In mathematics , specifically in category theory , an additivecategory is a preadditive category C such that all ... 1 sub A sub n sub in C . Recall that a category C is preadditive category preadditive if all its hom set s are Abelian groups and composition of morphisms is bilinear in other words, C is enriched category enriched over the monoidal category of Abelian groups. Recall also that a biproduct in a preadditive category is both a finite set finite product category theory product and a finite coproduct . Warning The term additivecategory is sometimes applied to any preadditive category, but Wikipedia does not follow this older practice. Definition A category C is additive if it has a zero object every ... category enriched over the category of pointed set s. Examples The original example of an additive ... . More generally, every module category over a ring mathematics ring R is additive, and so in particular, the category of vector spaces over a field mathematics field K is additive. The algebra of matrix mathematics matrices over a ring, thought of as a category as described below, is also additive ..., a semiadditive category is additive if and only if every morphism has an additive inverse. This shows that the addition law for an additivecategory is internal to that category. ref citation ... in an additivecategory, we can represent morphisms f A sub 1 sub A sub n sub B sub 1 sub B sub m sub ... R , and where composition is given by matrix multiplication. Then Mat R is an additivecategory, and A sub ... need to be included to get an additivecategory, since an additivecategory must have a zero object ... objects A and B in an additivecategory, there is exactly one morphism from A to 0 just as there is exactly ... theory are adjoints. Special cases A pre abelian category is an additivecategory in which ... biproduct s exist. Note that a category is called preadditive category preadditive if just the second ... biproduct is a zero object in the category, we may omit the first condition. If we do this, however ... more details
Wiktionary Additive may refer to Additive function , a function that preserves the addition operation Additive inverse , an arithmetic concept Additivecategory , a preadditive category with finite biproducts Additive rhythm , a larger period of time constructed from smaller ones Additive synthesis , an audio synthesis technique Additive color , as opposed to subtractive color Additivity, in biochemistry, the simple sum of effects due to multiple causes Food additive , a substance added to food to improve flavor or appearance Feed additive Gasoline additive , a substance used to improve the performance of a fuel, lower emissions or clean the engine Oil additive , a substance used to improve the performance of a lubricant Weakly additive , the quality of preferences in some logistics problems Additive Records , a record label Paint additive , a chemical added in to paint in very small quantities for a specific property improvement disambig bs Aditiv vor cs Aditivum es Aditivo fr Additif gl Aditivo hom nimos id Aditif it Additivo no Tilsetningsstoff ... more details
In mathematics the additive identity of a Set mathematics set which is equipped with the operation mathematics ... in the set, yields x . One of the most familiar additive identities is the number 0 number 0 from elementary mathematics , but additive identities occur in other mathematical structures where addition is defined, such as in group mathematics groups and ring mathematics rings . Elementary examples The additive ... s Q , the real number s R , or the complex number s C , the additive identity is 0. Thus for any one of these number s n , n 0 n 0 n . The additive identity is zero in an addition problem Formal definition ... , denoted . An additive identity for N is any element e such that for any element n in N , e n n n e . Further examples In a group mathematics group the additive identity is the identity element ... additive identity 0. This is defined to be different from the multiplicative identity 1 number 1 if the ring or field has more than one element. If the additive identity and the multiplicative identity ... sub R of m by n matrix mathematics matrices over a ring R , the additive identity is denoted 0 and is the m ... by 2 matrices over the integers M sub 2 sub Z the additive identity is math 0 begin pmatrix 0 & 0 0 & 0 end pmatrix . math In the quaternions , 0 is the additive identity. In the ring of function mathematics function s from R to R , the function map mathematics mapping every number to 0 is the additive identity. In the additive group of vector geometric vector s in R sup n sup , the origin or zero vector is the additive identity. Proofs The additive identity is unique in a group Let G , be a group and let 0 and 0 in G both denote additive identities, so for any g in G , 0 g g g 0 and 0 g g g 0 . It follows from the above that 0 0 0 0 0 0 . The additive identity annihilates ring elements In a system with a multiplication operation that distributes over addition, the additive identity ... s 0 s 0 0 s 0 s 0 s 0 0 by cancellation . The additive and multiplicative identities are different ... more details
