The cluster of differentiationcluster of designation often abbreviated as CD is a protocol used for the identification and investigation of cell surface molecule s present on white blood cells initially but found in almost any kind of cell of the body, providing targets for immunophenotyping of cells. Physiologically, CD molecules can act in numerous ways, often acting as receptor biochemistry receptors or ligand biochemistry ligands the molecule that activates a receptor important to the cell. A signal cascade is usually initiated, altering the behavior of the cell see cell signaling . Some CD proteins do not play a role in cell signaling, but have other functions, such as cell adhesion . There are approximately 250 different proteins. List of human clusters of differentiation CD for humans is numbered up to 350 most recently As of 2009 lc y . ref name hcdm cite web title HCDM, responsible ... Cluster of differentiation.svg thumb Cluster of Differentiation The CD system is commonly used as cell ..., with colors, arrows from one cell to another, from eBioscience. Clusters of differentiation Surface antigens Category Anatomical pathology Category Clusters of differentiation cs Diferencia n skupina de Cluster of differentiation es C mulo de diferenciaci n fr Cluster de diff renciation id Kluster ... work publisher Human Cell Differentiation Molecules Council successor to the HLDA Workshops date ... PJ, Malavasi F, Mason D, Stockinger H, Yang X. title CD molecules 2006 human cell differentiation ... International Workshop and Conference on Human Leukocyte Differentiation Antigens HLDA , which was held ... L title Human leukocyte differentiation antigens language French journal Presse Med volume 13 issue ... before and after T helper 2 cell differentiation journal Nat. Rev. Immunol. volume 9 issue 2 pages 125 ... are critical in antigen recognition. See also List of human clusters of differentiation for a list ... search maintained by the Human Cell Differentiation Molecules Council successor to the HLDA Workshops ... more details
Wiktionarypar differentiationDifferentiation may refer to Differentiation mathematics , the process of finding a derivative Differentiated instruction in education Cellular differentiation in biology Planetary differentiation in planetary science Inductive reasoning aptitude in psychology Igneous differentiation in geology Product differentiation in marketing Differentiation linguistics Differentiation sociology Differentiation economics , the making a product different from other similar products Differentiation ethnography , the invention of ostensible differences between cultures disambig cs Diferenciace de Differenzierung fa fr Diff renciation hr Diferencijacija it Differenziazione nn Differensiering sk Diferenci cia sr uk ... more details
wiktionarypar cluster A cluster is a small group or bunch of something. In science Cluster physics , a small group of atoms or molecules Cluster chemistry , an array of bound atoms intermediate in character between a molecule and a solid Cluster sampling , a sampling technique used when natural groupings are evident in a statistical population Cluster analysis , a technique for statistical data analysis Consonant cluster , in linguistics In astrophysics Star cluster , groups of stars which are gravitationally bound Galaxy groups and clusters , large gravitationally bound objects Globular cluster , a spherical collection of stars that orbits a galactic core as a satellite Cluster mission , a European Space Agency mission to study the magnetosphere In biology and health sciences Cancer cluster , in biomedicine, an occurrence of a greater than expected number of cancer cases Cluster headache , a neurological disease that involves an immense degree of pain Cluster of differentiation , protocol .... Winter cluster , in beekeeping, a well defined cluster of honey bees in cold temperatures Cluster epidemiology , a grouping of cases of disease Genetic cluster , a group of genes or proteins, or metabolites ... Cluster computing , a group of loosely coupled computers that work together closely Data cluster , a group of disk sectors used in a File Allocation Table In music Tone cluster , a musical chord comprising at least three consecutive tones in a scale Cluster band , a German rock band Cluster Italian musical group , an a cappella jazz fusion group from Genoa, Italy Cluster album Cluster album , the 1971 eponymous album by the band ClusterCluster , a track from the album Ben Bu Sarkiyi Sana Yazdim by Cem Adrian Cluster One , the first track on Pink Floyd s 1994 album The Division Bell In engineering A bicycle cogset , either a freewheel, or cassette The instrument cluster of an automobile Other Cluster bomb , air dropped or ground launched shells Cluster diagram , general type of diagram, which ... more details
