In mathematics , the product metric is a definition of metric mathematics metric on the Cartesian product of two metric spaces . As described below, the p product metric of the Cartesian product of n metric spaces is the Lp space p norm of the n vector of the norms of the n subspaces math d p mathbf x 1, dots, mathbf x n d 1 mathbf x 1 , dots, d n mathbf x n p math Definition Let math X, d X math and math Y, d Y math be metric spaces and let math 1 leq p leq infty math . Define the math p math product metric math d p math on math X times Y math by math d p left x 1 , y 1 , x 2 , y 2 right left d X x 1 , x 2 p d Y y 1 , y 2 p right 1 p math for math 1 leq p infty math math d infty left x 1 , y 1 , x 2 , y 2 right max left d X x 1 , x 2 , d Y y 1 , y 2 right . math for math x 1 , x 2 in X math , math y 1 , y 2 in Y math . Choice of norm For Euclidean space s, using the L sub 2 sub norm gives rise to the Euclidean metric in the product space however, any other choice of p will lead to a topologically equivalent metric space. In the category of metric spaces , the sup norm is used. References citation last1 Deza first1 Michel Marie author1 link Michel Deza last2 Deza first2 Elena page 83 publisher Springer Verlag title Encyclopedia of Distances url http books.google.com books?id LXEezzccwcoC&pg PA83 year 2009 . DEFAULTSORT Product Metric Category Metric geometry ... more details
In the mathematics mathematical study of metric spaces , one can consider the arclength of paths in the space ... to that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the length of all paths from one point to the other. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space. Definitions Let math M, d , math be a metric space . We define a new metric math d I , math on math M , math , known as the induced intrinsic metric , as follows math d I x,y , math is the infimum of the lengths ... M, d , math is a length space or a path metric space and the metric math d , math is intrinsic . We say that the metric math d , math has approximate midpoints if for any math varepsilon 0 math ... 2 varepsilon math . Examples Euclidean space R sup n sup with the ordinary Euclidean metric is a path metric space. R sup n sup 0 is as well. The unit circle S sup 1 sup with the metric inherited from the Euclidean metric of R sup 2 sup the chordal metric is not a path metric space. The induced intrinsic metric on S sup 1 sup measures distances as angle s in radian s, and the resulting length metric space is called the Riemannian circle . In two dimensions, the chordal metric on the sphere is not intrinsic, and the induced intrinsic metric is given by the great circle distance . Every Riemannian manifold can be turned into a path metric space by defining the distance of two points as the infimum ... is defined included Finsler manifold s and sub Riemannian manifold s. Any complete metric space complete and convex metric space is a length metric space harv Khamsi Kirk 2001 loc Theorem 2.16 , a result of Karl Menger . The converse does not hold in general, however there are length metric spaces ... by d . The space M , d sub l sub is always a path metric space with the caveat, as mentioned above, that d sub l sub can be infinite . The metric of a length space has approximate midpoints. Conversely ... more details
A spill metric is a Heuristic computer science heuristic metric used by Register allocation register allocators to decide which registers to spill. Popular spill metrics are cost degree introduced in Chaitin s algorithm cost degree sup 2 sup emphasizes the spill s effect on neighbours cost emphasizes Run time program lifecycle phase run time minimising number of spill operations Where cost is the estimated cost of spilling a value from registers into memory. DEFAULTSORT Spill Metric Category Digital registers compu stub ... more details
Notability date July 2010 Metric Today is the newsletter of the U.S. Metric Association . It features the latest developments in US metrication efforts. In the spirit of international standardization, it is dimensioned to the A4 paper size . External links http lamar.colostate.edu hillger mtoday.htm Official site Category Metrication ... more details
