 1974 NHL Expansion Draft 1979 NHL Expansion Draft 1991 NHL Dispersal and Expansion Drafts 1991 NHL Expansion Draft 1992 ... more details
Volume expansion may refer to Thermal expansion Increase of fluid in the blood. When reaching abnormally high levels, it is termed hypervolemia ref http www.prep4usmle.com forum thread 11546 Hyperosmotic volume contraction vs. expansion ref References reflist disambig ... more details
Unreferenced stub auto yes date December 2009 Orphan date December 2009 Lateral expansion sometimes known as horizontal expansion , in economics , is the growth of a business enterprise through the acquisition of similar companies, in the hope of achieving economies of scale or economies of scope . Unchecked lateral expansion can lead to powerful Conglomerate company conglomerates or monopolies . Related is vertical expansion , which is the growth of a business enterprise through the acquisition of companies that produce the intermediate goods needed by the business or help market and distribute its final goods . Any such value chain activities can be acquired through vertical expansion. DEFAULTSORT Lateral Expansion Category Business economics Econ stub ... more details
dablink For the railway specific expansion joints, see Breather switch . File BridgeExpansionJoint.jpg thumb Expansion joint on a bridge An expansion joint or movement joint is an assembly designed to safely absorb the Thermal expansion heat induced expansion and contraction of various construction materials ..., or due to other heat sources. Before expansion joint gaps were built into these structures, they would ... right thumb Saw cut expansion joints in concrete. Control joints often confused with expansion joints are cut into the concrete or asphalt, and are different from expansion joints as shown in the photo ... sealant such as rubber . clear Bridge expansion joints Bridge Expansion Joints, as shown ... structures. Bridge expansion joints also allow enough vertical movement to allow bearing replacement ... Ltd. retrieved 22 December 2011 ref without the need to dismantle the bridge expansion joint. There are various types of Bridge Expansion Joints that can accommodate movement from between 30 to 1000 mm these include small movement expansion joints JEP, WR and WOSd ,medium movement expansion joints Wd and large movement expansion joints WP . ref http www.freyssinet.co.uk pdfs products cipec expansion joints cv1 .pdf Freyssinet CIPEC Bridge Expansion Joints , Freyssinet Ltd. retrieved 21 December 2011 ref Pipe expansion joints File Flanged Rubber Bellows.jpg right thumb Single sphere rubber bellows expansion joint, with flange s. File Kompensator Rohr .jpg right thumb Stainless steel pipe expansion joint, with control rods. Pipe expansion joints are necessary in systems that convey high temperature ... type of expansion joint for pipe systems is a bellows which can be manufactured from metal most commonly ..., and or angular deflections. Expansion joints are also designed for other criteria, such as noise absorption, anti vibration, earthquake movement, and building settlement. Metal expansion joints have to be designed according to rules laid out by EJMA, while for fabric expansion joints only guidelines ... more details
Otheruses Thermal expansion valve An expansion valve is a slide valve used in a steam engine to control the cut off . It rides on the back of an adapted main slide valve and is driven by an additional Eccentric mechanism eccentric that has more advance than the main eccentric. The cut off is adjusted in one of two ways. The stroke of the expansion valve may be altered by adjusting the throw of the eccentric or by an expansion link and radius rod arrangement, usually under the control of a centrifugal governor . Alternatively, the effective length of the expansion valve can be altered. The Meyer expansion valve has two heads mounted on opposite handed threads on a rotatable valve rod, so that rotating the rod moves the heads either together or apart, according to the direction of rotation. ref Cite book title Some Early Robey Steam Engines last Southworth first P.J.M. publisher P.J.M. Southworth year 1986 isbn 0 9511856 0 8 ref harv pages 4,21 22,24 ref In this arrangement the cut off is normally controlled manually. The engines at Coleham Pumping Station have Meyer expansion valves on the high pressure cylinders. References Reflist Category Steam engines Category Steam engine technology mech engineering stub tech stub ... more details
unreferenced date May 2010 Image Expansion tank.jpg thumb Expansion tank in central heating system. An expansion tank or expansion vessel is a small Water tank tank used to protect closed water heating systems and domestic hot water systems from excessive pressure. The tank is partially filled with air, whose compressibility cushions shock caused by water hammer and absorbs excess water pressure caused by thermal expansion . The modern vessel is a small container divided in two by a rubber Diaphragm mechanical device diaphragm . One side is connected to the pipe work of the heating system and therefore contains water. The other, the dry side, contains air under pressure, and normally a Schrader valve car tire type valve stem for checking pressures and adding air. When the heating system is empty or at the low end of the normal range of working pressure the diaphragm will be pushed against the water inlet. As the water pressure increases, so the diaphragm moves compressing the air on its other side. An older style of expansion tank is larger, oriented horizontally, and has no rubber diaphragm. Image Expansion vessel for boilers.jpg thumb left 108px alt expansion tank for boilers Expansion tank for boilers. When expansion tanks are used in domestic hot water systems, the tank and the diaphragm .... Thus, expansion tanks are now used more frequently than in the past. In the UK, prior to the use of sealed expansion tanks, open tanks were installed in the roof space to accommodate the water s expansion these had the disadvantage of being exposed to the cold air in the roof space. This, without ... tap s sometimes unpredictable. In Europe the design and the construction of expansion tanks are ruled by EN 13831 according to Pressure Equipment Directive PED 97 23 EC Image SaabHengine.jpg thumb Expansion tank in a 1987 Saab 90 br the brown plastic tank with white lid in top of picture . An expansion ... cite web url http www.expansiontank.org title About the Expansion Tank DEFAULTSORT Expansion Tank Category ... more details
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