The term niche differentiation synonymous with niche segregation , niche separation and niche partitioning ... by the competitive exclusion principle thus, coexistence is obtained through the differentiation ... 6 pages 544 7 format PDF issue 4 ref Niche differentiation is a process which occurs through several different modes and on multiple temporal and spatial scales. In most cases, niche differentiation ... of this, the presence of niche differentiation can be methodologically difficult to prove or disprove ... species which occupy similar niches. It is important to keep in mind that niche differentiation and inter ... species . Niche differentiation detection and quantification The Lotka Volterra equation states that two ... inter specific between species competition Armstrong and McGehee 1980 . Since niche differentiation ... Volterra model predicts that niche differentiation of any degree will result in coexistence. In reality, this still leaves the question of how much differentiation is needed for coexistence Hutchinson ... to the amount of niche differentiation required for coexistence, and this can vary with the type of resource .... To answer questions about niche differentiation, it is necessary for ecologists to be able to detect ... the mechanisms of niche differentiation and competition, much data must be gathered on how the two species ... differentiation difficult and complex. Development of niche differentiation Over time, two competing species can either coexist, through niche differentiation or other means, or compete until one species becomes locally extinct . Several theories exist for how niche differentiation arises or evolves ... differentiation can arise from current competition. For instance, species X has a fundamental niche ... of niche differentiation through competition will be relatively easy. It is also important to remember ... niche. Via past extinctions The Ghost of Competition Past Another way by which niche differentiation ... no species is out competing any other species in the final community, the presence of niche differentiation ... more details
In mathematics , differentiation of measures may refer to the problem of differentiation of integrals , also known as the differentiation problem for measure theory measures the Radon Nikodym derivative of one measure with respect to another. mathdab ... more details
Refimprove date January 2009 Differentiation is a concept used in business strategy and describes one of the three ways to establish competitive advantage . Differentiation advantage occurs when a firm delivers greater services for a non unlimited higher price than its competitors. They are collectively known as positional advantages because they denote the firm s position in its industry as a leader in either superior services or cost. ref cite book title On Competition author Michael E. Porter publisher Harvard Business Review, Boston, 1998, p.40 42 ref Product differentiation is what allows firms in monopolistic competition a market structure to sell their products at different prices, even though they are essentially the same. See also Product differentiation Portal Business and economics References Reflist DEFAULTSORT Differentiation Economics Category Market structure and pricing econ term stub ar fr Diff renciation conomie it Vantaggio di differenziazione sv Differentiering marknadsf ring ... more details
In economics and marketing , product differentiation also known simply as Differentiation economics differentiation ... Chamberlin in his 1933 Theory of Monopolistic Competition . Rationale Differentiation can be a source ... in order to improve differentiation, the changes themselves are not differentiation. Marketing or product differentiation is the process of describing the differences between products or services ... s product and create a sense of value. Marketing textbooks are firm on the point that any differentiation ... to communicate a product s differentiation. ref Reeves, Rosser 1961 The Reality of Advertising. ref In economics , successful product differentiation leads to monopolistic competition and is inconsistent ... differentiation 1. Simple based on a variety of characteristics 2. Horizontal based on a single ... or an advertising theme. The physical product need not change, but it could. Differentiation is due to buyers perceiving a difference, hence causes of differentiation may be functional aspects of the product ... differentiation are as follows. Differences in Quality business quality which are usually accompanied ... and location . The Objective goal objective of differentiation is to develop a positioning marketing ... differentiated. Differentiation primarily impacts performance through reducing directness of competition ... fewer comparisons with its competition. A successful product differentiation strategy will move your ... . Most people would say that the implication of differentiation is the possibility of charging ... sensitive to aspects of competing offers price may not be one of these aspects. Differentiation .... ref Sharp, Byron Dawes, John 2001 , What is Differentiation and How Does it Work?, Journal of Marketing Management, 17, 739 59. ref Ethical concerns Some product differentiation approaches ... 1997 Jonathan B. Baker Director, Bureau of Economics Federal Trade Commission on Product Differentiation DEFAULTSORT Product Differentiation Category Marketing Category Product management Category ... more details
