In chemistry , residue is the material remaining after a distillation or an evaporation, or to a portion of a larger molecule, such as a methyl group . It may also refer to the undesired byproducts of a reaction. In biochemistry and molecular biology , a residue refers to a specific monomer within the polymer polymeric chain of a polysaccharide , protein or nucleic acid . For example, one might say, This protein consists of 118 amino acid residues or The histidine residue is considered to be basic due to its imidazole ring. Note that a residue is different from a Functional group moiety , which, in the above example would be constituted by the imidazole ring or the imidazole moiety . Note the origin of this usage during the process by which monomer ic building blocks e.g. amino acid s are strung together into a polymeric chain e.g. a protein , some material typically adding up to one molecule of water is discarded from each building block, and only a residue of the building block ends up in the finished product. For instance, a residue is an individual amino acid in a peptide chain. Interlang Category Distillation Chemistry stub de R ckstand Chemie nl Residu scheikunde ja tr Kal nt biyokimya zh ... more details
wiktionary Residue may refer to Residuechemistry , material remaining after a distillation or an evaporation, or portion of a larger molecule In particular, in biology, often refers specifically to an amino acid Residue law , portion of the testator s estate that is not specifically devised to someone in the will Residue complex analysis , mathematics, complex number describing the behavior of line integrals of a meromorphic function around a singularity Crop residue , materials left after agricultural processes Relationship residue , lingering feelings occurring after the commencement of a relationship often brought about by the unwillingness of one party to let go which can lead to sporadic emotional discharges. Residue may also be The remainder in modular arithmetic The heavier fractions of crude oil that fail to vaporize in an oil refinery disambig fr R sidu io Reziduo nl Residu ru ... more details
In mathematics , the Poincar residue is a generalization, to several complex variable s and complex manifold theory, of the residue at a pole of complex function theory . It is just one of a number of such possible extensions. The theory assumes given a meromorphic complex form &omega of degree n on C sup n sup or n dimensional complex manifold, but the definition is local . Along a hypersurface H defined by f 0 there is the meromorphic 1 form df f . The Poincar residue &rho along H is by definition a holomorphic n &minus 1 form on the hypersurface, for which there is an extension &rho &prime , locally to C sup n sup , such that &omega is the wedge product of df f with &rho &prime . While &rho &prime is not necessary unique, as a holomorphic extension of &rho , it is the case that &rho is uniquely defined. See also Grothendieck residue Leray residue References Boris A. Khesin, Robert Wendt, The Geometry of Infinite dimensional Groups 2008 p. 171 Category Several complex variables ... more details
Infobox Album See Wikipedia WikiProject Albums Name Residue Hymns Type EP Artist Magic Weapon Cover MagicWeaponResidueHymns.jpg Released October 2007 Recorded 2007 Genre Indie rock Length Label self released Reviews Last album Magic Weapon EP Magic Weapon br 2006 This album Residue Hymns br 2007 Next album Magic Weapon s second EP, Residue Hymns , was recorded at Breakglass Studios in Montreal , Canada with Dave Smith and was mixed by Graham Van Pelt at Friendship Cove. The album cover artwork was drawn by drummer Matt Shane. ref Magic Weapon, http www.myspace.com magicweapon Official MySpace page , retrieved November 20, 2007. ref Track listing Pipe Dreams Charles The Red One Residue Hymns Blood Songs The Movie s Dream Sandstorms References references Category 2007 EPs Category Magic Weapon albums 2000s indie rock album stub ... more details
Unreferenced date December 2009 Infobox Album See Wikipedia WikiProject Albums Name Residue of the Residents Type compilation Artist The Residents Cover Released 1984 Recorded 1971 1983 Genre Rock music Rock Length Label Producer Reviews Last album This album Next album Residue of the Residents is a compilation of The Residents outtakes, ranging from about 1971 1983. The compilation was released in 1984. Walter Westinghouse is an edited version of the song from the Babyfingers E.P. while another early song, Whoopy Snorp , was from a hard to find benefit album for Los Angeles artists. Although meant to have something released while fans were waiting for the next part of the Mole Trilogy, this album stands on its own. It was re released in 1998 on CD as Residue Deux , deleting