Unreferenced date December 2009 AW additives , or antiwear additives , are Oil additive additives for lubricants to prevent metal to metal contact between parts of gear s. EP additives are usually used in applications such as transmission mechanics gearboxes , while AW additives are used with lighter loads such as bush mechanical bushings . AW additives typically contain zinc and phosphorus compounds. Some popular AW additives are zinc dithiophosphate ZDP zinc dialkyl dithio phosphate ZDDP , probably the most widely used in formulated engine oil s, also acts as a corrosion inhibitor and antioxidant Tricresyl phosphate TCP , used for high temperature operation, often used as an AW and EP additive in turbine engine lubricants, and also in some crankcase oils and hydraulic fluid s Halocarbon s chlorinated paraffins , for extreme pressure operations Glycerol mono oleate Stearic acid , adhering to surfaces via reversible adsorption process under 150 C, which limits its use to mild contact conditions. Some formulations use colloid al polytetrafluorethylene PTFE Teflon , but its efficiency is controversial. Many AW additives function as EP additives, for example organophosphate s or sulfur compounds. The mechanism of function of TCP and ZDDP is explained in EP additive s. Under extreme pressure conditions, the performance of AW additives becomes insufficient and designated EP additive s are required. See also EP additive s Oil additive DEFAULTSORT Aw AdditiveCategory Lubricants Category Oil additives cs Protiot rov aditivum ... more details
Allyn and Bacon, Inc. DEFAULTSORT Additive Meter Category Musical notation Category Musical terminology Category Metres Music theory stub ...merge Time signature discuss Talk Additive meter Merger proposal date April 2010 In music, additive meter refers to a pattern of Beat music beats that subdivide into smaller, irregular groups. This is opposed to divisive or multiplicative rhythms or meters, which are produced by multiplying some integer unit into regular groupings forming beats of equal length London 2001 . Such meters are sometimes called imperfect , in contradistinction to perfect meters in which the Bar music bar is first divided into equal units Read 1964, Page number date December 2010 . Additive meter is common in Music of Eastern Europe Eastern European musics , and contemporary compositions attempting to emulate such a sound. For example, a time signature like 9 8 is normally subdivided as 3 3 3, or nine eighth notes with three to a beat. However, the composer or Conducting conductor may specify an additive meter for passages of music where it is more natural to conduct with a different pattern. Hence, a meter like 9 8 may instead be subdivided as 2 3 2 2 for musical effect most commonly such an additive meter is used when Accent music accented notes or Syncopation syncopated patterns do not match up with the normal subdivision. Flamenco music, for instance, is full of additive meter, particularly in rhythms of 10 3 3 2 2 . Alfred Reed s Armenian Dances Part I contains a movement written in the nonstandard time signature of 5 8, which can be conducted as either 2 3 or 3 2 depending on which is more musically natural. See also Additive rhythm Meter music Sources London, Justin. 2001. Rhythm, I Fundamental Concepts & Terminology, 8 Additive Versus Divisive Rhythm . The New Grove Dictionary of Music and Musicians , second edition, edited by Stanley Sadie and John Tyrrell professor of music John Tyrrell ... more details
Multiple issues orphan February 2009 unreferenced July 2007 notability February 2011 Drench is liquid water additive designed by Denko to fight Class A and B fire s. Designed to break the surface tension of water, it is able to increase the penetration of the treated water into the burning material. Drench reduces the friction of water moving through a handline and allows the solution to vaporize faster, increasing cooling. DEFAULTSORT Drench Additive Category Fire suppression agents Category Wildland fire suppression ... more details
Refimprove date January 2010 In mathematics, the additive inverse , or opposite , of a number mvar a is the number that, when addition added to mvar a , yields 0 number zero . The additive inverse of mvar ... there should be no space punctuation space after unary . For example, the additive inverse of 7 is 7, because 7 7 0, and the additive inverse of 0.3 is 0.3, because 0.3 0.3 0 . In other words, the additive inverse of a number is the number s negative. For example, the additive inverse of 8 is &minus 8, the additive inverse of 10002 is &minus 10002 and the additive inverse of mvar x is &minus mvar x . The additive inverse of a number is defined ... number all have additive inverses, as they contain negative as well as positive numbers. Natural number s, cardinal number s, and ordinal number s, on the other hand, do not have additive ... do have additive inverses, but because these additive inverses are not themselves natural numbers, the set of natural numbers is not closure mathematics closed under taking additive