Unreferenced date December 2009 In chemistry , the pathlength is defined as the distance that light UV Visible spectrum VIS travels through a sample in an analytical cell. Typically, a sample cell is made of quartz , glass, or a plastic rhombic cuvette with a volume typically ranging from 0.1 mL to 10 mL or larger used in a spectrophotometer . For the purposes of spectrophotometry i.e. when making calculations using the Beer Lambert law the pathlength is measured in centimeters rather than in meters . In a computer network , the pathlength is one of many possible router metrics used by a router computing router to help determine the best Routing route among multiple routes to a destination. It consists of the end to end hop count from a source to a destination over the network. More simply, in general computer terminology, it can mean simply the total number of instructions executed from point A to point B in a program Instruction pathlength . In physics, the pathlength is defined as the total distance an object travels. Unlike displacement, which is the total distance an object travels from a starting point, pathlength is the total distance travelled, regardless of where it travelled. DEFAULTSORT PathLength Category Spectroscopy Category Computer networking Category Computing terminology ... more details
In optics , optical pathlength OPL or optical distance is the product of the geometric length of the path light follows through the system, and the index of refraction of the Medium optics medium through which it propagates. A difference in optical pathlength between two paths is often called the optical path difference OPD . Optical pathlength is important because it determines the Phase waves phase of the light and governs Interference wave propagation interference and diffraction of light as it propagates. Optical Path Difference OPD Optical path difference is the phase shift which happens between two previously coherent sources when passed through different mediums. For example a wave passed through glass will appear to travel a greater distance than an identical wave in air. This is because the source in the glass will have experienced a greater number of wavelengths due to the higher refractive index of the glass . The OPD can be calculated from the following equation math mathrm ... side by d hence d n d is the optical path Details In a medium of constant refractive index, n , the OPL for a path of physical length d is just math mathrm OPL nd . , math If the refractive index varies along the path, the OPL is given by math mathrm OPL int C n s mathrm d s, quad math where n s is the local refractive index as a function of distance, s , along the path C . An electromagnetic wave that travels a path of given optical pathlength arrives with the same phase shift as if it had traveled a path of that physical length in a vacuum . Thus, if a wave is traveling through several different media, then the optical pathlength of each medium can be added to find the total optical pathlength. The optical path difference between the paths taken by two identical waves can then be used ... can be calculated. Fermat s principle states that the path light takes between two points is the path that has the minimum optical pathlength. See also Lagrangian optics Hamiltonian optics Fermat s principle ... more details
Average pathlength is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network Node networking nodes . It is a measure of the efficiency of information or mass transport on a network. TOC Concept Average pathlength is one of the three most robust measures of network topology, along with its clustering coefficient and its degree distribution . Some examples are the average number of clicks which will lead you from one website to another, or the number of people you will have to communicate through, on an average, to contact a complete stranger. It should not be confused with the diameter of the network, which is defined as the maximal distance between any two nodes in the network. The average pathlength distinguishes an easily negotiable network from one which is complicated and inefficient, with a shorter average pathlength being more desirable. However, the average pathlength is simply what the pathlength will most likely be. The network itself might have some very remotely connected nodes and many nodes ... pathlength math l G math is math l G frac 1 n cdot n 1 cdot sum i, j d v i, v j math , where ... Wide Web , a short average pathlength facilitates the quick transfer of information and reduces costs ... by studying its average pathlength. A power grid network will have less losses if its average pathlength is minimized. Most real networks have a very short average pathlength leading to the concept ... very short average pathlength. The average path lengths of some networks are listed in Table. 1 ... removed Image Comb0000.jpg center frame The average pathlength depends on the system size but does not change drastically with it. Small world network theory predicts that the average pathlength changes ... DEFAULTSORT Average PathLength Category Network theory Category Graph invariants hu tlagos t vols g ... short path. As a result, most models of real networks are created with this condition in mind. One ... more details