some of the songs which had appeared frequently as bonus tracks on 1980s CD releases and adding some later tracks. Residue Tracks The Sleeper Whoopy Snorp Kamakazi Lady Boy in Love Shut Up Shut Up Anvil Forest Diskomo Jailhouse Rock Ups and Downs Walter Westinghouse Saint Nix Open Up Residue Deux Tracks The Sleeper Whoopy Snorp Kamikazi Lady Boy in Love Shut Up Shut Up different from the original, from the Commercial Single Anvil Forest Diskomo Jailhouse Rock different version than original from a 1987 single Ups and Downs Saint Nix Open Up The Replacement In San Francisco Dumbo the Clown Is He Really Bringing Roses? Time s Up Daydream Believer Safety Is a Cootie Wootie Part 1 Prelude for a Toddler Part 2 Toddler s Lullaby Part 3 Safety Is a Cootie Wootie Daydream in Space DEFAULTSORT Residue Of The Residents Category The Residents albums Category 1984 compilation albums fr Residue of the Residents pl Residue of the Residents ... more details
In complex analysis a branch of mathematics, the residue at infinity is a Residue complex analysis residue of a holomorphic function on an Annulus mathematics annulus having an infinite external radius. The infinity math infty math is a point added to the local space math mathbb C math in order to render it compact space compact in this case it is a Alexandroff extension one point compactification . This space noted math hat mathbb C math is isomorphism isomorphic to the Riemann sphere . ref Mich le AUDIN, Analyse Complexe , cursus notes of the university of Strasbourg http www irma.u strasbg.fr maudin analysecomp.pdf available on the web , pp. 70 72 ref One can use the residue at infinity to calculate some integral s. Definition Given a holomorphic function f on an Annulus mathematics annulus math A 0, R, infty math centered at 0, with inner radius math R math and infinite outer radius , the residue at infinity of the function f can be defined in terms of the usual residue mathematics residue as follows math mathrm Res f, infty mathrm Res left 1 over z 2 f left 1 over z right , 0 right math Thus, one can transfer the study of math f z math at infinity to the study of math f 1 z math at the origin. Note that math forall r R math , we have math mathrm Res f, infty 1 over 2 pi i int C 0, r f z , dz math See also Riemann sphere Algebraic variety Residue theorem References Translation Ref fr R sidu l infini oldid 59523358 references Murray R. Spiegel, Variables complexes , Schaum, ISBN 2 7042 0020 3 Henri Cartan , Th orie analytique des fonctions d une ou plusieurs varaiables complexes , Hermann, 1961 Category Complex analysis fr R sidu l infini ... more details
In mathematics , the residue field is a basic construction in commutative algebra . If R is a commutative ring and m is a maximal ideal , then the residue field is the quotient ring k R m , which is a field mathematics field . Frequently, R is a local ring and m is then its unique maximal ideal. This construction is applied in algebraic geometry , where to every point x of a scheme mathematics scheme X one associates its residue field k x . One can say a little loosely that the residue field of a point of an abstract algebraic variety is the natural domain for the coordinates of the point. Definition Suppose that R is a commutative local ring , with the maximal ideal m . Then the residue field is the quotient ring R m . Now suppose that X is a scheme mathematics scheme and x is a point of X . By the definition of scheme, we may find an affine neighbourhood U Spec A , with A some commutative ring . Considered in the neighbourhood U , the point x corresponds to a prime ideal p A see Zariski topology . The local ring of X in x is by definition the localization of a ring localization R A sub p sub , with the maximal ideal m p A sub p sub . Applying the construction above, we obtain the residue field of the point x k x A sub p sub p A sub p sub . One can prove that this definition does not depend on the choice of the affine neighbourhood U . ref Intuitively, the residue field of a point is a local invariant. Axioms of schemes are set up in such a way as to assure the compatibility between various affine open neighborhoods of a point, which implies the statement. ref A point ... a , a k 0 , the zero ideal. The residue fields are math k t t a t a k t t a cong k math math k t 0 ... types arise, for example if k R , then the prime ideal x sup 2 sup 1 has residue field ... kind are closed, having residue field k , whereas the second point is the generic point , having transcendence ... a field is equal to the transcendence degree of the residue field of the generic point. Notes reflist ... more details