inverses. General ... x&prime mvar x&prime mvar x o , then mvar x&prime is called an additive inverse of mvar x . If is associativity associative math 1 x y z x y z for all mvar x , mvar y , mvar z , then an additive inverse ... numbers is associative, each real number has a unique additive inverse. Other examples All the following examples are in fact abelian group s addition of real valued functions here, the additive inverse ... kinds of functions. In a vector space additive inversion corresponds to scalar multiplication ... , the modular additive inverse of mvar x is also defined it is the number mvar a such that math 1 mvar a mvar x 0 mod mvar n . This additive inverse does always exist. For example, the inverse of 3 ... Additive identity References MathWorld title Additive Inverse urlname AdditiveInverse author Margherita Barile Category Abstract algebra Category Arithmetic Category Elementary algebra ar ... more details
nofootnotes date June 2011 In mathematics , the additive polynomials are an important topic in classical algebraic number theory . Definition Let k be a field mathematics field of characteristic algebra characteristic p , with p a prime number . A polynomial P x with coefficients in k is called an additive polynomial , or a Frobenius polynomial , if math P a b P a P b , math as polynomials in a and b ... k , such as its algebraic closure. Occasionally absolutely additive is used for the condition above, and additive is used for the weaker condition that P a b P a P b for all ... P b for all a and b in the field, but will usually not be absolutely additive. Examples The polynomial x sup p sup is additive. Indeed, for any a and b in the algebraic closure of k one has ... of the form math tau p n x x p n math are additive, where n is a non negative integer. The ring of additive polynomials It is quite easy to prove that any linear combination of polynomials math scriptstyle tau p n x math with coefficients in k is also an additive polynomial. An interesting question is whether there are other additive polynomials except these linear combinations. The answer is that these are the only ones. One can check that if P x and M x are additive polynomials, then so are P x M x and P M x . These imply that the additive polynomials form a ring mathematics ... modular arithmetic . Indeed, consider the additive polynomials ax and x sup p sup for a coefficient ... mathbb F p. math The fundamental theorem of additive polynomials Let P x be a polynomial with coefficients ... that the roots of P x are distinct that is, P x is separable polynomial separable , then P x is additive ... Field Arithmetic , 1996, Springer, Berlin. ISBN 3 540 61087 1. External links MathWorld title Additive Polynomial urlname AdditivePolynomial Category Algebraic number theory Category Modular arithmetic Category Field theory Category Polynomials ... more details
File Utzon Jeddah stadium model.jpg thumb Utzon s model for a Jeddah sports stadium 1967 Additive Architecture is an approach used by Denmark Danish architect J rn Utzon to describe his development of architectural projects on the basis of growth patterns in nature. ref http www.edition blondal.dk logbook v Richard Weston on Additive Architecture, J rn Utzon, Logbook Vol V , Edition Bl ndal. Retrieved 25 September 2011. ref Mogens Prip Buus, one of Utzon s closest colleagues, reports that the term was coined in 1965 in Utzon s Sydney office when, after a discussion of the social structures in Britain and Denmark, Utzon suddenly jumped up and wrote Additive Architecture on the wall. He saw it as part of an additive world where both natural and cultural forms contributed to additive systems and hierarchies. He realized that his own architecture reflected the same principle, just as the transitions in primitive societies between family, village and the surrounding world have visible links revealing differences, relations and distances. ref http www.forlaget eh.dk udgivelser additive architecture Thomas Bo Jensen, Om bogen Additive Architecture , Forlaget Ehrhorn Hummerston , published in Arkitekten , Vol 111, no. 14, November 2009. Retrieved 7 October 2011. ref Utzon observed the additive approach in Chinese temple s whose stacked timber structures are basically identical, differing only with the size of the building. In his Additive Architecture manifesto in 1970, he tells us how ... Bo Jensen, Review of Additive Architecture , Edition Bl ndal . Retrieved 25 September 2011. ref The application of the additive approach can be seen in many of Utzon s works including the courtyard housing ... made concrete. Retrieved 25 September 2011. ref Examples of the Additive Architecture approach ..., Additive Architecture Logbook Vol. V , Copenhagen, Edition Bl ndal, 2009, 312 pages. ISBN 87 91567 .... ISBN 87 88978 98 2 J rn Utzon Category Modernist architecture Category Architectural design Category ... more details