In computer performance , the instruction pathlength is the number of machine code instructions required to execute a section of a computer program . The total pathlength for the entire program could be deemed a measure of the algorithm s performance on a particular computer hardware . The pathlength ... pathlength is frequently taken as the number of assembly instructions required to perform ... considerable saving. Expressed in terms of instruction pathlength, this Software metric metric ... might be a secondary consideration compared to a good choice of algorithm requiring a shorter pathlength. The instruction pathlength of an assembly language program is generally vastly different than the number of source lines of code for that program, because the instruction pathlength includes ..., it is not always possible to determine instruction pathlength without, for example, an instruction ... the instruction pathlength by examining this list. Unfortunately most high level language programmers ... can have dramatic effects on instruction path lengths without the programmer having any means of knowing this in many cases. Factors determining instruction pathlength in line code versus the Subroutine ... into memory once versus external read afresh each time avoiding high pathlength through multiple I O function calls Use of instruction path lengths From the above, it can be realized that knowledge ... PA43&lpg PA43&dq 22instruction pathlength 22&source web&ots f1d 77XzLV&sig EuQVc3kKLMWN Wrvk Y0tHKSlZs ... condition is satisfied. The length of time to execute each instruction is not normally considered in determining pathlength and so pathlength is merely an indication of relative performance rather than in any sense absolute. When executing a benchmark program , most of the instruction pathlength is typically inside the program s inner loop . Assembly programs Since there is, typically, a one ... January 2010 and have no way to appreciate the instruction path lengths of their code except perhaps ... more details
In computer science , the shortest total pathlength spanning tree is, given an n node undirected graph G V , E positive integer B , does there exist a spanning tree T V , F of G such that the sum over all pairs of nodes u and v of the length of the path between u and v in T is no greater than B ? References cite book author Michael R. Garey and David S. Johnson year 1979 title Computers and Intractability A Guide to the Theory of NP Completeness publisher W.H. Freeman id ISBN 0 7167 1045 5 A2.1 ND3, pg.206. comp sci stub Category Spanning tree Category NP complete problems ... more details
The Path may refer to The Path album The Path album , a 2003 studio album by Show Of Hands The Path book The Path book , collection of short essayes by Konosuke Matsushita The Path comics The Path comics , an American comic book series by CrossGen Entertainment The Path video game The Path video game , a psychological horror art PC game See also Path disambiguation disambig fr The Path it The Path ... more details
About uses of path and pathway the acronym PATHPATH disambiguation PATH wiktionary path pathway TOC right Path , pathway or PATH may refer to Path Course navigation , the intended path of a vehicle over the surface of the Earth Trail , hiking trail , footpath , or bridle path See also Track disambiguation Footpath disambiguation Shining Path , Maoist guerrilla insurgent organization in Peru Sidewalk running along the edge of a road, in some varieties of English Bicycle path or bikeway way Golden Path Dune , a metaphysical theme from Frank Herbert s Dune novels Path Vol.2 is a 2000 single by Apocalyptica from their album Cult Mathematics Path graph theory , a sequence of vertices of a graph Path topology , a continuous function Computing Path computing , in computer file systems, the human readable address of a resource PATH variable , an environment variable specifying a list of directories where executable programs are located Path social network , a social networking enabled photo sharing and messaging service Clipping path , a computer image outlining option to remove background and create transparency Control flow path, a possible execution sequence in a program often depicted as a sequence of edges in a control flow graph The st connectivity problem is sometimes known as the path problem. Pathway Biology Genetic pathway , a group of genes interacting to form an aggregate biological function Metabolic pathway , a series of chemical reactions within a cell Signal transduction Signalling pathway , a series of interactions e.g. from cell receptors to affect gene expression. Neural pathway , a neural tract connecting one part of the nervous system with another Dopaminergic ... Path , various businesses founded and originally run by the Path Brothers of France PATH disambiguation , disambiguation page for the acronym PATH The Path disambiguation disambiguation cs Path da Sti de PATH fr Path ko nl Pad pt Caminho simple Path ... more details