Unreferenced date December 2009 In mathematics , the linearity of differentiation is a most fundamental property of the derivative , in differential calculus . It follows from the sum rule in differentiation and the constant factor rule in differentiation . Thus it can be said that the act of differentiation is Linear map linear , or the differential operator is a Linear map linear operator . Let f and g be functions, with math alpha math and math beta math fixed. Now consider math frac mbox d mbox d x alpha cdot f x beta cdot g x math By the sum rule in differentiation , this is math frac mbox d mbox d x alpha cdot f x frac mbox d mbox d x beta cdot g x math By the constant factor rule in differentiation , this reduces to math alpha cdot f x beta cdot g x math This in turn leads to math frac mbox d mbox d x alpha cdot f x beta cdot g x alpha cdot f x beta cdot g x math Omitting the bracket s, this is often written as math alpha cdot f beta cdot g alpha cdot f beta cdot g math DEFAULTSORT Linearity Of Differentiation Category Differential calculus ca Linealitat de la derivaci eo Lineareco de diferencialado ... more details
Dablink Logarithmic derivative is a separate article. Calculus In calculus , logarithmic differentiation or differentiation by taking logarithms is a method used to derivative differentiate function mathematics function s by employing the logarithmic derivative of a function , ref cite book title Calculus demystified pages 170 first Steven G. last Krantz publisher McGraw Hill Professional year 2003 isbn 0071393080 ref math ln f frac f f math The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself. Logarithmic differentiation ... be implemented, at least in part, in the differentiation of almost all differentiable function s, providing that these functions are non zero. Overview For a function math y f x , math logarithmic differentiation ... , math After implicit differentiation ref name One cite book title Calculus of One Variable first Keith ... and before the preliminary differentiation. The most commonly used logarithm laws ref name Bird ... sigma notation math ln f x sum i alpha i x cdot ln f i x , math and after differentiation, math ... the chain rule chain and the sum rule in differentiation sum rules math frac f x f x frac ... rule in differentiation sum rules math frac f x f x frac g x g x frac h x h x math and, after rearranging ... rule chain and the sum rule in differentiation product rules math frac f x f x h x ln g x h x ... Differentiation Rules Logarithmic differentiation extratext see for textbook examples of logarithmic differentiation. Portal Mathematics Darboux derivative , Maurer Cartan form for generalizations to arbitrary ... links cite web url http www.mathcentre.ac.uk students topics differentiation by logs title Differentiation ... differentiation accessdate 2009 03 10 cite web url http tutorial.math.lamar.edu Classes CalcI LogDiff.aspx title Calculus I Logarithmic differentiation accessdate 2009 03 10 DEFAULTSORT Logarithmic Differentiation Category Differential calculus et Logaritmiline diferentseerimine nl Logaritmisch ... more details
Unreferenced date December 2009 Delayed differentiation or Postponement is a concept in supply chain management where the manufacturing process starts by making a generic or family product that is later differentiated into a specific end product. This is a widely used method, especially in industries with high demand uncertainty, and can be effectively used to address the final demand even if forecasts cannot be improved. An example would be Benetton Group Benetton and their knitted sweaters that are initially all white, and then dyed into different colors only when the season customer color preference demand is known. It is usually necessary to redesign the product specifically for delayed differentiation, and resequence to modify the order of production manufacturing steps. See also Postponement Mass customization Typically all paint companies were burdened with the problem of having more than 200 shades, each available in more than 5 container sizes, making more than 1000 Stock keeping Units SKUs . The cost of keeping so many final products was almost killing the business. Paint companies changed their process to make white paint and the dyes of three basic colours. The final mixing was done by a machine at the retail end. This minimised the inventory kept by the retailer whilst improving customer service by giving the customer a choice of millions of shades in the exact quantity required. DEFAULTSORT Delayed Differentiation Category Supply chain management ... more details