Gunshot residue GSR is principally composed of burnt and unburnt particles from the explosive primer , the propellant , as well as components from the bullet , the Cartridge firearms cartridge case and the firearm used. There are authors who use other definitions, such as cartridge discharge residue CDR or firearm discharge residue FDR . Gunshot Residue GSR is the residue that gets deposited on the hands ... of suspect is more. Gunshot residue can travel out from the gun to distances of 3 5 feet 0.3 1.5 ... barrel, the residue deposits more heavily on surfaces like skin and clothing, to the point of being visible as a dark stain. Detection of a significant amount of residue, therefore, is a powerful ... case, target hole , if proper attention is paid to avoid secondary gunshot residue transfer .... organic compound Organic gunshot residue can be analysed by analytical techniques such as chromatography ..., Analysis of Gunshot Residue and Associated Materials A Review, J. Forens. Sci. 55 2010 924 943. M ... residue, Science and Justice 2011 doi 10.1016 j.scijus.2011.04.005. H.H. Meng, B. Caddy, Gunshot residue analysis review, J. Forens. Sci. 42 1997 553 570. P.V. Mosher, M.J. McVicar, E.D. Randall, E.H. Sild, Gunshot residue similar particles produced by fireworks, Journal of the Canadian Society of Forens. Sci. 31 3 1998 157 168. F.S. Romolo, P. Margot, Identification of gunshot residue a critical ... Gunshot Residue Analysis, 2000 CRC Press LLC. J.S. Wallace, J. McQuillan, Discharge residues ... Analysis of Firearms, Ammunition, and Gunshot Residue, 2008 CRC Press LLC. G.M. Wolten, R.S. Nesbitt, A.R. Calloway, G.L. Loper, P.F. Jones, Particle analysis for the detection of gunshot residue ... analysis for the detection of gunshot residue. II occupational and environmental particles, J. Forens ... of gunshot residue. III the case record, J. Forens. Sci. 24 1979 864 869. External links New Scientist ... on firearm forensics DEFAULTSORT Gunshot Residue Category Forensic evidence de Schmauch nl Gunshot residue ... more details
Wikify date April 2011 Residue depth RD is a solvent exposure measure that describes to what extent a residue is buried in the protein structure space. ref citation title Residue depth a novel parameter for the analysis of protein structure and stability first1 S. last1 Chakravarty first2 R last2 Varadarajan journal Structure year 1999 volume 7 issue 7 pages 723 732 pmid 10425675 . ref ref citation title Atom depth as a descriptor of the protein interior first1 A. last1 Pintar first2 O. last2 Carugo first3 S. last3 Pongor journal Biophys. J year 2003 volume 84 issue 4 pages 2553 2561 pmid 12668463 doi 10.1016 S0006 3495 03 75060 7 . ref ref citation title Atom depth in protein structure and function first1 A. last1 Pintar first2 O. last2 Carugo first3 S. last3 Pongor journal Trends Biochem Sci year 2003 volume 28 issue 11 pages 593 597 pmid 14607089 doi 10.1016 j.tibs.2003.09.004 . ref It complements the information provided by conventional accessible surface area ASA . Currently, predictions in regards to whether a residue is exposed or buried are used in a wide variety of protein structure prediction engines. Such prediction can provide valuable information for Protein folding protein fold recognition, Functional residual capacity functional residue prediction and protein drug design . To date several approaches have been proposed to predict RD values from protein sequence s. Yuan ... to predict RD values based on predicted secondary structure , residue position and PSI BLAST profile. ref citation title Sequence based residue depth prediction using evolutionary information and predicted .... ref citation title Prodepth predict residue depth by support vector regression approach from ... value for each residue for users submitted sequence. Based on the predicted ASA and RD values, it will further output the two state solvent accessibility prediction by classifying a residue as being exposed ... references DEFAULTSORT Residue Depth Category Amino acids Category Solvent accessibility ... more details
In forensic science , blood residue wet and dry remnants of blood , as well the discoloration of surfaces on which blood has been shed can help investigators identify weapons, reconstruct a criminal action, and link suspects to the crime. ref name Robinson 152 cite book last Robinson first James L. title Forensic Science chapter Blood residue and bloodstains editor Ayn Embar seddon, Allan D. Pass eds. publisher Salem Press date 2008 page 152 isbn 978 1587654237 ref Blood residue analysis is also an important technique in archeology . Forensic significance Blood constitutes about eight percent of a person s weight normally about five liters , and it circulates near the surface of the skin. Almost all Physical trauma trauma to the body, therefore, results in the shedding of blood. Its red color makes it readily apparent