About the acronym PATH other uses of pathPath disambiguation PathPATH may refer to Port Authority Trans Hudson , a subway system linking Manhattan, New York with locations in northern New Jersey PATH Atlanta , trail building organization Georgia, USA PATH Toronto , a network of underground pedestrian tunnels in Toronto, Ontario, Canada Partners for Advanced Transit and Highways , a research organization operated by the University of California The Performance Assessment Tool For Quality Improvement In Hospitals , a performance assessment system designed by the World Health Organization to support hospitals in defining quality improvement strategies, questioning their own results and translating them into actions for improvement. Positive Alternatives to Homosexuality , a coalition of ex gay organizations Program for Appropriate Technology in Health , an international, nonprofit organization based in Seattle, Washington, USA Projects for Assistance in Transition from Homelessness , to support service delivery to individuals with serious mental illnesses who are homeless or at risk of becoming homeless Potomac Appalachian Transmission Highline , proposed electrical line PATH variable , a computer operating system environment variable specifying a list of directories where executable programs are located disambig ... more details
Infobox film name On the Path image On the Path.jpg image size caption director Jasmila bani producer Damir Ibrahimovic writer Jasmila bani starring Mirjana Karanovi music cinematography Christine A. Maier editing distributor released Film date 2010 2 18 60th Berlin International Film Festival Berlinale 2010 2 20 Bosnia and Herzegovina runtime country Bosnia and Herzegovina language Bosnian budget On the Path lang bs Na putu is a 2010 Bosnian and Herzegovinan drama film directed by Jasmila bani . Plot Luna and Amar are a young Bosniaks Bosnian couple living in Sarajevo. Both have traumatic memories from the Bosnian War of the 1990 s. Luna had seen her parents killed by an anti Muslim militia in Bijeljina , and had come to Sarajevo with her grandparents as a child refugee. Amar had served as a soldier in the war and lost his brother. At present, however, they have apparently built up a successful life she as an air hostess with B&H Airlines , he as an air traffic controller at the Sarajevo International Airport . When she comes back from a flight they make love passionately and go to have a good time at a local nightclub. Though identifying as Islam in Bosnia and Herzegovina Muslim s in the context of Bosnia s ethnic set up, religion plays no part in their life. In fact, Amar drinks alcoholic drinks a bit too much which is forbidden by Islam and it is this which begins to put their relationship under strain. First of all, Amar loses his job for being drunk at work. Luna is very worried and has little hope of realizing her fragile dream of having a child with Amar. But her fears for their future increase when Amar takes on a well paid job in a Muslim community hours away from where they live. Only after quite some time has elapsed during which they have had no contact ... and Amar together on the path to a lifetime of happiness. Cast Zrinka Cvite i Leon Lu ev Mirjana ... accessdate 2011 01 01 ref References reflist External links imdb title 1156531 DEFAULTSORT On The Path ... more details
zero value for L . Proper length of a path The above formula for the proper length between two events ..., possible to define the proper length of a Path topology path in any spacetime, curved or flat. In a flat spacetime, the proper length between two events is the proper length of a straight path between the two events. In a curved spacetime, there may be more than one straight path Geodesic general relativity geodesic between two events, so the proper length of a straight path between two events would not uniquely define the proper length between the two events. Along an arbitrary spacelike path P , the proper length is given in tensor syntax by the line integral math L c int P sqrt g mu nu dx ...For the cosmological notion of proper distance Comoving distance In relativistic physics, proper length is an invariant physics invariant measure of the distance between two spacelike separated Spacetime Basic concepts event s, or of the length of a spacelike Path topology path within a spacetime . The measurement of lengths is more complicated in the theory of relativity than in classical mechanics . In classical mechanics, lengths are measured based on the assumption that the locations of all points ..., whose value is the same for all observers. Proper length is analogous to proper time . The difference is that proper length is the invariant spacetime interval interval of a spacelike path or pair of spacelike separated events, while proper time is the invariant interval of a timelike path or pair of timelike separated events. Proper length between two events In special relativity , the proper length between two spacelike separated events is the distance between the two events, as measured ... at opposite ends of an object, the proper length of the object is the length of the object as measured ... length L is math L sqrt Delta x 2 Delta y 2 Delta z 2 c 2 Delta t 2 math , where t is the difference ... events along the path P . In the equation above, the metric tensor is assumed to use the tt tt ... more details