See articles sociology , sociological theory , social theory , and system theory Differentiation is a term ... of modern society is the increased process of system differentiation as a way of dealing with the complexity ... in an effort to copy within a system the difference between it and the environment. The differentiation ... to respond to variation in the environment. Increased variation facilitated by differentiation not only ... diversity variation the more differentiation and thus variation that is available, the better the selection. Ritzer 2007 95 96 Image Mosaicr seagull.jpg thumb 150px left Exemplifying Differentiation and System ... a cybernetic process of differentiation. Luhmann who studied under Talcott Parsons has adapted Parsons ... tendencies and the related path of structural differentiation but it would occur in a constant ... differentiation between subsystem would occur or not. In contrast to Luhmann, Parsons would ... of system differentiation. Generally, Parsons was of the opinion that the main gatekeeper blocking ... and evaluative lines of differentiation for example, the flower power movement in the 60s and early ... symbolization would tend to increase its impact vis a vis other factors of system differentiation ... of differentiation segmentation, stratification, center periphery, and functional. Niklas Luhmann main ... differentiation Segmentary differentiation divides parts of the system on the basis of the need to fulfill ... producing cars Ritzer 2007 96 . Stratifactory differentiation Stratificatory differentiation is a vertical differentiation according to Social rank rank or Social status status in a system conceived ... Management manager , trickling down to the assembly line worker. In Segmentary Differentiation Social ... to their level. Ritzer 2007 97 . Center periphery differentiation Center periphery differentiation ..., and to whatever extent controlling, the peripheral factories Ritzer 2007 98 . Functional differentiation Functional differentiation is the form that dominates modern society and is also the most ... more details
Sexual differentiation is the process of development of the differences between male s and female ... nurture nature and nurture . The early stages of human differentiation appear to be quite similar ... been found to direct production of a protein which binds to DNA, inducing differentiation of cells ... XX male s , SRY alone is sufficient to induce male differentiation. Investigation of other cases of human ... genes crucial to testicular differentiation on autosome s e.g., WT 1 , SOX9 , SF 1 , and the short arm of X DSS . Timeline Human prenatal sexual differentiation Fetal age br weeks Crown rump length ... of m llerian duct s 7 13 20 Differentiation of seminiferous tubules 8 30 Regression of m llerian ... Reproductive health Human sexual differentiation Table1.html PC Sizonenko in Pediatric Endocrinology .... 88 99. Gonadal differentiation Early in fetal life, germ cell s migrate from structures known ... cell s, supporting cells, and steroidogenic cells. In a male, SRY and other genes induce differentiation .... Hormonal differentiation In a male fetus, testes produce steroid hormone steroid and protein hormones essential for internal and external anatomic differentiation. Leydig cell s begin to make testosterone ... of prenatal sexual differentiation, as maternal estrogen floods fetuses of both sexes. Genital differentiation Main Development of the urinary and reproductive organs A differentiation of the sex organ can be seen. However, this is only the external genital differentiation. There is also an internal genital differentiation. Internal genital differentiation Gonad s are histologically distinguishable ... evidence of absence of testes than the state of the external genitalia . External genital differentiation .... Further sex differentiation of the external genitalia occurs at puberty , when androgen levels again ... via DHT the prostate . Breast differentiation Visible differentiation occurs at puberty , when estradiol ... . Hair differentiation The amount and distribution of body hair differs between the sexes. Males ... more details
Disputed date July 2009 Differentiation in semantics is defined by L bner 2002 as a meaning shift reached by adding concepts to the original concepts . His example is James Joyce is hard to understand , where understand is differentiated from perceiving the meaning to interpret the text meaning . A related meaning shift is metonymy , where one builds a new concept out of an element of the original concept. In the example mentioned, James Joyce most likely refers to the work of James Joyce and not to the author a metonymical shift. If the name were to refer to the man, understand would be differently differentiated, perhaps one would read it as interpret the speech articulation or comprehend the actions of the person James Joyce. Meaning shifts are very common among language users, and allow for great flexibility of word usage. It is not to be confused with lexical ambiguity though, words as uttered in a context may have perfectly precise meanings even though in varying contexts they may be used to express widely different meanings. See also meaning shift metonymy metaphor References Sebastian L bner, Understanding Semantics 2002 . Oxford University Press , ISBN 0 340 73198 2. DEFAULTSORT Differentiation Linguistics Category Semantics nn Tydingsskifte ... more details
Plant process by which the meristem shoot apical meristem changes its anatomy to generate a flower or inflorescence in lieu of new Node botany nodes with leaves . Anatomical changes begin at the edge of the meristem , generating first the outer whorls of the flower the sepal calyx and the Corolla flower corolla , and later the androecium and gynoecium . Flower differentiation can take from only a few days in annual plants to 4 11 months in fruit crops . The process is preceded by flower induction . Unreferenced date April 2008 Category Plant physiology ca Diferenciaci floral ... more details