at crime scenes, and its residues are very difficult to completely remove. Blood residue has even been recovered from 100,000 year old stone tools. ref name Robinson 152 Laboratory testing can reveal whether a substance is indeed blood, whether the blood is of animal or human origin, and the Human blood group systems blood group to which it belongs. This allows investigators to include or exclude persons as perpetrators or victims. The antigens that allow blood group testing, however, deteriorate with age or improper storage. ref name Robinson 154 Robinson, 154. ref ... matching of blood residue to individuals with DNA profiling techniques. ref name Robinson 154 ... distribution of bloodstains. Forensic procedure Finding and documenting blood residue Freshly dried ... searched for blood residue. Flashlights held at an angle to the surfaces under examination assist .... ref name Robinson 153 Robinson, 153. ref The standard documentation of blood residue includes ... and sketches are also produced to show the relationship of the blood residue to other elements of the scene ... residue samples are stored under refrigeration and, in the case of stains, air dried. ref name Robinson ... more details
Pesticide residue refers to the pesticide s that may remain on or in food after they are applied to food crops. ref GoldBookRef title pesticide residue file P04520 ref The levels of these residues in foods is often stipulated by regulatory bodies in many countries. Exposure of the general population to these residues most commonly occurs through consumption of treated food sources, or being in close contact to areas treated with pesticides such as farms or lawns around houses. ref name EPAres cite web url http cfpub.epa.gov eroe index.cfm?fuseaction detail.viewInd&lv list.listByAlpha&r 224028&subtop 312 title Pesticide Residue publisher Environmental Protection Agency ref Many of these chemical residues, especially derivatives of chlorinated pesticides, exhibit bioaccumulation which could build up to harmful levels in the body as well as in the environment. ref name chlorinatedpest Cite journal ... ref Pesticide residue by country expand section date February 2009 European Union See also Pesticides in the European Union In September 2008, the European Union issued new and revised Maximum Residue ... over by the Pesticide Residue Committee PRC . The PRC advise the government through the Pesticides ... of pesticide residue that may remain on food are set by the United States Environmental Protection ... food can significantly lower residue exposure by as much as about 90 . The group came up with a list ... of residue levels that are persistent in the environment. The methods of organic farming prohibit ... residue that was available in commercially produced food. Also, in comparison to food that was grown using Integrated pest management techniques, organic produce showed about 50 less residue. Organic ... Residue Workshop http www.pesticide residues.org Pesticide residue in Europe http www.mrldatabase.com International Maximum Residue Level Database http www.pesticides.gov.uk UK Pesticides Safety ... pesticide residue limits food stub chem stub pesticides DEFAULTSORT Pesticide Residue Category Pesticides ... more details
In mathematics , noncommutative residue , defined independently by M. harvtxt Wodzicki 1984 and harvtxt Guillemin 1985 , is a certain trace on the algebra of pseudodifferential operator s on a compact space compact differentiable manifold that is expressed via a local density. In the case of the circle , the noncommutative residue had been studied earlier by M. harvtxt Adler 1979 and Y. harvtxt Manin 1978 in the context of one dimensional integrable system s. See also Dixmier trace References Citation last1 Adler first1 M. title On a trace functional for formal pseudo differential operators and the symplectic structure of the Korteweg de Vries type equations doi 10.1007 BF01410079 mr 520927 year 79 month 1978 journal Inventiones Mathematicae issn 0020 9910 volume 50 issue 3 pages 219 248 Citation last1 Guillemin first1 Victor title A new proof of Weyl s formula on the asymptotic distribution of eigenvalues doi 10.1016 0001 8708 85 90018 0 mr 772612 year 1985 journal Advances in Mathematics issn 0001 8708 volume 55 issue 2 pages 131 160 Citation last1 Kassel first1 Christian title Le r sidu non commutatif d apr s M. Wodzicki url http www.numdam.org item?id SB 1988 1989 31 199 0 mr 1040574 year 1989 journal Ast risque issn 0303 1179 issue 177 pages 199 229 Citation last1 Manin first1 Ju. I. title Current problems in mathematics, Vol. 11 Russian publisher Akad. Nauk SSSR Vsesojuz. Inst. Nau n. i Tehn. Informacii, Moscow mr 0501136 year 1978 chapter Algebraic aspects of nonlinear differential equations pages 5 152 citation last Wodzicki first M. title Spectral asymmetry and noncommutative residue series PhD thesis publisher Steklov institute of mathematics year 1984 place Moscow Citation last1 Wodzicki first1 Mariusz title K theory, arithmetic and geometry Moscow, 1984 1986 publisher Springer Verlag location Berlin, New York series Lecture Notes in Math. doi 10.1007 BFb0078372 mr 923140 year 1987 volume 1289 chapter Noncommutative residue. I. Fundamentals pages 320 399 Category ... more details