Image Metric Marvels.png thumb right The Metric Marvels, from left to right Meter Man, Liter Leader, Wonder Gram and Super Celsius The Metric Marvels is a series of seven animation animated educational short film shorts featuring songs about metre meters , litre liters , Celsius , and gram s, designed to teach United States American children how to use the metric system . They were produced by George Newall Newall & Thomas G. Yohe Yohe , the same advertising agency which produced American Broadcasting Company ABC s popular Schoolhouse Rock series, and first aired on the NBC television network in September 1978. Voices for the Metric Marvels shorts included Lynn Ahrens , Bob Dorough , Bob Kaliban , and Paul Winchell . Origins On December 23, 1975, President Gerald Ford signed the Metric Conversion Act into law this act gave official sanction for the United States to convert to the metric system of measurement. Traditionally, the United States has used and continues to prefer the United States customary units U.S. Customary system over metric measurements. Ford s presidential successor, Jimmy Carter , began to implement this law in earnest, helping to set up the U.S. Metric Board as a task force to determine when and how the U.S. would Metrication in the United States convert to metrics ... service announcement s on radio and television. The Metric Marvels was one such television PSA, aired during NBC s Saturday morning cartoons. The shorts featured four animated metric superheroes Liter ... children the difference between the old English system and the new metric system. Episodes 1 1 Meet Meter Man superhero Meter Man helps people convert length and distance to metric terms 1 2 Mara Mara ... Baby a young Wonder Gram converts pounds to kilograms Effectiveness Ultimately, The Metric Marvels failed to convince Americans to convert to the metric system. Although it shared the animation style ... 0320888 The Metric Marvels tv.com 19791 The Metric Marvels DEFAULTSORT Metric Marvels, The Category ... more details
This article is about the concept in Riemannian geometry . For the typographic concept, see Typeface Font metrics . Merge to metric connection discuss Talk metric connection merge metric compatibility here? date September 2011 In mathematics, given a metric tensor math g ab math , a covariant derivative is said to be compatible with the metric if the following condition is satisfied math nabla c , g ab 0. math Although other covariant derivatives may be supported within the metric, usually one only ever considers the metric compatible one. This is because given two covariant derivatives, math nabla math and math nabla math , there exists a tensor for transforming from one to the other math nabla a x b nabla a x b C ab c x c. math If the space is also torsion tensor torsion free , then the tensor math C ab c math is symmetric in its first two indices. References cite arxiv last Rodrigues first W. A. last2 Fern ndez first2 V. V. last3 Moya first3 A. M. year 2005 title Metric compatible covariant derivatives eprint math 0501561 Citation last Wald first Robert M. title General Relativity book General Relativity publisher University of Chicago Press year 1984 isbn 0 226 87033 2 Category Differential geometry Category Riemannian geometry Relativity stub ... more details
In mathematics , a metric connection is a connection vector bundle connection in a vector bundle E equipped with a metric vector bundle metric Red link until someone wants to write an appropriate article. metric tensor isn t right. for which the inner product of any two vectors will remain the same when those vectors are parallel transport ed along any curve. Other common equivalent formulations of a metric connection include A connection for which the connection vector bundle covariant derivative s of the metric on E vanish. A connection principal bundle principal connection on the bundle of orthonormal frame s of E . A special case of a metric connection is the Levi Civita connection . Here the bundle E is the tangent bundle of a manifold. In addition to being a metric connection, the Levi Civita connection is required to be torsion tensor torsion free . Riemannian connections An important special case of a metric connection is a Riemannian connection . This is a connection math nabla math on the tangent bundle of a pseudo Riemannian manifold M , g such that math nabla X g 0 math for all vector fields X on M . Equivalently, math nabla math is Riemannian if the parallel transport it defines preserves the metric g . A given connection math nabla math is Riemannian if and only if math Xg Y,Z g nabla XY,Z g Y, nabla XZ math for all vector fields X , Y and Z on M , where math Xg Y,Z math denotes the derivative of the function math g Y,Z math along this vector field math X math . The Levi Civita connection is the torsion tensor torsion free Riemannian connection on a manifold. It is unique by the fundamental theorem of Riemannian geometry . External links http projecteuclid.org Dienst UI 1.0 Summarize euclid.cmp 1103858479 a pdf about this Category Connection mathematics Category Riemannian geometry differential geometry stub de Metrischer Zusammenhang ru ... more details