definition of coherence length has been suggested The coherence length can be measured using a Michelson interferometer and is the optical pathlength difference of a self interfering laser beam which ...In physics , coherence length is the wave propagation propagation distance from a coherence physics coherent source to a point where a wave e.g. an electromagnetic wave maintains a specified degree of coherence . The significance is that Interference wave propagation interference will be strong within a coherence length of the source, but not beyond it. This concept is also commonly used in telecommunication engineering. This article focuses on the coherence of Classical physics classical electromagnetic fields. In quantum mechanics , there is a mathematically analogous concept of the Coherence physics Quantum coherence quantum coherence length of a wave function . Formulas In radio band systems, the coherence length is approximated by math L c over n , Delta f , math where c is the speed of light in a vacuum, n is the refractive index of the Medium optics medium , and math Delta f math is the Bandwidth ... , the coherence length math L math is given by math L 2 ln 2 over pi n lambda 2 over Delta lambda ... Delta lambda math , then a path offset of math L math will reduce the fringe visibility to 50 . Coherence length is usually applied to the optical regime. The expression above is a frequently used approximation ... length may be reduced by propagation factors such as dispersion optics dispersion , scattering , and diffraction . Lasers Multimode helium neon laser s have a typical coherence length of 20 cm, while the coherence length of singlemode ones can exceed 100 m. Semiconductor laser s reach ... repeated after cavity length distances up to this long coherence length. See also Portal Physics Coherence time Superconducting coherence length References Reflist 2 FS1037C MS188 DEFAULTSORT Coherence Length Category Electromagnetic radiation Category Optics Category Waves de Koh renzl nge ja ... more details
Orphan date January 2011 The transport length in a strongly diffusing medium noted l is the length over which the direction of propagation of the photon is randomized. It is related to the mean free path l by the relation ref A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978. ref math l frac l 1 g math with g the asymmetry coefficient. math g cos theta math or averaging of the scattering angle over a high number of scattering events. g can be evaluated with the Mie theory . br If g 0, l l . A single scattering is already isotropic. br If g 1, l infinite. A single scattering doesn t deviate the photons. Then the scattering never gets isotropic. This length is useful for renormalizing a non isotropic scattering problem into an isotropic one in order to use classical diffusion laws Fick law and Brownian motion . The transport length might be measured by transmission experiments of backscattering experiments. ref Talanta, Volume 50, Issue 2, 13 September 1999, Pages 445 456 ref ref P. Snabre, A. Arhaliass, Anisotropic scattering of light in random media. Incoherent backscattered spot light, Appl. Optics 37 18 1998 211 225. ref gallery Image figure mean free path.png Mean free path simple scheme gallery References references External links http www.formulaction.com tech mls gb.html Illustrated description movies of multiple light scattering and application to colloid stability Category Optics Category Colloids ... more details
No footnotes date January 2010 In physics , the attenuation length or absorption length is the distance math lambda math into a material when the probability has dropped to math 1 e math that a Elementary particle particle has not been Absorption electromagnetic radiation absorbed . Alternatively, if there is a beam of particles incident on the material, the attenuation length is the distance where the intensity physics intensity of the beam has dropped to math 1 e math , or about 63 of the particles have been stopped. Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer Lambert law math P x e x lambda , math . In general math lambda math is material dependent. See also Beer s Law Mean free path Attenuation coefficient Attenuation electromagnetic radiation Radiation length References S. Eidelman et al. Particle Data Group , Review of particle physics , Phys. Lett. B 592 2004 http pdg.lbl.gov http www.ct.infn.it rivel Glossario node2.html External links http henke.lbl.gov optical constants atten2.html Category Particle physics Category Experimental particle physics particle stub de Absorptionsl nge it Lunghezza di attenuazione ... more details