In mathematics and computer algebra , automatic differentiation AD , sometimes alternatively called algorithmic differentiation , is a set of techniques to numerically evaluate the derivative of a function ... to working precision. Automatic differentiation is not Image AutomaticDifferentiationNutshell.png right thumb 300px Figure 1 How automatic differentiation relates to symbolic differentiation Symbolic differentiation , or Numerical differentiation the method of finite differences . These classical methods run into problems symbolic differentiation works at low speed, and faces the difficulty of converting a computer program into a single expression, while numerical differentiation can ... algorithms. Automatic differentiation solves all of these problems. The chain rule, forward and reverse ... Forward accumulation Forward accumulation automatic differentiation is the easiest to understand and to implement ... that all edge labels are unique and algebraically independent. Automatic differentiation using dual numbers Forward mode automatic differentiation is accomplished by augmenting the algebra ... , with ordinary arithmetics on the first component, and first order differentiation arithmetic on the second ... matlabcentral fileexchange 26807 automatic differentiation with matlab objects Adiff BSD lic OO ... 15235 automatic differentiation for matlab myAD BSD lic OO Forward 1st & 2nd derivative Python class ..., etc. http forre.st pyderiv pyderiv GPL lic OO automatic differentiation and co variance ... autodiff.codeplex.com AutoDiff GPL lic OO Automatic differentiation with C operators overloading. http funclib.codeplex.com FuncLib MIT License MIT OO Automatic differentiation and numerical optimization, operator overloading, unlimited order of differentiation, compilation to IL code for very fast ... Automatic Differentiation Techniques and Applications publisher Springer Science Business Media ... of Algorithmic Differentiation edition 2nd publisher Society for Industrial and Applied ... more details
In numerical analysis , numerical differentiation describes algorithm s for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function. Image Derivative.png right Finite difference formulae The simplest method is to use finite difference approximations. A simple two point estimation is to compute the slope of a nearby secant line through the points x , f x and x h , f x h . ref Richard L. Burden, J. Douglas Faires 2000 , Numerical Analysis , 7th Ed , Brooks Cole. ISBN 0 534 38216 9 ref Choosing a small number h , h represents a small change in x , and it can be either positive or negative. The slope of this line is math f x h f x over h . math This expression is Isaac Newton Newton s difference quotient . The slope of this secant line differs from the slope of the tangent line by an amount that is approximately proportional to h . As h approaches zero, the slope of the secant line approaches the slope ... the finite difference formulae are ill conditioned ref name Fornberg1 Numerical Differentiation of Analytic ... finite difference approximations for numerical differentiation are ill conditioned. However, if math ... . Using complex variables for numerical differentiation was started by Lyness and Moler in 1967. ref name LynessMoler1 J. N. Lyness AND C. B. Moler, Numerical differentiation of analytic functions ... of the function was developed by Fornberg. ref name Fornberg1 See also Automatic differentiation Finite ... Numerical smoothing and differentiation List of numerical analysis software Notes reflist External links ... 02dif.html Numerical Differentiation Resources Textbook notes, PPT, Worksheets, Audiovisual YouTube ... pavel ?page id 236 Smooth Noise Robust Numerical Derivative Numerical differentiation ... and smooth noise robust differentiators with reference tables. DEFAULTSORT Numerical Differentiation Category Numerical analysis Category Differential calculus cs Numerick derivace de Numerische Differentiation ... more details
unreferenced date May 2008 article In planetary science , planetary differentiation is the process of separating out different constituents of a planetary body as a consequence of their physical or chemical behaviour, where the body develops into compositionally distinct layers the density denser materials of a planet sink to the center, while less dense materials rise to the surface. Such a process tends to create a Planetary core core and Mantle geology mantle . Sometimes a chemically distinct Crust geology crust forms on top of the mantle. The process of planetary differentiation has occurred on planets, dwarf planet s, the asteroid 4 Vesta , and natural satellite s such as the Moon . Heating When the Sun ignited in the solar nebula , hydrogen , helium and other volatile materials were evaporated in the area near the Sun. The solar wind and radiation pressure forced such low density material away from the Sun. Rocks, and the elements