In mathematics , the metric derivative is a notion of derivative appropriate to Parametric equation parametrized path topology paths in metric space s. It generalizes the notion of speed or absolute velocity to spaces which have a notion of distance i.e. metric spaces but not direction such as vector space s . Definition Let math M, d math be a metric space. Let math E subseteq mathbb R math have a limit point at math t in mathbb R math . Let math gamma E to M math be a path. Then the metric derivative of math gamma math at math t math , denoted math gamma t math , is defined by math gamma t lim s to 0 frac d gamma t s , gamma t s , math if this Limit mathematics limit exists. Properties Recall that absolute continuity AC sup p sup I X is the space of curves I X such that math d left gamma s , gamma t right leq int s t m tau , mathrm d tau mbox for all s, t subseteq I math for some m in the Lp space L sup p sup space L sup p sup I R . For AC sup p sup I X , the metric derivative of exists for Lebesgue measure Lebesgue almost all times in I , and the metric derivative is the smallest m L sup p sup I R such that the above inequality holds. If Euclidean space math mathbb R n math is equipped with its usual Euclidean norm math math , and math dot gamma E to V math is the usual Fr chet derivative with respect to time, then math gamma t dot gamma t , math where math d x, y x y math is the Euclidean metric. References cite book author Ambrosio, L., Gigli, N. & Savar , G. title Gradient Flows in Metric Spaces and in the Space of Probability Measures publisher ETH Z rich, Birkh user Verlag, Basel year 2005 isbn 3 7643 2428 7 Category Differential calculus Category Metric geometry ... more details
In mathematics , a metric space is a Set mathematics set where a notion of distance called a metric mathematics metric between elements of the set is defined. The metric space which most closely corresponds ... of metric is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length ... depend on the metric chosen, and by using a different metric we can construct interesting non Euclidean geometries such as those used in the theory of general relativity . A metric space also induces ... abstract topological space s. History Expand section Reasons for generalizing the Euclidean metric, first ... metric spaces in his work Sur quelques points du calcul fonctionnel , Rendic. Circ. Mat. Palermo 22 1906 1 74. Definition A metric space is an ordered pair math M,d math where math M math is a set and math d math is a metric mathematics metric on math M math , i.e., a function math d colon ... writes math M math for a metric space if it is clear from the context what metric is used. Examples of metric spaces Finite Metric space redirects here Ignoring mathematical details, for any system of roads ... route connecting those locations. To be a metric there shouldn t be any one way roads. The triangle ... n math space with the Euclidean distance , are complete space complete metric spaces. The rational number s with the same distance also form a metric space, but are not complete. The positive real numbers with distance function math d x,y vert log y x vert math is a complete metric space. Any normed vector space is a metric space by defining math d x,y lVert y x rVert math , see also Metric 28mathematics ... metric space complete , we call it a Banach space . Examples The Norm mathematics Taxicab norm or Manhattan ... chess chess king would take to travel from math x math to math y math . The British Rail metric also called the Post Office metric or the SNCF metric on a normed vector space is given by math d x ... more details
In psychology and sociology , a trust metric is a measurement of the degree to which one social actor an individual or a group trusts another social actor. Trust metrics may be abstracted in a manner that can ... that make a particular metric better than others, as each metric is designed to serve different .... of Eleventh Americas Conf. on Information Systems, Omaha, NE, USA pp. 2419 2427. ref uses a survey ... , or lack of information, or a deep distrust. Negative values, if allowed, usually indicate distrust ..., information available to him etc. In the same situation other trustors may have a different level of a subjective ..., disbelief, uncertainty, atomicity . The logic for uncertain probabilities is an example of a metric ... link between this formal metric and empirically observable behaviour. Finally, there are CertainTrust .... Properties of trust metrics The set of properties that should be satisfied by the trust metric ... metric. Transitivity Transitivity is a highly desired property of a trust metric. ref Richters, O., Peixoto ... transitivity does not always hold, based on information on the Advogato model and, consequently ... is contextual is a foundation of a collaborative filtering . Operations For the formal metric to be useful ... by another one. The exact semantic of both operators are specific to the metric. Even within one representation ... another desired property, meaning that it is computationally feasible to calculate the metric for large networks. Scalability usually puts two requirements of the metric The elementary operation e.g. ... which reflects their ability not to be overly influenced by agents who try to manipulate the trust metric ... trust metric rather similar to that behind