In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic interacting elementary particle particles with it. Definition High energy electrons 10 MeV predominantly lose energy in matter by bremsstrahlung , and high energy photons by SubatomicParticle Antielectron SubatomicParticle Electron pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length math X sub 0 sub , usually measured in g cm sup 2 sup . It is both the mean distance over which a high energy electron loses all but math frac 1 e mathematical constant e of its energy by bremsstrahlung, and frac 7 9 of the mean free path for pair production by a high energy photon. It is also the appropriate scale length for describing high energy electromagnetic cascades. The radiation length for a given material consisting of a single type of nuclei can be approximated by the following expression ref cite book last Eidelman first S. title Review of Particle Physics ref math X 0 frac 716.4 cdot A Z Z 1 ln frac 287 sqrt Z mathrm g cdot mathrm cm 2 frac 1432.8 cdot A Z Z 1 11.319 ln Z mathrm g cdot mathrm cm 2 math , where math Z is the atomic number and math A is mass number of the nucleus. For electrons at lower energies below few tens of MeV s , the energy loss by ionization is predominant. While this definition may also be used for other electromagnetic interacting particles beyond lepton s and photons, the presence of the stronger strong interaction hadronic and Nuclear force nuclear interaction makes it a far less interesting characterisation of the material the nuclear collision length and nuclear interaction length are more relevant. Comprehensive tables for radiation lengths and other properties of materials are available from http pdg.lbl.gov AtomicNuclearProperties See also Mean free path Attenuation length Attenuation coefficient Attenuation Range particle radiation Stopping power ... more details
math . The math rho math length of a path is defined as the sum of math rho e math over all edges ... is math A rho sum v in V rho v 2 math , and the length of a path is the sum of math rho v math over ... length of a collection of curve s math Gamma math is a conformal invariant of math Gamma ... length of math Gamma math is equal to the extremal length of the image of math Gamma math under math f math . For this reason, the extremal length is a useful tool in the study of conformal mappings. Extremal length can also be useful in dimensions greater than two, but the following deals primarily with the two dimensional setting. Definition of extremal length To define extremal length ... gamma math we let math L rho gamma int gamma rho , dz math denote the math rho math length of math gamma math , where math dz math denotes the Euclidean distance Euclidean element of length. It is possible ... the measure of every subinterval math J subset I math is the length of the restriction of math ... integral math int I rho gamma t ,d mathrm length gamma t math , where math mathrm length gamma t math is the length of the restriction of math gamma math to math s in I s le t math . Also set math ... int D rho 2 ,dx ,dy, math and the extremal length of math Gamma math is math EL Gamma sup rho frac ... length of the collection of curves in math D math with one endpoint in one set and the other endpoint in the other set. Examples In this section the extremal length is calculated in several examples. The first three of these examples are actually useful in applications of extremal length. Extremal ... math R 0,w times 0,h math . Let math Gamma math be the set of all finite length curves math gamma ... gamma math has finite length. We will now prove that in this case math EL Gamma w h math First .... As the proof shows, the extremal length of math Gamma math is the same as the extremal length ... length of the family of curves math Gamma , math that connect the bottom edge of math ... more details
Sentence length may refer to In linguistics, the length of a Sentence linguistics In penology, the length of a Sentence law In music, the length of a Sentence music dab ... more details