The residue theorem , sometimes called Cauchy s Residue Theorem , in complex analysis is a powerful tool to evaluate line integral s of analytic function s over closed curves and can often be used to compute real integrals as well. It generalizes the Cauchy integral theorem and Cauchy s integral formula . From a geometrical perspective, it is a special case of the Stokes theorem generalized Stokes theorem . Image Residue theorem illustration.png right 250px thumb Illustration of the setting. The statement is as follows. Suppose U is a simply connected open subset of the complex plane , and a sub 1 sub ,..., a sub n sub are finitely many points of U and f is a function mathematics function which is defined and holomorphic function holomorphic on U a sub 1 sub ,..., a sub n sub . If is a rectifiable curve in U which does not meet any of the a sub k sub , and whose start point equals its endpoint, then math oint gamma f z , dz 2 pi i sum k 1 n operatorname I gamma, a k operatorname Res f, a k . math If is a Curve orientation positively oriented Jordan curve , I , a sub k sub 1 if a sub ... sub denotes the residue complex analysis residue of f at a sub k sub , and I , a sub k sub is the winding ... around a sub k sub at all. The relationship of the residue theorem to Stokes theorem is given by the Jordan ... k sub . In order to evaluate real integrals, the residue theorem is used in the following manner the integrand ... half plane, forming a semicircle. The integral over this curve can then be computed using the residue ... i frac 1 z i right , math math frac e itz 2i z i frac e itz 2i z i , , math the residue complex analysis residue of f z at z i is math operatorname Res z i f z e t over 2i . math According to the residue ... Morera s theorem Nachbin s theorem Residue at infinity Logarithmic form References General references ... ResidueTheorem.html Residue theorem in MathWorld http math.fullerton.edu mathews c2003 ResidueCalcMod.html Residue Theorem Module by John H. Mathews Category Complex analysis Category ... more details
There are two types of agriculture agricultural crop residues br Field residues are materials left in an agricultural field or orchard after the crop has been harvest ed. These residues include stalks and stubble plant stem stems , leaf leaves , and seed pods. Good management of field residues can increase efficiency of irrigation and control of erosion . br Process residues are those materials left after the processing of the crop into a usable resource. These residues include husk s, seeds, bagasse , and root s. They can be used as animal fodder and soil amendments soil amendment , fertilizers and in manufacturing . See also Conventional tillage External links http www.ctic.purdue.edu Core4 CT CRM Benefits.html Field residue management benefits Category Crops Agri stub ... more details
In number theory , an integer q is called a quadratic residue modular arithmetic modulo n if it is Congruence ... the terminology quadratic residue and quadratic nonresidue , and states that, if the context makes it clear ... of two residues is always a residue. Prime modulus Modulo 2, every integer is a quadratic residue ..., the multiplicative inverse of a residue is a residue, and the inverse of a nonresidue is a nonresidue ... a prime, the product of two nonresidues is a residue and the product of a nonresidue and a nonzero residue is a nonresidue. ref name Gauss, DA, art. 98 The first supplement ref Gauss, DA, art 111 ref to the law of quadratic reciprocity is that if p 1 mod 4 then &minus 1 is a quadratic residue modulo ... of a residue modulo p is a residue and the negative of a nonresidue is a nonresidue. If p 3 mod 4 the negative of a residue modulo p is a nonresidue and the negative of a nonresidue is a residue ... 8, 16, or some higher power of 2, then a is a residue modulo m if and only if a 1 mod 8 . ref Gauss ... 4 sup 2 sup &equiv 12 sup 2 sup &equiv 16 blockquote So a nonzero number is a residue mod 8, 16, etc ... p is a residue modulo any power of p if and only if it is a residue modulo p . ref name Gauss, DA, art. 101 Gauss, DA, art. 101 ref If the modulus is p sup n sup , then p sup k sup A is a residue modulo p sup n sup if k &ge n is a nonresidue modulo p sup n sup if k < n is odd is a residue modulo p sup n sup if k < n is even and A is a residue is a nonresidue modulo p sup n sup if k < n is even ... is if a is a residue modulo n , then a is a residue modulo p sup k sup for every prime power dividing ... prime power dividing n . Modulo a composite number, the product of two residues is a residue. The product of a residue and a nonresidue may be a residue, a nonresidue, or zero. blockquote For example, from the table for modulus 6 1 , 2, 3 , 4 , 5 residues in bold . The product of the residue 3 and the nonresidue 5 is the residue 3, whereas the product of the residue 4 and the nonresidue 2 ... more details