comprising them, were stripped of their early atmospheres, but themselves remained, to accumulate in protoplanet s. Protoplanets had higher concentrations of radioactive elements early in their history, the quantity of which has reduced over time due to radioactive decay . Heating due to radioactivity, impacts, and gravitational pressure melted parts of protoplanets as they grew toward being planet s. In melted zones, it was possible for denser materials ... meteorite s show that differentiation took place in some asteroids. When protoplanets Accretion ... such as methane , water as liquid or ice, or frozen carbon dioxide . Chemical differentiation Note ... in the Earth s light, silicate rich crust than in the dense metallic core. Physical differentiation ... differentiation in magma chamber s. Differentiation through collision Earth s Moon has probably formed out of material splashed into orbit by the impact of a large body into the early Earth. Differentiation ... to its lack of a large iron core. Density differences on Earth On Earth , physical and chemical differentiation ... more details
Update EB date January 2011 In geology , igneous differentiation is an umbrella term for the various processes by which magma s undergo bulk chemical change during the partial melting process, cooling, emplacement or volcanic eruption eruption . Definitions Primary melts When a rock melts it melts to form a liquid, the liquid is known as a primary melt . Primary melts have not undergone any differentiation and represent the starting composition of a magma. In nature, primary melts are rarely seen. The leucosomes of migmatite s are examples of primary melts. Primary melts derived from the mantle ... the observed range of magma chemistries has been derived by the processes of igneous differentiation ... during the differentiation process of a magmatic event are known as cumulate rocks . Identifying whether ... important even for rocks which carry no phenocryst s. Underlying causes of differentiation The primary ... phenocrysts . Contamination is another cause of magma differentiation. Contamination can be caused ... chamber with fresh, hot magma. The whole gamut of mechanisms for differentiation has been referred ... between basalt and rhyolite literally an intermediate composition. Other mechanisms of differentiation ... layer. This can change the composition of the melt in large intrusion s, leading to differentiation ... sequence. ref name EB1911 Quantifying igneous differentiation There are several methods of directly measuring and quantifying igneous differentiation processes Whole rock geochemistry of representative ... radiogenic isotopes In all cases, the primary and most valuable method for identifying magma differentiation ... and describing field relationships and rock microstructure textural evidence for magma differentiation ... modeling of igneous differentiation http melts.ofm research.org MELTS Software package designed ... DEFAULTSORT Igneous Differentiation Category Igneous petrology Category Igneous rocks Category ... Magmatische Differentiation hr Magmatska diferencijacija he nl Magmadifferentiatie pl Dyferencjacja ... more details
In mathematics , the problem of differentiation of integrals is that of determining under what circumstances the average mean value integral of a suitable function mathematics function on a small neighbourhood topology neighbourhood of a point approximates the value of the function at that point. More formally, given a space X with a measure mathematics measure &mu and a metric space metric d , one asks for what functions f X &rarr R does math lim r to 0 frac1 mu big B r x big int B r x f y , mathrm d mu y f x math for all or at least &mu almost all x &isin X ? Here, as in the rest of the article, B sub r sub x denotes the open ball in X with d radius r and centre x . This is a natural question to ask, especially in view of the heuristic construction of the Riemann integral , in which it is almost implicit that f x is a good representative for the values of f near x . Theorems on the differentiation of integrals Lebesgue measure One result on the differentiation of integrals is the Lebesgue differentiation theorem , as proved by Henri Lebesgue in 1910. Consider n dimension al Lebesgue measure &lambda sup n sup on n dimensional Euclidean space R sup n sup . Then, for any locally integrable function f R sup n sup &rarr R , one has math lim r to 0 frac1 lambda n big B r x big int B r x f y , mathrm d lambda n y f x math for &lambda sup n sup almost all points x &isin R sup n sup . It is important to note, however, that the measure zero set of bad points depends on the function f . Borel measures on R sup n ... for &mu almost all points x &isin R sup n sup . Gaussian measures The problem of the differentiation ... very rapidly. See also Differentiation under the integral sign References cite book last Preiss first David coauthors Ti er, Jaroslav chapter Differentiation of measures on Hilbert spaces title Measure ... Jaroslav title Differentiation theorem for Gaussian measures on Hilbert space journal Trans. Amer ... more details