Determining the length of an irregular arc segment is also called rectification of a curve . Historically ... points on the curve using line segment s to create a polygonal chain polygonal path . Since it is straightforward to calculate the length of each linear segment using the Pythagorean theorem in Euclidean space, for example , the total length of the approximation can be found by summation summing ... approximation are at the origin. If the curve is not already a polygonal path, better approximations ... arbitrarily small . For some curves there is a smallest number L that is an upper bound on the length ... and the curve is defined to have arc length L . Definition See also Curve Lengths of curves l1 Lengths ... is the length of the line segment connecting the two points. The arc length L of C is then defined to be math ... over all possible partitions of a , b and n is unbounded. The arc length L is either wiktionary .... This definition of arc length does not require that C be defined by a derivative differentiable ... a sum involving g can be made equal to a sum involving f. So the arc length is an intrinsic property ... of arc length for the curve is analogous to the definition of the total variation of a real valued function. Finding arc lengths by integrating See also Differential geometry of curves Length and natural ... continuous on a , b . The length s of the part of the graph of f between x a and x b can be found ... X t and y Y t , then its arc length between t a and t b is math s int a b sqrt X t 2 Y t 2 , dt. math ... length is given by math s int a b sqrt r 2 left frac dr d theta right 2 , d theta. math In most ... length and numerical integration is necessary. Curves with closed form solution for arc length ... length of an Ellipse Circumference elliptic arc led to the development of the elliptic integral s. Derivation ... Nowrap 1 y t sup 5 sup , x t sup 3 sup In order to approximate the arc length of the curve, it is split ... image and observe that its length element of the arc length will be the differential mathematics ... more details
Length measurement is implemented in practice in many ways. The most commonly used approaches are the transit ... Cosmic distance ladder . Transit time measurement The basic idea behind a transit time measurement of length is to send a signal from one end of the length to be measured to the other, and back again. The time for the round trip is the transit time t, and the length is then 2 t v , with v the speed ... is used in a transit time approach, length measurements are not subject to knowledge of the source ... Michelson interferometer with corner cubes.png thumb Measuring a length in wavelengths of light using ... using transit time measurements is used only as an initial indicator of length and is refined using ... how length is determined using a Michelson interferometer the two panels show a laser source ... leg as the left hand spacing is adjusted to compare the length of the object to be measured. In the top panel the path is such that the two beams reinforce each other after reassembly, leading to a strong light pattern sun . The bottom panel shows a path that is made a half wavelength longer by moving the left hand mirror a quarter wavelength further away, increasing the path difference by a half ... of path difference changes, and the observed intensity alternately peaks bright sun and dims ... an interferometer . By counting fringes it is found how many wavelengths long the measured path ... corresponding to a particular Atomic spectral line atomic transition . The length in wavelengths can be converted to a length in units of metres if the selected transition has a known frequency f . The length ... sub 0 sub f . With c sub 0 sub a defined value of 299,792,458 m s, the error in a measured length ... name Zheng ref name Roy ref name Paul This methodology for length determination requires a careful specification ... sup 11 sup depending upon the length measured, the wavelength and the type of interferometer used. ref .... It may be noted again, by way of contrast, that the transit time measurement of length is independent ... more details
wiktionarypar LengthLength in its basic meaning is the long dimension of an object. Length may also refer to Length measurement Length phonetics , in phonetics Vowel length Geminate consonant Arc lengthLength of a module , in abstract algebra Length of a polynomial Vector field length in vector calculus Line and length in cricket Horse length in equestrianism Nautical term Length overall disambig als L nge az Uzunluq d qiql dirm be x old ca Longitud desambiguaci de L nge es Longitud desambiguaci n nl Lengte nds L ng pl D ugo sv L ngd olika betydelser ... more details
orphan date December 2009 Scantling Length is a distance slightly less than the waterline length of a ship, and generally less than the overall length of a ship. In the American Bureau of Shipping ABS Rules for Building and Classing Steel Vessels, it is defined as the distance on the Waterline summer load line from the fore side of the stem to the centerline of the rudder stock. Scantling length need not be less than 96 , nor more than 97 of the length of the summer load line. Most other Classification society classification societies use a similar definition of scantling length to define the general length of a ship . The scantling length is used by classification society classification societies for all calculations where the waterline length, overall length, displacement fluid displacement length, etc is called for. Naval architects wishing to comply with class rules would also use the scantling length. References http www.eagle.org absdownloads downloads senddownload.cfm?id 443 ABS Rules for Building and Classing Steel Vessels, Part 3, Hull Construction and Equipment, Rule 3.1.1 3.1, 2007. Category Naval architecture ... more details