Other uses pp semi protected small yes Image Chemicals in flasks.jpg thumb right Chemistry is the science ... changes during interactions and chemical reactions. science Chemistry is the science of matter , especially ... cite web url http chemweb.ucc.ie what is chemistry.htm title What is Chemistry? publisher Chemweb.ucc.ie date accessdate 2011 06 12 ref ref http dictionary.reference.com browse ChemistryChemistry . n.d. . Merriam Webster s Medical Dictionary. Retrieved August 19, 2007. ref Chemistry is concerned ... bond s. Chemistry is sometimes called the central science because it connects physics with other ... Bursten, H. Lemay. Chemistry The Central Science . Prentice Hall 8 edition 1999 . ISBN 0 13 010310 1. Pages 3 4. ref ref Chemistry is seen as occupying an intermediate position in a hierarchy of the sciences ... in the 20th Century Bridging Boundaries . Wiley VCH, 2001. ISBN 3 527 30271 9. Pages 1 2. ref Chemistry is a branch of physical science but Difference between chemistry and physics distinct from physics . ref http www.springerlink.com content k97523j471763374 Is chemistry a branch of physics? a paper by Mario Bunge ref The etymology of the word chemistry has been much disputed. ref See Chemistry etymology for possible origins of this word. ref The genesis of chemistry can be traced to certain practices ... . Traditional chemistry starts with the study of elementary particles , atom s, molecule s, ref .... The chemical interaction interactions , reactions and transformations that are studied in chemistry ... . Such behaviors are studied in a chemistry laboratory using various forms of laboratory glassware ... sub disciplines. History Main History of chemistry See also Alchemy Timeline of chemistry Nobel Prize in Chemistry Ancient Egypt ians pioneered the art of synthetic wet chemistry up to 4,000 years ... the basis of the various branches of chemistry such as extracting metal from their ores, making ... atomist philosophy was later adopted by Epicurus 341 270 BCE . The genesis of chemistry can be traced ... more details
Orphan date February 2009 Ramsbottom Carbon Residue , which abbreviation is RCR, is well known in the petroleum industry as a method to calculate the carbon residue of a fuel. The carbon residue value is considered by some to give an approximate indication of the combustibility and deposit forming tendencies of the fuel. ref http www.kittiwake.com Default.aspx Page KB KB 29 http www.kittiwake.com Default.aspx Page KB KB 29 ref History This method originated from Dr J.R. Ramsbottom. under the supervision of Pr. Abdullah Ateeg. The carbon residue of a fuel The Ramsbottom test ASTM D 524 is used to measure carbon residues of an oil. In brief, the carbon residue of a fuel is the tendency to form carbon deposits under high temperature conditions in an inert atmosphere. This is an important value for the crude oil refinery, and usually one of the measurements in a crude oil assay . Carbon residue is an important measurement for the feed to the refinery process fluid catalytic cracking and coker unit delayed coking . Calculation methods There are three methods to calculate this carbon residue. It may be expressed as Ramsbottom Carbon Residue RCR , Conradson Carbon Residue CCR or Micro Carbon Residue MCR . Numerically, the CCR value is the same as that of MCR. Sometimes the carbon residue value can be listed as residual carbon content, RCC, which is normally the same as MCR CCR. For the test 4 grams of the sample are put into a weighted glass bulb. The sample in the bulb is heated in a bath at 553 C for 20 minutes. After cooling the bulb is weight again and the difference noted. See Also Crude oil assay Oil refinery Petroleum Cracking chemistry References reflist Category Petroleum petroleum stub ... more details