Advogato. See also Trust sociology Trustworthiness .... Raph Levien , 2000. http www.advogato.org trust metric.html Advogato s trust metric . Electronic ... Metric Metadata HOWTO . Electronic manuscript. http p2pfoundation.net Trust Metrics Trust Metrics by P2P ... a Trust Network API for 3rd parties DEFAULTSORT Trust Metric Category Reputation management Category ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name Alex Metric background non performing personnel alias Alex Drury origin London , England genre House music House , techno , funk years active 2008 present associated acts The Infadels br Charli XCX website URL alexmetric.com Alex Metric born Alex Drury is a British musician, DJ and producer. He has released numerous EPs, remixed artists ... for acts such as The Infadels , Charli XCX and Adam Freeland . Career Alex Metric started ... http www.marineparade.net artists alex metric ref In 2009, Metric joined Radio 1 s In New DJs We Trust with his first show on June 12, 2009. Metric quit the station at the end of 2010 to concentrate ... alex metric brodinski ref 2011 saw the release of his collaboration with Steve Angello open Your Eyes on Virgin Positive which stayed on the BBC Radio 1 A list for 4 weeks. A compilation of Alex Metric ... Boys. In 2010, Metric completed his rock n rave production work for the Infadel s forthcoming ... . Gravity Boy is expected to be released sometime in the fall of 2011. More recently, Alex Metric & Steve ... for their vocal version of the electro house centric track, Open Your Eyes . Metric also collaborated ... Bush. Alex Metric is a regular at clubs and festivals around the world with his DJ sets and Live shows ... 4 , as intro and gameplay music. Discography ref http www.discogs.com artist Alex Metric ref Singles ... Alex Metric Bootleg Metric Monster Hospital Alex Metric Bootleg Stress Thriller Alex Metric Mash Up Cassius Sound of Violence Alex Metric Re Edit Blur Song 2 Alex Metric Festival Edit Eurythmics Sweet Dreams Alex Metric Bootleg Cheryl Cole Parachute Alex Metric Bootleg References reflist colwidth ... alexmetric youtube u alexmetric Persondata Metadata see Wikipedia Persondata . NAME Metric, Alex ... Metric, Alex Category British electronic musicians Category British radio presenters Category Remixers Category Living people it Alex Metric ru Alex Metric ... more details
A risk metric is the abstract concept in financial risk management quantified by risk measure s. When choosing a risk metric, an agent is picking an aspect of perceived risk to investigate, such as volatility finance volatility or mean return. ref name Holton cite journal last Holton first Glyn A. year 2004 title Defining risk journal Financial Analysts Journal volume 60 issue 6 pages 19 25 url http www.riskexpertise.com papers risk.pdf format pdf accessdate March 11, 2012 ref Risk measure and risk metric In a general sense, a measure is an algorithm for quantifying something. A metric is our interpretation of the number. ref name glossary cite web author Glyn A. Holton year 2002 title Risk Measure and Risk Metric url http www.riskglossary.com link risk metric and risk measure.htm accessdate March 11, 2012 ref In other words, the method or formula to calculate a risk metric is called a risk measure. Value at risk metric The VaR risk metric summarizes the Probability distribution distribution of possible losses by a Quantile function quantile , a point with a specified probability of greater losses. ref name Jorion cite book last Jorion first Philippe title Value at Risk The New Benchmark for Managing Financial Risk edition 3rd publisher McGraw Hill year 2006 isbn 978 0071464956 ref Examples Standard deviation or volatility finance Volatility Mean Absolute deviation Expected shortfall Sharpe ratio Sortino ratio Value at risk See also Risk measure Coherent risk measure Deviation risk measure Spectral risk measure Distortion risk measure References Reflist Finance stub Category Financial risk ... more details
Unit of length m 1600 accuracy 4 number of significant figures Metric mile is a distance which approximates one statute mile 1609.344 m at a round figure of metre s the SI or metric unit of length . The term is most commonly used in track running and swimming sport swimming . In track running, the 1500 metres 1500 m race became the standard middle distance track event middle distance race in Europe in the late 19th century, ref name nelsonpluquercetania cite book last Nelson first Cordner coauthors Quercetani, Roberto title The Milers url date 1985 isbn 0 911521 15 1 unused data p.14 ref and has been the standard distance in the Olympic Games since 1896. The distance of the race is sometimes referred to as a metric mile. ref cite web url http www.britannica.com eb article 9052542 middle distance running title Middle distance running accessdate 2008 01 13 ref However, even in countries which do not embrace the metric system, most running tracks have a lap distance of 400 metres in the innermost lane. The standard middle distance in many United States high school competitions, for instance, is four times around the track, and this 1600 m distance is sometimes referred to as a metric mile as well. See also Metric foot Metrication Scandinavian mile References reflist Category Units of length Category Athletics track and field terminology Category Middle distance running Track running Category Decimalisation ... more details