disambig Length scale , or scale length a significant concept in physics used to define the order of magnitude of a system Scale height , or scale length a specific parameter in physics denoting the distance over which a quantity decreases by a factor of e Scale string instruments a measurement of the length of a musical instrument string ... more details
In abstract algebra , the length of a module mathematics module is a measure of the module s size . It is defined to be the length of the longest chain of submodule s and is a generalization of the concept of dimension linear algebra dimension for vector space s. Modules with finite length share many important properties with finite dimensional vector spaces. Other concepts used to count in ring and module ... to define. There are also various ideas of dimension that are useful. Finite length commutative ... math N 0 subsetneq N 1 subsetneq cdots subsetneq N n math we say that n is the length of the chain. The length of M is defined to be the largest length of any of its chains. If no such largest length exists, we say that M has infinite length. A ring R is said to have finite length as a ring if it has finite length as left R module. Examples The zero module is the only one with length 0. Modules with length 1 are precisely the simple module s. For every finite dimensional vector space viewed as a module over the base field mathematics field , the length and the dimension coincide. The length ... M has finite length if and only if it is both Artinian module Artinian and Noetherian module Noetherian . If M has finite length and N is a submodule of M , then N has finite length as well, and we have length N length M . Furthermore, if N is a proper submodule of M i.e. if it is unequal to M , then length N length M . If the modules M sub 1 sub and M sub 2 sub have finite length, then so does their direct sum of modules direct sum , and the length of the direct sum equals the sum of the lengths ... sequence of R modules. Then M has finite length if and only if L and N have finite length, and we have length M length L length N . This statement implies the two previous ones. A composition series ... such that math N i 1 N i mbox is simple for i 0, dots,n 1 math Every finite length module M has a composition series, and the length of every such composition series is equal to the length of M . References ... more details
Contour length is a term used in molecular physics . The contour length of a polymer chain a big molecule consisting of many similar smaller molecules is its length at maximum physically possible Extension metaphysics extension . ref http iupac.org goldbook C01308.pdf Contour length in polymers http www.iupac.org publications compendium index.html IUPAC Compendium of Chemical Terminology , 2nd Edition, 1997 ref References small references small Category Polymer physics ... more details
Context date September 2010 A characteristic length is an important dimension that defines the scale of a physical system. Often such a length is used as an input to a formula in order to predict some characteristics of the system. Examples Reynolds number Biot number Nusselt number External links http www.answers.com topic characteristic length Definition physics stub DEFAULTSORT Characteristic Length Category Physical constants de Charakteristische L nge nl Hydraulische diameter pt Comprimento caracter stico ... more details
Unreferenced stub auto yes date December 2009 In physics , length scale is a particular length or distance determined with the precision of one order or a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group . In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength ... that is being probed. In relativistic mechanics time and length scales are related by the speed of light . In relativistic quantum mechanics or relativistic quantum field theory , length scales .... Often in high energy physics natural units are used where length, time, energy and momentum scales are described in the same units usually with units of energy such as GeV . Length scales are usually ... units of length squared and is measured in barn unit barn s. The cross section of a given process is usually the square of the length scale. Examples The atomic length scale is math ell a sim 10 10 ... ell a sim 1 alpha m e math . The length scale for the strong interaction s or the one derived from ... are roughly comparable. This length scale is determined by the range of the Yukawa potential . The lifetimes of strongly interacting particles, such as the rho meson , are given by this length scale ... are several times the associated energy scale 500 MeV to 3000 MeV . The electroweak length scale is shorter ... which is roughly 100 GeV. This length scale would be the distance where a Yukawa force is mediated ... more details
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