Calculus cTopic Differentiation This is a summary of differentiation rules , that is, rules for computing the derivative of a function in calculus . Elementary rules of differentiation Unless otherwise stated, all functions are functions of real, R , numbers that return real, R , values although more generally, the formulae below apply wherever they are well defined . Differentiation is linear main Linearity of differentiation For any functions f and g and any real numbers a and b the derivative of the function nowrap 1 h x af x bg x with respect to x is math h x a f x b g x . , math In Leibniz s notation this is written as math frac d af bg dx a frac df dx b frac dg dx . math Special cases include The Constant factor rule in differentiation constant multiple rule math af af , math The Sum rule in differentiation sum rule math f g f g , math The subtraction rule math f g f g . , math The product rule Leibniz rule main Product rule For the functions f and g , the derivative of the function h x f x g x with respect to x is math h x f x g x f x g x . , math In Leibniz s notation this is written math frac d fg dx frac df dx g f frac dg dx . math The chain rule main Chain rule The derivative of the function of a function h x f g x with respect to x is math h x f g x g x . , math In Leibniz s notation this is written as math frac df dx frac df dg frac dg dx . , math The inverse function rule main inverse functions and differentiation If the function f has an inverse function g , meaning that nowrap 1 g f x x and nowrap 1 f g y y , then math g frac 1 f circ g . , math In Leibniz notation, this is written as math frac dx dy frac 1 dy dx . math Power laws, polynomials, quotients, and reciprocals ... is positive. Derivatives of trigonometric functions details Differentiation of trigonometric functions ... calculus and analysis table of derivatives A Table of Derivatives DEFAULTSORT Differentiation Rules Category Differential calculus Category Differentiation rules Category Mathematics related lists Derivatives ... more details
In differential calculus , there is no single uniform notation for differentiation . Instead, several different notations for the derivative of a function mathematics function or dependent variable variable have been proposed by different mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation are listed below. Leibniz s notation see also Leibniz s notation The original notation employed by Gottfried Leibniz is used throughout mathematics. It is particularly common when the equation y f x is regarded as a functional relationship between dependent and independent variables y and x . In this case the derivative can be written as math frac dy dx math The function whose value at x is the derivative of f at x is therefore written math frac d bigl f x bigr dx text or frac d dx bigl f x bigr math although strictly speaking this denotes the variable value of the derivative function rather than the derivative function itself . Higher derivatives are expressed as math frac d ny dx n , quad frac d n bigl f x bigr dx n , text or frac d n dx n bigl f x bigr math for the n th derivative of y f x . Historically, this came from the fact ... allows one to specify the variable for differentiation in the denominator . This is especially helpful ... y x · dy as formal axiom s for differentiation. See differential algebra . In non ... modern notations for differentiation is due to Joseph Louis Lagrange and uses the Prime symbol ... s notation Newton s notation for differentiation also called the dot notation for differentiation ... calculus concerns derivative differentiation and integral integration of vector field vector or scalar ... notations of differentiation. In a Cartesian coordinate o xyz , assuming a vector field A is math mathbf ... sub x sub f sub xy sub div When more specific types of differentiation are necessary, such as in multivariate ... more details
Essay like date February 2010 NOTOC Cluster grouping is an educational process in which four to six gifted ... cluster grouping the intellectual, social, and emotional needs of the gifted students can be addressed. ref Schuler, Patricia A., Cluster Grouping Coast to Coast , Neag Center for Gifted Education ... elementary grades 3 6 , cluster grouping has been used in grades K through 12. ref Schuler ref The methods for selecting children for cluster groups usually mirror those for other gifted and talented services. ref Schuler ref Within a cluster, several instructional options are typically used, including ... grade s gifted children in one classroom will neither form a cluster nor produce positive academic ... difficult or demanding students, and d the curriculum for the cluster must be appropriately differentiated ..., who might otherwise be exclude from gifted Gifted Pull out pull outs , can be placed in the cluster ... the cluster classroom. ref Gentry, M. 1996 , Cluster grouping An investigation of student achievement ..., Storrs. ref Cluster grouping is not experimental it has been used successfully since 1974 ... may not be appropriate in all districts. In these situations, the study goes on to state, The Cluster ... . Cluster grouping is distinct from tracking in that tracking organizes entire classrooms by ability .... 178. ref Conversely, cluster groups tends to expand over time rather than remain fixed. ref Gentry, Marcia L. Promoting Student Achievement and Exemplary Classroom Practices Through Cluster Grouping ..., CT NRC GT, University of Connecticut, 1999. ref While cluster groups allow GT children to spend ... cluster grouping. ref Winebrenner, Susan, and Devlin, Barbara, Cluster Grouping Fact Sheet ... and for which they have no certification. Concerns and Criticism Cluster grouping has experienced some negative reception Teachers in schools that did not limit the extremes with the cluster ..., Winebrenner recommends that the cluster classroom teacher not also have the neediest ... more details
