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Encyclopedia results for Subscript

  1. Iota subscript

    Iota subscript Greek language Greek lang grc in Greek language Greek polytonic orthography is a way of writing the letter iota as a small vertical stroke beneath a vowel. It was used in the so called long diphthongs in Ancient Greek phonology Ancient Greek , that is, diphthong s the first part of which is a long vowel lang grc , and lang grc . In Latin based transliteration, it is not usually written. Before History of the Greek alphabet Standardization .E2.80.93 the Ionic alphabet the reforms of Eucleides and the adoption of the letters omega and eta 403 402 BC , there was no way of distinguishing between long and short vowels in Attic Greek . The classical Greek diphthongs , and were composed of a vowel and the letter iota whether or not the vowel was long. From the mid fifth to the mid fourth centuries, most of the Greek diphthongs began to lose their final elements. The pronunciation of i began to merge with that of e in Attic Greek and with that of i in Koine . The long a i came to be pronounced in the same way as the long a and o i in the same way as o . The loss of the diphthongs from the Greek language and the merging of the long diphthong phoneme s with other Greek vowel phonemes led to the omission of the final from digraphs that had formerly represented long diphthongs. The iota subscript was created when the iota was reintroduced in the Byzantine period, to correct the loss of from copies of earlier manuscripts ... of Eustathius of Thessalonica provide an instance of with iota subscript in the word lang grc ... vowel. History The iota subscript also known as hypogegrammeni was an editorial marking invented ... of Greek transliteration of Greek into the Latin alphabet , the iota subscript is usually omitted ... iota subscript is encoded at unichar 0345 COMBINING GREEK YPOGEGRAMMENI html cwith & x25cc ... Greek diacritics Iota adscript Ogonek DEFAULTSORT Iota Subscript Category Alphabetic diacritics Category ...   more details



  1. Subscript and superscript

    , see Wikipedia Manual of Style superscripts and subscripts . SpecialChars Image Subscript superscript ... 2 is a professionally designed subscript included as part of the glyph set the second 2 is a manual ... matches the other letters better. The top typeface is Adobe Garamond Pro the size of the subscript ... Myriad Pro the superscript is about 60 of the original characters, raised by about 44 . A subscript ... compound s or isotopes , but have many other uses as well. In professional typography , subscript and superscript ... contexts, not all alphanumerics may be available in all positions. For example, subscript letters ... letters. Despite these differences, all reduced sized glyphs go by the same generic name of subscript and superscript. Note that the terms subscript and superscript are synonymous with the terms inferior ... with 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms . A subscript can also distinguish ..., variables with a zero in the subscript are referred to as the variable name followed by naught ... to the third member of sequence O , which is 800. Also in mathematics and computing, subscript can ... aligned with the top of the full height numerals. Alignment examples Image Subscript superscript ... too high, and the weight of all the subscript and superscript glyphs would be too light. Software support ... in size and moved up or down they are not true subscript or superscript glyphs. Professional typesetting ... regular type to subscript or superscript. These programs, however, may also offer native OpenType support for the special subscript and superscript glyphs included in many professional typeface ... non professional glyphs colspan 2 style text align center Keyboard Shortcuts size subscript position superscript position user modifiable settings? subscript superscript OpenOffice 2.3 style text ... stuff sup 5 sup colspan 8 Notes Default subscript and superscript options can be overcome by manually ... subscript and superscript rendered in HTML for fonts in normal styles. style width 10.5em Example ...   more details



  1. Double subscript notation

    In engineering , double subscript notation is notation used to indicate some variable between two points each point being represented by one of the subscripts . In electronics , the notation is usually used to indicate the direction of current or voltage, while in mechanical engineering it is sometimes used to describe the force or Stress physics stress between two points, and sometimes even a component that spans between two points like a beam on a bridge or truss . Note that, although there are many cases where multiple subscripts are used, they are not necessarily called double subscript notation specifically. ref citation title Circuit Analysis for Power Engineering Handbook author Moses E. Zarudi, Shenkman, Arieh L. Shenkman year 1998 publisher Springer isbn 0412831805 ref This is a Convention norm convention to standardize the directions of double subscript labels. The following uses transistors as an example, but shows how the direction is read generally. The convention works like this math V mathrm CB math means the V from C to B. In this case, V would probably stand for voltage, C would probably denote the collector end of a transistor, and B would denote the base end of the same transistor. This is the same as saying the voltage drop from C to B . Although this assumes what the letters are, presumably this notation can be used in other contexts. math I mathrm CE math means the I from C to E. In this case, I would probably stand for current, C would again probably denote the collector end of a transistor, and E would denote the emitter end of the transistor. This is the same as saying the current in the direction going from C to E . Although this assumes what the letters mean, presumably this notation can be used in other contexts. The names given to IC power supply pin power supply pins on integrated circuits are independent from the conventions used in double subscript notations. They are coincidentally named in a similar way, for example V sub CC sub . References ...   more details