Image AdditiveColor.svg thumb Additive color mixing adding red to green yields yellow adding all three primary colors together yields white. Image J C Maxwell with top.jpg thumb James Clerk Maxwell, with his color top that he used for investigation of color vision and additive color Additive color describes the situation where color is created by mixing the visible light emitted from differently colored light sources. This is in contrast to subtractive color s where light is removed from various part of the visible spectrum to create colors. Computer monitors and televisions are the most common form of additive light, while subtractive color is used in paint s and pigment s and color filter s. The additive reproduction process usually uses red , green and blue light to produce the other colors. Combining one of these additive primary color s with another in equal amounts produces the additive secondary color s cyan , magenta , and yellow . The colored pixels in displays do not overlap on the screen, but when viewed from a sufficient distance, the light from the pixels diffuses to overlap on the retina. Another common use of additive light is the projected light used in theatrical lighting ... gamut of those three lights colors . Results obtained when mixing additive colors are often ... of yellow and blue in additive color, red green yellow and no simple combination will yield green. Additive ... Maxwell is credited as being the father of additive color. ref cite web title James Clerk Maxwell url ... of additive color. ref cite book title Exploring Colour Photography A Complete Guide author ... books?id 4Gx2WItWGYoC&pg PA28&dq maxwell additive color photograph register PPA28,M1 ref Examples ... Flash demo comparing additive and subtractive color mixing. Color topics DEFAULTSORT Additive Color Category Color space ar ca S ntesi additiva de color cs Aditivn m ch n barev da Additiv farveblanding de Additive Farbmischung es S ntesis aditiva de color fr Synth se additive it Mescolanza ... more details
A feed additive is a vitamin for farm animals that can t get enough nutrients from regular meals that the farmers provide. ref http www.fefana.org ref In some cases if an animal does not have some type of feed in its diet it may not grow properly. Nutritional content of an animal feed is influenced not only by nutrient content but also by many other aspects such as, feed presentation, hygiene, digestibility, and effect on intestinal health to name a few. Even with all of the benefits of feed most of a farm animals diet still consist of maize, wheat and soybean meal because of the cost of quality feed. ref Fefana Asbl. Additives and premixtures. Fefana EU Feed & Additives Premixtures Association. Fefana, 2009. Web. 27 Oct. 2009. http www.fefana.org . ref Types of feed additives A sensory additive is an additive that stimulates the appetite, improving the voluntary intake of a diet. A nutritional additive provides specific nutrients for an animal for optimal growth. A zootechnical additive improves the nutritional value of a diet. It doesn t give nutrients directly to the animal, but through its diet. A coccidiostats and histomonostats controls the health of poultry through direct effects. The benefits of feed additives Environment. The feed additives would reduce the amount of ammonia found in the manure of the animals. Thus, with feed additives we can lessen the pollution of our globe. Welfare If there was less manure then the air quality would be much healthier for all kinds of animals, and their welfare. See also Fodder Compound feed References references External Links http www.livestocktrail.uiuc.edu dairynet paperDisplay.cfm?ContentID 642 http agebb.missouri.edu commag beef premierbeef pbdocs feedadditives.htm DEFAULTSORT Feed AdditiveCategory Food additives Category Excipients Category Livestock ... more details
Category A may refer to any of the following Category A Listed building Scotland Category A Prison UK Category A Bioterrorism agent Category A services Canada The most serious category of disease recognized by the Centers for Disease Control and Prevention USA disambig ... more details
common categorization of hurricane intensities Lexical category Categories of New Testament manuscripts See also intitle Category Categorical disambiguation Categorization Category 1 disambiguation Category 2 disambiguation Category 3 disambiguation Category 4 disambiguation Category 5 disambiguation Category 6 disambiguation Category 7 The End of the World Category A disambiguation Category B disambiguation Category C disambiguation disambig Category Greek loanwords ceb Kategoriya cs Kategorie ... ujednoznacznienie pt Categoria ro Categorie dezambiguizare ru simple Category ... more details