In mathematics , the Wasserstein or Vasershtein metric is a metric mathematics distance function defined between probability measure probability distribution s on a given metric space M . Intuitively, if each distribution is viewed as a unit amount of dirt piled on M , the metric is the minimum cost of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved. Because of this analogy, the metric is known in computer science ... Germanic origin . Definition Let M , d be a metric space for which every probability measure on M ... of all probability measures on M with Moment mathematics Moments in metric spaces finite ... sub p sub notation. The Wasserstein metric may be equivalently defined by math W p mu, nu p inf ... and respectively. Applications The Wasserstein metric is a natural way to compare the probability ... uniform perturbations random or deterministic . In computer science, for example, the metric W sub ... images . Properties Metric structure It can be shown that W sub p sub satisfies all the axiom s of a metric mathematics metric on P sub p sub M . Furthermore, convergence with respect to W sub p sub ... Radon metric math rho mu, nu sup left left. int M f x , mathrm d mu nu x right mbox continuous f M to 1, 1 right . math If the metric d is bounded by some constant C , then math 2 W 1 mu, nu leq C rho mu, nu , math and so convergence in the Radon metric also known as strong convergence implies convergence in the Wasserstein metric, but not vice versa. Separability and completeness For any p 1, the metric space P sub p sub M , W sub p sub is Separable space separable , and is Complete space complete if M , d is separable and complete. See also L vy metric L vy Prokhorov metric Transportation theory References cite book author Ambrosio, L., Gigli, N. & Savar , G. title Gradient Flows in Metric ... metric title Wasserstein metric Category Measure theory Category Metric geometry Category Probability ... more details
black hole has a Schwarzschild metric, and cannot be distinguished from any other Schwarzschild ... metric would cross the r r sub s sub singularity in a finite amount of proper time even ... metric, again showing that the singularity at r r sub s sub was a coordinate artifact ... title Maximal extension of Schwarzschild metric journal Phys.Rev. volume 119 pages 1743 1745 doi 10.1103 ... identification of the r r sub s sub singularity in the Schwarzschild metric as an event ... metric Main Deriving the Schwarzschild solution In Schwarzschild coordinates , the Schwarzschild metric has the form math c 2 d tau 2 left 1 frac r s r right c 2 dt 2 left 1 frac r s r ... metric is a solution of Einstein s field equation Vacuum field equations Einstein s field equations ... at r 0 and r r sub s sub some of the metric components blow up at these radii. Since the Schwarzschild metric is only expected to be valid for radii larger than the radius ... the metric becomes regular at r r sub s sub and can extend the external patch ... the metric, and space time itself, is no longer well defined. For a long time it was thought ... of the Schwarzschild metric The original form of the Schwarzschild metric involves anisotropic ... metric in terms of isotropic coordinates provided r 2GM c sup 2 sup ref H. A. Buchdahl, Isotropic coordinates and Schwarzschild metric , International Journal of Theoretical Physics, Vol.24 1985 pp. 731 ... sub 1 sub , the metric is math c 2 d tau 2 frac 1 frac GM 2c 2 r 1 2 1 frac GM 2c 2 r 1 2 , c 2 d t 2 ... the metric then becomes math c 2 d tau 2 frac 1 frac GM 2c 2 r 1 2 1 frac GM 2c 2 r 1 2 , c 2 d ... within it match distances in the Schwarzschild metric, because with the definition of w above, math ... is useful for visualizing the spatial curvature of the Schwarzschild metric. It should not, however ... mass, not away. See the gravity well article for more information. Flamm s paraboloid may be derived ... more details