unreferenced date June 2008 Galaxy cluster name Horologium Cluster image epoch J2000 ra RA 0 0 dec DEC 0 0 constellation Horologium member no brightest member other names The Horologium cluster is a Galaxy groups and clusters cluster of galaxies which is a part of the Horologium Supercluster . It is 900 million light year s away from the Milky Way . See also Horologium Supercluster galaxy stub Category Horologium Supercluster ko ms Gugusan Horologium ... more details
Ndb Cluster is the distributed database system underlying MySQL Cluster . It can be used independently of a MySQL Server. From the MySQL Server perspective the Ndb Cluster is a Database engine Storage engine for storing tables of rows. From the Ndb Cluster perspective, a MySQL Server instance is an API process connected to the Cluster. Ndb Cluster can concurrently support access from other types of API processes. All API processes can operate on the same tables and data stored in the Ndb Cluster. Standalone Ndb Cluster Ndb Cluster has the following capabilities independent of any attached MySQL Server Persistent, distributed storage of tables with unique or ordered indexes Redo logging, checkpointing, system recovery Primary key, unique key, table scan and ordered index scan Parallel scan execution with pushed down filters Row locks, transactional updates Synchronous data replication within the cluster, automatic failover recovery Automatic connection failover for API processes Standard SQL datatypes including Blobs etc. Storage of data on disk Asynchronous data change triggers mechanism Data Definition Language DDL operations although independent DDL will not currently be recognised by any attached MySQL servers Online index add, online table alter Online add node, table reorganisation Online backup Online upgrade MySQL Cluster Ndb Cluster MySQL Server s MySQL Cluster currently uses the MySQL Server to provide the following capabilities on top of Ndb Cluster SQL parsing optimising execution capability Connectors to applications via JDBC , ODBC ... Cross table Join SQL join ... Ndb Cluster is often configured as a MySQL Cluster An Ndb Cluster with attached MySQL Server processes ... Server use the NDBAPI ref name NdbApiDocs http dev.mysql.com doc ndbapi en index.html The MySQL Cluster API Developer Guide ref C client library to connect to the Ndb Cluster and perform operations. It is currently recommended that at least one MySQL Server is connected to an Ndb Cluster to perform ... more details
Infobox album See Wikipedia WikiProject Albums Name Apropos Cluster Type studio Artist Dieter Moebius Moebius and Hans Joachim Roedelius Roedelius Cover Apropos cluster.jpg Released 1991 Recorded 1989 1990 Genre Krautrock br Experimental Music br Electronic music br Ambient Music Length Label Curious Music Producer Chronology Cluster band Cluster Last album Curiosum br 1981 This album Apropos Cluster br 1991 Next album One Hour br 1995 Apropos Cluster is a full length studio album by Dieter Moebius and Hans Joachim Roedelius also known as German electronic music outfit Cluster band Cluster . It was also their first album after an eight year long hiatus. In 1989 Dieter Moebius and Hans Joachim Roedelius reunited to the delight of their fans, recording Apropos Cluster during 1989 and 1990 in Blumau , Austria . The album was released on the Curious Music label in 1991. It was Cluster s first U.S. release. Apropos Cluster is musically and structurally similar to Grosses Wasser though it lacked the rhythmic tracks of the 1979 release, instead comprising a mixture of gentle, ambient pieces in the four shorter tracks followed by the nearly 22 minute long, more experimental title piece. Emmental became the signature track for Cluster. It was included on the 1997 live album First Encounter Tour 1996 and was often performed live by Roedelius at solo concerts during the band s second hiatus. Apropos Cluster was reissued on the Swirldisc Records label on August 23, 1996. Track listing Grenzganger 7 24 Emmental 3 24 Gespiegelt 6 58 Falls 2 57 Apropos Cluster 21 41 Personnel Hans Joachim Roedelius Dieter Moebius Stanislaw Michalik bass on Emmental References Curry, Russ http www.thing.de delektro www eng cluhist.html A Curious History of Cluster Retrieved August 17, 2007. Discogs http www.discogs.com release 232071 Retrieved August 19, 2007. Category 1991 albums Category Cluster albums 1990s electronic album stub ... more details
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