  1. Iota adscript

    Unreferenced date December 2009 In Greek language Greek polytonic orthography , the iota adscript Greek lang grc is a iota written after a vowel length long vowel in a long diphthong , as opposed to below the vowel as a small vertical stroke iota subscript lang grc . The iota subscript was created when the iota was reintroduced in the Byzantine period, to correct the loss of from copies of earlier manuscripts, but was placed below rather than beside the vowel to reflect the fact that it was not, by then, pronounced. This is still the most common convention today, although over the past few decades, many editors have preferred to reinstate the iota as an adscript. Others take a mixed approach, using the adscript for Upper case capitals , but the subscript for lower case letters. See also Greek diacritics Iota subscript DEFAULTSORT Iota Adscript Category Alphabetic diacritics Category Greek letters br Iota kenskrivet de Iota adscriptum Writingsystem stub ...   more details



  1. Sub

    Wiktionary sub sub Sub may refer to Submarine Submarine sandwich Subscription Substitute disambiguation Substitute teacher Subtitle captioning Bottom BDSM , also called sub short for submissive Subwoofer loudspeaker Sub TV channel Substitute character , one of the C0 and C1 control codes .sub disambiguation , several file extensions code nowiki sub nowiki code , an HTML tag used to put a character as a subscript SUB Seafarers Union of Burma Summit Bancorp Juanda International Airport in Surabaya, Indonesia See also Subroutine Subscriber Subscript Subeditor Subcontractor Disambiguation cs Sub de Sub eo SUB it SUB nl Sub ja ...   more details



  1. Adscript

    Orphan date February 2009 Adscript from Lat. ad, on or to, and scribere, to write means something written after, as opposed to subscript which means written under. A laborer was called an adscript of the soil adscriptus glebae when he could be sold or transferred with it, as in feudal days, and as in Russia until 1861. Carlyle speaks of the Java blacks as a kind of adscript. wiktionary References 1911 Category Typography typography stub pt Adscrito ...   more details



  1. Crisscross method

    Multiple issues refimprove March 2011 orphan February 2009 context December 2011 about the naming of molecules in analytical chemistry an algorithm for optimization mathematics mathematical optimization criss cross algorithm The Crisscross method is a method of finding out the chemical formula of a metal and non metal that combine to form an ionic bond. ref name BewickEdge cite book author1 Sharon Bewick author2 Jonathan Edge author3 Therese Forsythe coauthors and Richard Parsons title CK12 Chemistry url http books.google.com books?id pGh6afAR2joC&pg PA348 accessdate 25 March 2011 publisher CK 12 Foundation pages 348 349 id GGKEY J8HDA9JYCCN ref To use this method, the absolute value of the oxidation number of the first ion is used as the subscript of the second, and vice versa. The subscripts are then reduced by the greatest common factor . For instance, to find the formula for magnesium oxide The first word is the metal, which retains its name. The second word is the non metal, which retains its element prefix and add ... IDE as its suffix. The subscript number of an element doesn t affect the name e.g. a. Al sup 3 sup S sup 2 sup Al sub 2 sub S sub 3 sub Which then becomes Aluminum Sulfide References reflist External links http www.sparknotes.com testprep books sat2 chemistry chapter13section1.rhtml Formula Writing , SparkNotes Use dmy dates date March 2011 Category Analytical chemistry chemistry stub ...   more details



  1. Nuclear notation

    Unreferenced date December 2009 Nuclear notation is a common notation used in chemistry and physics to indicate the atomic number and mass number of an isotope . Nuclear notation is formed by writing an List of elements by symbol elemental symbol preceded by a subscript indicating its atomic number number of proton s and a superscript indicating its mass number number of nucleon s . For example, carbon 12 has an atomic number of 6 and a mass number of 12 and would thus be written as Nuclide Carbon 12 . If the isotope is in a metastable isomer metastable state , an m can be added to the mass number. For example technetium 99m can be written as Nuclide Technetium 99m . It is also common to drop the atomic number, as it is redundant with the symbol SimpleNuclide Carbon 12 , SimpleNuclide Technetium 99m . DEFAULTSORT Nuclear Notation Category Isotopes isotope stub ...   more details