Metric time is the measure of time interval using the metric system , which defines the second as the base unit of time, and multiple and submultiple units formed with SI prefix metric prefixes , such as kiloseconds ... scales, which may be based upon the metric definition of the second. Other units of time, the minute , hour , and day , are accepted for use with the SI modern metric system , but are not part of it. History When the metric system was introduced in France in 1795, it included units for length, area ... of day had been introduced in France two years earlier, but was set aside at the same time the metric system was inaugurated, and did not follow the metric pattern of a base unit and prefixed units. James ... and magnetic metric units, following the recommendation of Carl Friedrich Gauss in 1832. The ephemeris ... metric system, or International System of Units SI , at the 10th Conf rence G n rale des Poids et ... see also Decimal time Numerous proposals have been made for alternative base units of metric time. On March 28, 1794, the president of the commission which developed the metric system , Joseph Louis ..., meck, chi, chron, moment, etc., and multiple and submultiple units formed with metric prefixes ... it was a decimal multiple, not a sexagesimal one . Adopting a metric time system would suggest that a new base unit not named a second would be more consistent with the base 10 structure of the metric ... unit of metric time, but the proposal did not gain acceptance and was eventually abandoned. ref ... Louis Galison ref Alternative meaning Metric time is sometimes used to mean decimal time . Metric ... upon the metric base unit of time, the second. Some proposals for alternative units of metric time .... Other proposals called metric time refer only to decimal time, and therefore are not truly metric. France French decimal time is sometimes called metric time because it was introduced around the same time as the metric system and both were decimal, but it was not part of the decree creating the original ... more details
dablink This article is about the measurement of performance. For metric units, see Metric system and International System of Units . For disambiguous use, see Metric disambiguation A metric is a standard unit of measure , such as meter or mile for length, or gram or ton for weight, or more generally, part of a system of parameters, or systems of measurement , or a set of ways of for quantitatively and periodically measuring, assessing, controlling or selecting a person, process, event, or institution, along with the procedures to carry out measurements and the procedures for the interpretation of the assessment in the light of previous or comparable assessments. Metrics are usually specialized by the subject area, in which case they are valid only within a certain domain and cannot be directly benchmarked or interpreted outside it. This factor severely limits the applicability of metrics, for instance in comparing performance across domains. The prestige attached to them may be said to relate to a quantifiability fallacy , the erroneous belief that if a conclusion is reached by quantitative measurement, it must be vindicated, irrespective of what parameters or purpose the investigation is supposed to have. In business, they are sometimes referred to as key performance indicators , such as overall equipment effectiveness , or key risk indicators . In the field of Facilities Management, a key metric is the Facility Condition Index , or FCI . For a measure to be a metric it has to satisfy four properties 1 non negativity, 2 reflexivity, 3 symmetry, and 4 triangular inequality ref name AG S. Theodoridis and K. Koutroumbas, Pattern Recognition , Fourth Edition, Academic Press, 2009, p. 602. ref references See also Indicator Measure mathematics Measurement Metric mathematics Metrics networking Software metric Category Metrics de Metrik ... more details
The Vaidya metric describes exterior gravitational field due to a radiating star. The metric was proposed by P. C. Vaidya in 1943. It is a non static generalization of the Schwarzschild metric . math ds 2 left 1 frac 2M u r right du 2 2dudr r 2 left d theta 2 sin 2 theta d varphi 2 right math where M u is the mass parameter. References T. Padmanabhan 2010 . http books.google.com books?id BSfe2MjbQ3gC Gravitation Foundations and Frontiers . Cambridge University Press. ISBN 0521882230. pp. 313 314. Category Exact solutions in general relativity Category Gravitation Category Astrophysics ... more details
A software metric is a measure of some property of a piece of software or its specifications. Since quantitative measurements are essential in all sciences, there is a continuous effort by computer science practitioners and theoreticians to bring similar approaches to software development. The goal is obtaining objective, reproducible and quantifiable measurements, which may have numerous valuable applications in schedule and budget planning, cost estimation, quality assurance testing, software debugging, software performance optimization, and optimal personnel task assignments. Common software measurements Common software measurements include Balanced scorecard Software bug Bugs per line of code COCOMO Code coverage Cohesion computer science Cohesion Comment density ref cite web title Descriptive Information DI Metric Thresholds url http www.lsec.dnd.ca qsd current version eng support di metrics.htm