In mathematics the term additive function has two different definitions, depending on the specific field of application. In algebra an additive function or additive map is a function that preserves the addition operation f x y f x f y for any two elements x and y in the domain. For example, any linear map is additive. When the domain is the real numbers , this is Cauchy s functional equation . In number theory , an additive function is an arithmetic function f n of the positive integer n such that whenever a and b are coprime , the function of the product is the sum of the functions f ab f a f b . The remainder of this article discusses number theoretic additive functions, using the second definition. For a specific case of the first definition see additive polynomial . Note also that any homomorphism f between Abelian group s is additive by the first definition. Completely additive An additive function f n is said to be completely additive if f ab f a f b holds for all positive integers a and b , even when they are not co prime. Totally additive is also used in this sense by analogy with totally multiplicative functions. If f is a completely additive function then f 1 0. Every completely additive function is additive, but not vice versa. Examples Example of arithmetic functions which are completely additive are The restriction of the logarithm logarithmic function to N . The multiplicity of a prime factor p in n , that is the largest exponent m for which p sup m sup divides n . a sub 0 sub n the sum of primes dividing n counting multiplicity, sometimes called sopfr n , the potency ... 7 Example of arithmetic functions which are additive but not completely additive are ... a sub 1 sub 20,802,650,704,327,415 1238677 Multiplicative functions From any additive function f n ... span refend Category Arithmetic functions ar ca Funci additiva de Additivit t et Aditiivne funktsioon es Funci n aditiva eo Alsuma funkcio fr Fonction additive arithm tique it Funzione additiva ... more details
In fair division , a set of preferences is weakly additive if the following condition is met ref cite book title Fair Division From cake cutting to dispute resolution last Brams first Steven J. authorlink Steven Brams coauthors Alan D. Taylor year 1996 publisher Cambridge University Press isbn 0 521 55390 3 ref If A is larger than B, and C is larger than D and pieces A and C do not overlap then A together with C is preferable to B together with D. Weak additivity is often a realistic assumption when dividing up Good economics goods between claimants, and simplifies the mathematics of certain fair division problems considerably. Use of weak additivity Some procedures in fair division do not need the value of goods to be additive and only require weak additivity. In particular the adjusted winner procedure only requires weak additivity. Case where the assumptions might fail would be either The value of A and C together is the less than the sum of their values. For instance two versions of the same CD may not be as valuable to a person as the sum of the values of the individual CDs on their own. The values of B and D together may be more than their individual values added. For instance two matching bookends may be much more valuable than twice the value of an individual bookend. The use of money as compensation can often turn real cases like these into situations where the weak additivity condition is satisfied even if the values are not exactly additive. The value of a type of goods, e.g. chairs, dependent on having some of those goods already is called the marginal utility . References reflist DEFAULTSORT Weakly AdditiveCategory Utility Category Fair division econometrics stub eo Malforte alsuma ... more details
Wiktionary An additive group may refer to an abelian group , when it is written using the symbol for its binary operation a group scheme representing the underlying additive group functor the elements of a ring mathematics considered as a group under addition mathdab es Grupo aditivo ... more details
In statistics , additive smoothing , also called Pierre Simon Laplace Laplace smoothing ref C.D. Manning, P. Raghavan and M. Sch tze 2008 . Introduction to Information Retrieval . Cambridge University Press, p. 240. ref not to be confused with Laplacian smoothing , or George James Lidstone Lidstone smoothing , is a technique used to smoothing smooth Level of measurement Nominal scale categorical data . Given an observation x x sub 1 sub , , x sub d sub from a multinomial distribution with N trials and parameter vector sub 1 sub , , sub d sub , a smoothed version of the data gives the estimator math hat theta i frac x i alpha N alpha d qquad i 1, ldots,d , math where 0 is the smoothing parameter 0 corresponds to no smoothing . Additive smoothing is a type of shrinkage estimator , as the resulting estimate will be between the empirical estimate x sub i sub n , and the uniform probability 1 d . Using Laplace s rule of succession , some authors have argued that should be 1 in which case the term add one smoothing ref Cite book last1 Jurafsky first1 Daniel last2 Martin first2 James H. isbn 978 0131873216 title Speech and Language Processing edition 2nd year 2008 month June publisher Prentice Hall pages 132 ref ref Cite book last1 Russell first1 Stuart last2 Norvig first2 Peter title Artificial Intelligence A Modern Approach edition 2nd year 2010 publisher Pearson Education, Inc. pages 863 ref is also used ... distribution with parameter as a prior distribution prior . Applications Classification Additive smoothing ... of occurrences of each word in a document. Additive smoothing allows the assignment of non zero ... additive smoothing to a variety of other techniques, using both fixed at one and a more general value ... modeling . Proceedings of the 34th annual meeting on Association for Computational Linguistics . Category Statistical natural language processing Category Categorical data Ling stub Statistics stub ... more details