  1. Dentolabial consonant

    Unreferenced stub auto yes date December 2009 Place of articulation Dentolabial consonants are consonants articulated with the lower teeth against the upper lip , the reverse of labiodental consonant s. They are rare cross linguistically, but one allophone of Swedish language Swedish IPAslink has been described as a velarization velarized dentolabial fricative. The diacritic for dentolabial consonants in the International Phonetic Alphabet Extended IPA diacritics Extended IPA is a superscript bridge, &thinsp IPA   &thinsp , by analogy with the subscript bridge used for labiodentals. For example, the voiced dentolabial fricative is transcribed IPA v , and the dentolabial nasal IPA m . DEFAULTSORT Dentolabial Consonant Category Consonants Phonetics stub ...   more details



  1. Echo vowel

    In speech, an echo vowel is a vowel that repeats the final vowel in a word. For example, in Chumash language Chumash , when a word ends with a glottal stop and comes at the end of an intonation unit , the final vowel is repeated after the glottal stop, but is whispered and faint, as in IPA sal ja for IPA ja arrow written ya . In Rukai language Rukai Taiwan , echo vowels are pronounced as full vowels. However, they are not only predictable, but disappear when under reduplication or when a suffix beginning with a is added to the word. class wikitable Rukai echo vowels and phonemic vowels Agent focus suffix reduplication echo vowel wa u ulu u ul a ara u ul u ulu drinks drink don t drink phonemic vowel wa kan kan a ara kan kan eats eat don t eat Echo vowels are also found in writing, especially with syllabary syllabaries . For example, a word kab may be written as if it were kaba, and keb would be written as if it were kebe. Such as system is found in Maya script Maya , though with complications depending on the quality of the preceding vowel. In Linear B , such final consonants were simply not written. However, consonant clusters were separated with echo vowels, for example writing the city Knossos as if it were konoso. In Hokkaid Ainu language Writing Ainu , some writers write final r with a subscript kana for ra, re, ri, ro, or ru, depending on the preceding vowel, whereas others use a subscript ru in all cases. See also Paragoge paragogic vowel References http www.chumashlanguage.com glossary gloss fr 00.html Chumash Glossarry DEFAULTSORT Echo Vowel Category Orthography Category Phonetics phonetics stub ...   more details



  1. B?

    Unreferenced date December 2009 B sub 0 sub , that is B subscript zero , is also generally used in Magnetic Resonance Imaging to denote the net magnetization vector . Although in physics and mathematics the notation to represent a physical quantity can be arbitrary, it is generally accepted in the literature, such as the International Society for Magnetic Resonance in Medicine that B sub 0 sub represents net magnetization. This is particularly prominent in areas of science where magnetic fields are important such as spectroscopy . By convention, B sub 0 sub is interpreted as a vector geometric vector quantity pointing the z direction, with subsequent x and y cartesian coordinate system cartesian axes oriented with the right hand rule . B sub 0 sub is also the symbol often used to denote the reference magnetization in which equations with electromagnetic fields are normalized. DEFAULTSORT B0 Category Magnetic resonance imaging ...   more details



  1. SUP

    Wiktionary sup Sup may refer to Supper , a name of the meal that is consumed before bed Supremum , in mathematics , the least upper bound of a partially ordered set Sup sfermion Squarks squark , the supersymmetric partner of the up quark, in particle physics code nowiki sup nowiki code , an HTML tag used to display characters as Subscript and superscript HTML superscript Short for supervisor Abbreviation for What s up disambiguation What s up ? SUP may refer to Sailors Union of the Pacific Socialist Party disambiguation Socialist Unity Party Scottish Unionist Party modern , established in the mid 1980s Stanford University Press Sydney University Press SUP Media or Sup Fabrik , a Russian internet company, owners of LiveJournal Selective Ultraviolet Phototherapy Stand up paddle surfing Simple Update Protocol , a proposal for making RSS and Atom feed updates faster and more efficient Software Upgrade Protocol disambig cs Sup rozcestn k de SUP es SUP eo SUP fr Sup it SUP he ru Sup sv Sup ...   more details



  1. Multi-user BASIC

    Unreferenced date March 2008 Multi user BASIC was a dialect of the BASIC language for the Digital Equipment Corporation DEC PDP 11 running the RT 11 operating system . One or more users were supported in separate address spaces sharing the same language interpreter. The syntax of the language was similar to but not identical to BASIC 11 . A key language element was the support for virtual files. These were similar to the virtual arrays in BASIC PLUS in but more limited. An array of integers, floatingpoint, or character strings of length 1, 2, 4, 8, 16, 32, or 64 could be placed in file and accessed with a subscript. The file could actually be opened or re opened with a different definition allowing integers, characters, and floating point numbers to be stored in the same file. Like BASIC 11, Multi User BASIC provided some support for lab equipment, support for character terminals LA30 , VT100 . Because it was a multi user system, it did not support real time data collection. compu lang stub Category BASIC interpreters Category PDP 11 ...   more details