work Land Software Engineering Centre accessdate 19 October 2010 ref Connascent software components Coupling computer science Coupling Cyclomatic complexity McCabe s complexity DSQI design structure quality index Function point analysis Halstead complexity measures Halstead Complexity Instruction path length Number of classes and interfaces Source lines of code Number of lines of code Number of lines of customer requirements Run time program lifecycle phase Program execution time Loader computing Program load time Binary file Program size binary Robert Cecil Martin s software package metrics Weighted Micro Function Points Limitations As software development is a complex process, with high variance on both methodologies and objectives, it is difficult to define or measure software qualities and quantities and to determine a valid and concurrent measurement metric, especially ... Metric Ohloh quantitative analysis of hundreds of open source projects Programming complexity ... treatment of software engineering metrics DEFAULTSORT Software Metric Category Software metrics ... more details
In mathematics , a metric or distance function is a function mathematics function which defines a distance between elements of a Set mathematics set . A set with a metric is called a metric space . A metric induces a topology on a set but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable . In differential geometry , the word metric is also used to refer to a structure defined only on a differentiable manifold which is more properly termed a metric tensor or Riemannian or pseudo Riemannian metric . Definition A metric ... by the others. A metric is called an ultrametric space ultrametric if it satisfies the following ... x , y , z in X , d x , z max d x , y , d y , z A metric d on X is called intrinsic metric intrinsic ... invariance translation invariant metric if d x , y d x a , y a for all x , y and a in X . Notes ... Main Metric space Examples of metric spaces The discrete space discrete metric if x y then d x , y 0. Otherwise, d x , y 1. The Euclidean metric is translation and rotation invariant. The Taxicab geometry taxicab metric is translation invariant. More generally, any metric induced by a norm ... x y 1 p n x y math is a metric defining the same topology . One can replace math frac 1 2 n math by any absolute convergence summable sequence math a n math of strictly positive number s. Graph metric , a metric defined in terms of distances in a certain graph. The Hamming distance in coding theory. The Fubini Study metric on complex projective space . Equivalence of metrics For a given set X , two ..., if math d math is a metric, then math min d, 1 math and math d over 1 d math are metrics equivalent to math d. math See also Metric space Notions of metric space equivalence notions of metric ... words, every norm determines a metric, and some metrics determine a norm. Given a normed vector space math X, cdot math we can define a metric on X by math d x,y x y math . The metric d is said to be induced ... more details
, pp. 1203 1225 ref See also Acoustic metric Apophysis software Complete metric Fractal compression Fractal image compression Image differencing Metric tensor Multifractal system Sources and notes ... of the Hutchinson Metric Between Digitized Images Category Metric geometry Category Topology ... more details
Kavanagh, M.J. & Thite, M. 2009 . Human Resource Information Systems Basics, Applications, and Future ... functions Kavanagh & Thite, 2009 ref Kavanagh, M.J. & Thite, M. 2009 . Human Resource Information ... in terms of reducing cost. HR metric & Human Capital Human Capital is another big topic in nowadays ... programs and concrete action plans Working with HR to simplify metric and automate data collection ... more details
cleanup date January 2012 refimprove date January 2012 Infobox musical artist name Metric image Metric ... br Post punk revival years active 1998&ndash present label Metric Music International br Last Gang ... past members Metric is a Canadian indie rock ref name autogenerated1 and New Wave music New Wave band ... , New York City and Los Angeles . Metric consists of vocalist Emily Haines who also plays the synthesizer ... network.nationalpost.com np blogs theampersand archive 2009 03 12 250672.aspx title Metric moves up ... Awards . Metric won as well in 2010 Juno Award for Group of the Year Group of the Year . History ... title Metric Music Podcast work Access All Areas date 7 September 2009 ref and AAA Shaw said ... to eat. In 1999, Shaw and Haines decided to call their partnership Metric , after a synthesizer beat ... in this period and offered to bring Metric to the UK for a possible record deal. Eager ... acts as Erasure , New Order , and the Pet Shop Boys , Metric worked on a new batch of New Wave ... in the years ahead with their musical mix. Although Metric already had a semi mainstream appeal, they felt ... Metric continued to work on their debut album in the first few months of 2001. Now dubbed Grow Up ... . Image Jimmy Shaw of Metric.jpg thumb right upright Jimmy Shaw of MetricMetric had also gained ... a decade and they met Haines and Shaw at the Brooklyn loft and at local performances. Metric at the time ... show at Black Betty s in Williamsburg. Metric performed in New York in early Spring and late Summer ..., eventually giving the music away for free on the internet. Metric received their first major ... 