In statistics , an additive model AM is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle 1981 and is an essential part of the Alternating conditional expectation model ACE algorithm. The AM uses a one dimensional Smoothing smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a p dimensional smoother. Furthermore, the AM is more flexible than a linear regression standard linear model , while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM include model selection , overfitting , and multicollinearity . Description Given a data set math y i, , x i1 , ldots, x ip i 1 n math of n statistical unit s, where math x i1 , ldots, x ip i 1 n math represent predictors and math y i math is the outcome, the additive model takes the form math E y i x i1 , ldots, x ip beta 0 sum j 1 p f j x ij math or math Y beta 0 sum j 1 p f j X j varepsilon math Where math E epsilon 0 math , math Var epsilon sigma 2 math and math E f j X j 0 math . The functions math f j x ij math are unknown Smooth function smooth functions fit from the data. Fitting the AM i.e. the functions math f j x ij math can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani 1989 . See also Generalized additive model Backfitting algorithm Alternating conditional expectation model Projection pursuit regression Generalized additive model for location, scale, and shape GAMLSS References Buja, A., Hastie, T., and Tibshirani, R. 1989 . Linear Smoothers and Additive Models , The Annals of Statistics 17 2 453&ndash 555. Breiman, L. and Friedman, J.H. 1985 . Estimating Optimal Transformations for Multiple Regression and Correlation , Journal of the American Statistical Association ... Statistical Association 76 817&ndash 823 Category Regression analysis Category Nonparametric ... more details
Keyboards Synergy Sound synthesis types DEFAULTSORT Additive Synthesis Category Sound synthesis ...Use dmy dates date April 2012 Listen filename Additive synthesis bell.ogg title Additive synthesis example description A bell like sound generated by additive synthesis of 21 inharmonic partials. pos right Additive synthesis is a sound synthesis technique that creates timbre by adding sine function sine waves together. ref name JOS Additive cite web title Additive Synthesis Early Sinusoidal Modeling author Julius O. Smith III url https ccrma.stanford.edu jos sasp Additive Synthesis Early Sinusoidal.html quote The term additive synthesis refers to sound being formed by adding together many sinusoidal ... To Additive Synthesis author Gordon Reid work Sound On Sound url http www.soundonsound.com sos ... and amplitude that swells and decays ADSR envelope over time . Additive synthesis generates sound by adding ... Fourier analysis style float right border 0 valign top File Additive synthesis.svg 250px thumb Schematic diagram of additive synthesis. The inputs to the oscillators are frequencies math f k , math and amplitudes math r k , math . Harmonic additive synthesis is closely related to the concept of a Fourier ... in additive synthesis. As a result only a finite number of sinusoidal terms with frequencies that lie within the audible range are modeled in additive synthesis. A waveform or function is said ... of additive synthesis. Harmonic form The simplest harmonic additive synthesis can be mathematically ... wikitable align right width 420px File Harmonic additive synthesis spectrum.png 280px span style font size 85 line height 130 Example of harmonic additive synthesis in which each harmonic has a time dependent amplitude. The fundamental frequency is 440 Hz. span File Harmonic additive synthesis.ogg ... of math r k t , math should be significantly less than math f 0 , math . Inharmonic form Additive ... year 2005 chapter Additive Synthesis chapterurl https ccrma.stanford.edu jos parshl Additive Synthesis.html ... more details
in Europe, but is simply known as additive 260 in some countries. Additive 103, alkanet , is not approved ... foods. Each food additive has to be named or numbered. The numbers are the same as in Europe ... concluded that a low additive diet is a valid intervention for children with ADHD Although quite complicated ... behaviors associated with the food additive drink in virtually every assessment. Thus, the overall ... to obtain approval for a new food additive. This includes five years of safety testing, followed by two years for evaluation by the European Food Safety Authority and another three years before the additive ... can be used to determine the concenttration of an additive in a sample using external ... on Food Additives Food chemistry Category Food additives Category Food science ar bg ... ru simple Food additive sk Pr davn l tka v potravin ch sr su ... more details