  1. TUTT (linguistics)

    no footnotes date February 2012 DISPLAYTITLE T sub UTT sub linguistics In linguistics, T sub UTT sub always written as uppercase T plus uppercase UTT in subscript is an abbreviation for the time of utterance , the primary temporal reference in establishing tense. Grammatical tense represents the contrast between two measurements along the timeline of an utterance, with one of those measurements being the time of utterance T sub UTT sub the time at which the actual utterance is made . T sub UTT sub is always the primary point of reference for tense. There are three additional references to which T sub UTT sub can be contrasted T sub AST sub the time of assertion , T sub COM sub the time of completion , and T sub EVL sub the time of evaluation these are secondary references. The type used for the secondary reference is determined by Grammatical aspect aspect and type of utterance. References Mezhevich, Ilana 2008 Time Relational Approach to Tense and Mood. Bybee, Joan 1995 Modality & Grammar in Discourse. Amsterdam, John Benjamins. Ward, Drew 2009 An Inventory & Discussion of English Futurity. CALLE Category Linguistics Category Grammar ...   more details



  1. D-value (microbiology)

    In microbiology , D value refers to decimal reduction time is the time required at a certain temperature to kill 90 of the organisms being studied. Thus after a colony is reduced by 1 D, only 10 of the original organisms remain. The population number has been reduced by one decimal place in the counting scheme. Generally, each lot of a sterilization resistant organism is given a unique D value. When referring to D values it is proper to give the temperature as a subscript to the D. For example, a hypothetical organism is reduced by 90 after exposure to temperatures of 300 degrees Fahrenheit for 2 minutes, thus the D value would be written as D sub 300F sub 2 minutes. D value determination http www.biomedcentral.com 1471 2334 3 24 is often carried out to measure a disinfectant s efficiency to reduce the number of microbes, present in a given environment. See also Z value temperature Category Microbiology bioinformatics stub ...   more details



  1. Book:Greek alphabet

    saved book title The Greek Alphabet subtitle cover image Alpha uc lc.svg cover color The Greek Alphabet Overview Greek alphabet History of the Greek alphabet Main letters Alpha Beta Gamma Delta letter Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu letter Mu Nu letter Nu Xi letter Xi Omicron Pi letter Pi Rho Sigma Tau Upsilon Phi Chi letter Chi Psi letter Psi Omega Other letters Digamma Heta letter Heta Koppa letter Koppa Sampi San letter San Sho letter Sho Related topics Ancient Greek accent Archaic Greek alphabets Greek diacritics Greek ligatures Greek numerals Greek orthography Iota adscript Iota subscript Movable nu English pronunciation of Greek letters English pronunciation Romanization of Greek Greek letters used in mathematics, science, and engineering Use in mathematics, science, and engineering ...   more details



  1. Parisine

    figures, oldstyle figures, tabular figures, fractions, superscript subscript, superior inferior ..., caps figures, oldstyle figures, semi oldstyle figures, tabular figures, fractions, superscript subscript ... figures, tabular figures, fractions, superscript subscript, superior inferior figures, ordinals ...   more details



  1. Unicode subscripts and superscripts

    true superscript and subscript, H sub 2 sub O probably looks better using a subscript ... at U 2070 to U 209F. The two tables below show these characters. Each superscript or subscript character ... the actual Unicode characters the one on the right contains the equivalents using HTML markup for the subscript ... superscript and subscript characters Unicode also includes subscript and superscript characters that are intended ... of subscript and superscript characters References http www.unicode.org charts PDF U2070.pdf Superscripts ...   more details