2003 2004 In 2003, Metric released their first official album Old World Underground, Where Are You .... The album was produced by Michael Andrews Metric was featured as themselves in the 2004 independent ... also features songs by Brian Eno , Daniel Lanois , Emily Haines , Metric and Tricky . Live It Out and Grow Up and Blow Away 2005 2007 Two years later, Metric released their second studio album, Live ... more details
In mathematics, the original Kobayashi metric is a pseudometric space pseudometric or pseudodistance on complex manifold s introduced by harvs txt authorlink Shoshichi Kobayashi last Kobayashi year 1967 . It can be viewed as the dual mathematics dual of the Carath odory metric , and has been extended to complex analytic space s and almost complex manifold s. On Teichm ller space the Kobayashi metric coincides with the Teichm ller metric on the unit ball, it coincides with the Bergman metric . An analogous pseudodistance was constructed for flat affine and projective structures in harvs txt authorlink Shoshichi Kobayashi last Kobayashi year 1977 and then generalized to normal projective connection s. Essentially the same construction has been applied to normal, pseudo Riemannian conformal connection s and, more recently, to general regular parabolic geometries. Definition If X is a complex manifold, the Kobayashi pseudometric d may be characterized as the largest pseudometric on X such that math d f x ,f y le rho x,y math , for all holomorphic maps f from the unit disk D to X where math rho x,y math denotes distance in the Poincar metric on D . References Cite journal last Kobayashi first Shoshichi title Intrinsic Metrics on Complex Manifolds journal Bull. Amer. Math. Soc. year 1967 volume 73 pages 347 349 url http www.ams.org journals bull 1967 73 03 S0002 9904 1967 11745 2 S0002 9904 1967 11745 2.pdf Citation last1 Kobayashi first1 Shoshichi title Hyperbolic manifolds and holomorphic mappings url http books.google.com books?id rleQdMhML6kC publisher Marcel Dekker Inc. location New York series Pure and Applied Mathematics isbn 978 0 8247 1380 5 mr 0277770 year 1970 volume 2 cite journal last Shoshichi first Kobayashi title Intrinsic distances associated with flat affine or projective structures journal J. Fac. Sci. Univ. Tokyo year 1977 volume 24 pages 129 135 mr 445016 Category Complex manifolds ... more details
General relativity cTopic Exact solutions in general relativity Solutions The Kasner metric is an Exact solutions in general relativity exact solution to Einstein s theory of general relativity . It describes an anisotropic universe without matter i.e., it is a vacuum solution . It can be written in any spacetime dimension math D 3 math and has strong connections with the study of gravitational Chaos theory chaos . The Metric and Kasner Conditions The Metric mathematics metric in math D 3 math spacetime dimensions is math text d s 2 text d t 2 sum j 1 D 1 t 2p j text d x j 2 math , and contains math D 1 math constants math p j math , called the Kasner exponents. The metric describes a spacetime whose equal time slices are spatially flat, however space is expanding or contracting at different rates in different directions, depending on the values of the math p j math . Test particles in this metric whose comoving coordinate differs by math Delta x j math are separated by a physical distance math t p j Delta x j math . The Kasner metric is an exact solution to Einstein s equations in vacuum when the Kasner exponents satisfy the following Kasner conditions, math sum j 1 D 1 p j 1, math math sum j 1 D 1 p j 2 1. math The first condition defines a plane geometry plane , the Kasner plane, and the second describes a sphere , the Kasner sphere. The solutions choices of math p j math satisfying the two conditions therefore lie on the sphere where the two intersect sometimes confusingly ... lie on a math D 3 math dimensional sphere math S D 3 math . Features of the Kasner Metric There are several ... Isotropic metric expansion of space expansion or contraction of space is not allowed. If the spatial ... be satisfied, for math sum j 1 D 1 p j 2 frac 1 D 1 ne 1. math The FRW metric employed in cosmology ... is actually contracting. The Kasner metric is a solution to the vacuum Einstein equations, and so ... in general relativity Category Metric tensors fr M trique de Kasner it Metrica di Kasner ... more details
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