EP additive Extreme pressure agents bond to metal surfaces, keeping them from touching even at high pressure . AW additive Antiwear additives or wear inhibiting additives cause a film to surround metal ... techarticles mump 0907 zddp zinc additive engine oil index.html ref or zinc dithiophosphate s are typically ... the ability of oil filter s to separate wax from oil. This type of additive has applications in the refining ... QMI Products ad ref it would hardly do any good if it remains in the oil filter . See also Fuel additive Gasoline additive Oil analysis External links The American Chemistry Council s http www.americanchemistry.com ... Petroleum Additives Panel link to oil additive manufacturers. List of http www.lubrizol.com products ... references Category Oil additives Oil additives Category Corrosion inhibitors cs Aditiva do maziv de ... more details
unreferenced date September 2010 In mathematics , the abstract additive Schwarz method , named after Hermann Schwarz , is an abstract version of the additive Schwarz method , formulated only in terms of linear algebra without reference to domains, subdomains, etc. Many if not all domain decomposition methods can be cast as abstract additive Schwarz method, which is often the first and most convenient approach to their analysis. Numerical PDE DEFAULTSORT Abstract Additive Schwarz Method Category Domain decomposition methods mathapplied stub ... more details
refimprove date June 2009 The additive genetic effect is an estimate of the quantitative change in a trait that is associated with substituting one allele one genotype with that of another allele within an interbreeding population. Additive effects are often calculated by genotyping and phenotyping offspring of a genetic test cross . If there are two alleles at a gene locus then the additive effect is half of the difference between the mean of all cases that are homozygous for one version of the allele a a compared to the mean of all cases that are homozygous for the other allele A A . References Reflist DEFAULTSORT Additive Genetic Effects Category Genetics Genetics stub ... more details
category is also called an Ab category , after the notation Ab for the category of abelian groups . Some authors have used the term additivecategory for preadditive categories, but Wikipedia follows ... over a ring, thought of as a category as described in the article Additivecategory . Any ring, thought of as a category with only one object, is a preadditive category. Here composition of morphisms ... D is additive if it too is enriched functor enriched over the category Ab . That is, F is additive .... If C is preadditive too, then the category Add C , D of additive functors and all natural transformations ... object is called additivecategoryadditive . Further facts about biproducts that are mainly useful .... A ring algebra ring is a preadditive category with exactly one object. An additivecategory is a preadditive category with all finite biproducts. A pre Abelian category is an additivecategory ... of print CategoryAdditive categories nl Pre additieve categorie ru ...In mathematics , specifically in category theory , a preadditive category is a category mathematics category that is enriched category enriched over the monoidal category of abelian group s. In other words, the category C is preadditive if every hom set Hom A , B in C has the structure of an abelian ... special cases below . Examples The most obvious example of a preadditive category is the category Ab itself. More precisely, Ab is a closed monoidal category . Note that commutativity is crucial here it ensures that the sum of two group homomorphism s is again a homomorphism. In contrast, the category of all group mathematics group s is not closed. See medial category . Other common examples The category of left module mathematics module s over a ring mathematics ring R , in particular the category ... addition. Focusing on a single object A in a preadditive category, these facts say that the endomorphism ... is the endomorphism ring of some object in some preadditive category. Indeed, given a ring R , we ... more details
In mathematics , additive K theory means some version of algebraic K theory in which, according to Spencer Bloch , the general linear group GL has everywhere been replaced by its Lie algebra gl . ref http www.math.uchicago.edu bloch addchow rept.pdf ref It is not, therefore, one theory but a way of creating additive or infinitesimal analogues of multiplicative theories. Formulation Following Feigin and Tsygan ref B. Feigin, B. Tsygan. Additive K theory , LNM 1289, Springer ref , let math A math be an algebra over a field math k math of characteristic zero and let math mathfrak gl A math be the algebra of infinite matrices over math A math with only finitely many nonzero entries. Then the Lie algebra homology math H cdot mathfrak gl A ,k , math has a natural structure of a Hopf algebra . The space of its primitive element s of degree math i math is denoted by math K i A math and called the math i math th additive K functor of A . The additive K functors are related to cyclic homology groups by the isomorphism math HC i A cong K i 1 A . , math References Reflist Category K theory algebra stub ... more details
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