Any subset R of the set of integers is called a reduced residue system modulo n if gcd r , n 1 for each r contained in R R contains n elements no two elements of R are congruent modulo n . ref harvtxt Long 1972 p 85 ref ref harvtxt Pettofrezzo Byrkit 1970 p 104 ref Here math varphi math denotes Euler s totient function . A reduced residue system modulo n can be formed from a complete residue system modulo m complete residue system modulo n by removing all integers not relatively prime to n . For example, a complete residue system modulo 12 is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 . 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is 1,5,7,11 . Note that the cardinality of this set is math varphi 12 4 math . Some other reduced residue systems modulo 12 are 13,17,19,23 11, 7, 5, 1 7, 13,13,31 35,43,53,61 Facts If math r sub 1 sub , r sub 2 sub , ... , r sub n sub is a reduced residue system with n 2, then math sum r i equiv 0 pmod n math . Every number in a reduced residue system mod n except for 1 is a generator for the multiplicative group of integers modulo n multiplicative group of integers mod n . See also Complete residue system modulo m Congruence relation Euler s totient function Greatest common divisor Least residue system modulo m Modular arithmetic Number theory Residue number system Notes references References citation first1 Calvin T. last1 Long year 1972 title Elementary Introduction to Number Theory edition 2nd publisher D. C. Heath and Company location Lexington . citation first1 Anthony J. last1 Pettofrezzo first2 Donald R. last2 Byrkit year 1970 title Elements of Number Theory publisher Prentice Hall location Englewood Cliffs . External links http planetmath.org encyclopedia AbsolutelyLeastRemainder.html Residue systems at PlanetMath http mathworld.wolfram.com ReducedResidueSystem.html Reduced residue system at MathWorld Category Modular arithmetic Category ... more details
enzyme Name dihydrolipoyllysine residue 2 methylpropanoyl transferase EC number 2.3.1.168 CAS number IUBMB EC number 2 3 1 168 GO code 0043754 image width caption Cleanup date November 2008 In enzymology , a dihydrolipoyllysine residue 2 methylpropanoyl transferase EC number 2.3.1.168 is an enzyme that catalysis catalyzes the chemical reaction 2 methylpropanoyl CoA enzyme N sub 6 sub dihydrolipoyl lysine math rightleftharpoons math CoA enzyme N sub 6 sub S 2 methylpropanoyl dihydrolipoyl lysine Thus, the two substrate biochemistry substrates of this enzyme are 2 methylpropanoyl CoA and enzyme N6 dihydrolipoyl lysine , whereas its two product chemistry products are coenzyme A CoA and enzyme N6 S 2 methylpropanoyl dihydrolipoyl lysine . This enzyme belongs to the family of transferase s, specifically those acyltransferase s transferring groups other than aminoacyl groups. The systematic name of this enzyme class is 2 methylpropanoyl CoA enzyme N6 dihydrolipoyl lysine S 2 methylpropanoyl transferase . Other names in common use include dihydrolipoyl transacylase , enzyme dihydrolipoyllysine 2 methylpropanoyl CoA , S 2 methylpropanoyl transferase , 2 methylpropanoyl CoA enzyme 6 N dihydrolipoyl lysine , and S 2 methylpropanoyl transferase . This enzyme participates in valine, leucine and isoleucine degradation . Structural studies As of late 2007, 6 tertiary structure structures have been solved for this class of enzymes, with Protein Data Bank PDB accession codes PDB link 1ZWV , PDB link 2COO , PDB link 2IHW , PDB link 2II3 , PDB link 2II4 , and PDB link 2II5 . References reflist 1 cite journal author Massey LK, Sokatch JR, Conrad RS date 1976 title Branched chain amino acid catabolism in bacteria journal Bacteriol. Rev. volume 40 pages 42&ndash 54 pmid 773366 issue 1 pmc 413937 cite journal author Chuang DT, Hu CC, Ku LS, Niu WL, Myers DE, Cox RP date 1984 title Catalytic and structural properties of the dihydrolipoyl transacylase component of bovine branched chain alpha ... more details
enzyme Name dihydrolipoyllysine residue succinyltransferase EC number 2.3.1.61 CAS number 9032 28 4 IUBMB EC number 2 3 1 61 GO code 0004149 image width caption In enzymology , a dihydrolipoyllysine residue succinyltransferase EC number 2.3.1.61 is an enzyme that catalysis catalyzes the chemical reaction succinyl CoA enzyme N sub 6 sub dihydrolipoyl lysine math rightleftharpoons math CoA enzyme N sub 6 sub S succinyldihydrolipoyl lysine Thus, the two substrate biochemistry substrates of this enzyme are succinyl CoA and enzyme N6 dihydrolipoyl lysine , whereas its two product chemistry products are coenzyme A CoA and enzyme N6 S succinyldihydrolipoyl lysine . This enzyme belongs to the family of transferase s, specifically those acyltransferase s transferring groups other than aminoacyl groups. The systematic name of this enzyme class is succinyl CoA enzyme N6 dihydrolipoyl lysine S succinyltransferase . Other names in common use include dihydrolipoamide S succinyltransferase , dihydrolipoamide succinyltransferase , dihydrolipoic transsuccinylase , dihydrolipolyl transsuccinylase , dihydrolipoyl transsuccinylase , lipoate succinyltransferase Escherichia coli , lipoic transsuccinylase , lipoyl transsuccinylase , succinyl CoA dihydrolipoamide S succinyltransferase , succinyl CoA dihydrolipoate S succinyltransferase , and enzyme dihydrolipoyllysine succinyl CoA S succinyltransferase . This enzyme participates in citrate cycle tca cycle and lysine degradation . Structural studies As of late 2007, 11 tertiary structure structures have been solved for this class of enzymes, with Protein Data Bank PDB accession codes PDB link 1BAL , PDB link 1BBL , PDB link 1C4T , PDB link 1E2O , PDB link 1GHJ , PDB link 1GHK , PDB link 1PMR , PDB link 1SCZ , PDB link 2BTG , PDB link 2BTH , and PDB link 2CYU . References reflist 1 cite journal author Derosier DJ, Oliver RM, Reed LJ date 1971 title Crystallization and preliminary structural analysis of dihydrolipoyl transsuccinylase, the core ... more details
A quadratic residue code is a type of cyclic code . There is a quadratic residue code of length math p math over the finite field math GF l math whenever math p math and math l math are primes, math p math is odd and math l math is a quadratic residue modulo math p math . Its generator polynomial as a cyclic code is given by math f x prod j in Q x zeta j math where math Q math is the set of quadratic residues of math p math in the set math 1,2, ldots,p 1 math and math zeta math is a primitive math p math th root of unity in some finite extension field of math GF l math . The condition that math l math is a quadratic residue of math p math ensures that the coefficients of math f math lie in math GF l math . The dimension of the code is math p 1 2 math Replacing math zeta math by another primitive math p math th root of unity math zeta r math either results in the same code or an equivalent code, according to whether or not math r math is a quadratic residue of math p math . An alternative construction avoids roots of unity. Define math g x c sum j in Q x j math for a suitable math c in GF l math . When math l 2 math choose math c math to ensure that math g 1 1 math while if math l math is odd math c 1 sqrt p 2 math where math p p math or math p math according to whether math p math ... residue code more precisely the ideal of math F l X langle X p 1 rangle math generated by math g x math corresponds to the quadratic residue code. The minimum weight of a quadratic residue ... parity check digit to a quadratic residue code gives an extended quadratic residue code . When math p equiv 3 math mod math 4 math an extended quadratic residue code is self dual otherwise it is equivalent ... of an extended quadratic residue code has a subgroup which is isomorphic to either math PSL 2 p math or math SL 2 p math . Examples of quadratic residue codes include the math 7,4 math Hamming code ... Quadratic residue Category Coding theory math stub ... more details
A high residue diet is a diet high in dietary fiber , which aids in bowel movement. ref name intro cite book last1 Frey first1 Rita last2 Shearer Cooper first2 Lisa Anne title Introduction to nursing assisting building language skills url http books.google.com books?id 5mCn7y B16sC&pg PA285 year 1985 publisher Cengage Learning isbn 9780827362338 page 285 ref General guidelines Women should aim for at least 21 to 25 grams of fiber daily. Men should try for 30 to 38 grams daily. ref name mayoclinic http www.mayoclinic.com health high fiber foods NU00582 High Fiber Diet . Mayo Clinic . August 15, 2009. Retrieved 11 October 2011 ref Foods to include High fiber foods include whole grain breads and cereals, vegetables and fruits especially dried fruits such as apricots, prunes and raisins . ref name intro References Reflist External links http www.livestrong.com article 325753 list of foods in a high residue diet List of foods in a High Residue Diet livestrong.com food stub Category Diets ... more details
The shredding of automobiles and major household appliances is a process where a hammermill acts as a giant tree chipper by grinding the materials fed into it to fist size pieces. The shredding of automobiles results in a mixture of ferrous metal , non ferrous metal e.g. alloy s of copper and aluminium and shredder waste, called automotive shredder residue or automobile shredder residue ASR . ASR consists of glass , fiber , rubber , automobile liquids, plastic s and dirt . ASR is sometimes differentiated into shredder light fraction and dust . ASR often contains hazardous substance s such as lead , cadmium , and Polychlorinated biphenyl PCB . Therefore, some countries have classified ASR as hazardous waste and have established legislative controls. See also Bulky waste Industrial shredder External links http www.stiftung autorecycling.ch index e.php?page resh What is ASR? Category Vehicle recycling de RESH ... more details
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