  1. Chemical symbol

    A chemical or atomic symbol is a 1 or 2 letter internationally agreed code for a chemical element , usually derived from the name of the element, often in Latin . File Atomic Symbol.jpg thumb This is an example of an atomic symbol. The text boxes explain where the numbers are derived from. Only the first letter is capitalised. For example, He is the symbol for Helium he lium English name, not known in ancient Roman times , Pb for lead p lum b um in Latin , W for tungsten w olfram in German, not known in Roman times . Systematic element name Temporary symbols assigned to newly or not yet synthesized elements use 3 letter symbols based on their atomic numbers. For example, Uno was the temporary symbol for Hassium which had the temporary name of U n n il o ctium . Chemical symbols may be modified by the use of Subscript and superscript superscripts or subscripts to specify a particular isotope of an atom. Additionally, superscripts may be used to indicate the ionization or oxidation state of an element. Attached subscripts or superscripts specifying a nucleotide or molecule have the following meanings and positions The nucleon number mass number is shown in the left superscript position e.g., sup 14 sup N The proton number atomic number may be indicated in the left subscript position e.g., sub 64 sub Gd If necessary, a state of ionization or an excited state may be indicated in the right superscript position e.g., state of ionization Ca sup 2 sup . In astronomy , non ionised atomic hydrogen is often known as HI , and ionised hydrogen as HII . ref http csep10.phys.utk.edu astr162 lect milkyway ism.html The interstellar medium, with definition of HI and HII regions ref The number of atoms of an element in a molecule or chemical compound is shown in the right subscript position e.g., N sub 2 sub or Fe sub 2 sub O sub 3 sub A radical chemistry radical is indicated by a dot on the right side e.g., Cl for a chloride radical In Chinese language Chinese each chemical element h ...   more details



  1. Truncated power function

    lead missing date January 2012 Definition The truncated power function ref cite book title Interpolation and Approximation with Splines and Fractals first Peter last Massopust publisher Oxford University Press, USA year 2010 isbn 0195336542 page 46 ref with exponent math n math is defined as math x n begin cases x n & x 0 0 & x le 0. end cases math Alternatively, you may consider the subscript plus as an individual function with math x begin cases x & x 0 0 & x le 0. end cases math and interpret the exponent as conventional power function power . Relations Truncated power functions can be used for construction of B Spline s. math x mapsto x 0 math is the Heaviside function . math chi a,b x b x 0 a x 0 math where math chi math is the indicator function . Truncated power functions are refinable function refinable . External links http mathworld.wolfram.com TruncatedPowerFunction.html Truncated Power Function on MathWorld References references Category Numerical analysis ...   more details



  1. Strident vowel

    phonation Nofootnotes date August 2008 Onesource date August 2008 Strident vowels also called sphincteric vowels are strongly pharyngealization pharyngealized vowels accompanied by epiglottal trill ary epiglottal trill , where the larynx is raised and the pharynx constricted, so that either the epiglottis or the arytenoid cartilage s vibrate instead of the vocal cords . Strident vowels are fairly common in Khoisan languages , where they contrast with simple pharyngealized vowels. Stridency may be a type of phonation called harsh voice . A similar phonation, but without the trill, is called pressed voice or ventricular voice . The Bai language of southern China has a register phonology register system with allophone allophonic strident and pressed vowels. There is no official symbol for stridency in the International Phonetic Alphabet IPA , though a superscript IPA sup sup is often used. In some literature a subscript double tilde is sometimes used, as seen here on the letter a IPA a center Image Strident vowel a.png 25px center This is found in the Charis SIL Charis and Doulos SIL Doulos fonts IPA a , and has been accepted into Unicode at code point U 1DFD. References SOWL Category Phonation phonetics stub br Vogalenn skiltr ...   more details



  1. Bidental consonant

    Place of articulation Bidental consonants are consonants pronounced with both the lower and upper teeth. They are normally found only in speech pathology . The Extensions to the IPA symbol is both a superscript and a subscript bridge, &thinsp IPA   &thinsp . Besides interdental consonant s such as IPA n , which involve the tongue, there is at least one confirmed attestation of a true bidental consonant in normal language. The Black Sea sub dialect of the Shapsug dialect of Adyghe language Adyghe has a voiceless bidental fricative voiceless bidental non sibilant fricative where other dialects have IPA x , such as x six and dax pretty . Therefore it might best be transcribed phonemically as IPA x . However, there is no frication at the soft palate velum . The teeth themselves are the only constriction The lips are fully open, the teeth clenched and the tongue flat, the air passing between the teeth the sound is intermediate between IPA and IPA f L&M 1996 144 145 . This can be transcribed phonetically as IPA h , since IPA h has no place of articulation of its own. The Extensions to the IPA specify one other purely bidental consonant sound, the bidental percussive . References SOWL Category Dental consonants phonetics stub br Kensonenn daouzant lv Bident ls l dzskanis ms Konsonan dwigigi ...   more details



  1. Palatal lateral flap

    refimprove date February 2010 Infobox IPA ipa symbol The palatal lateral flap is a rare type of consonant al sound, used in some spoken language s. There is no symbol in the International Phonetic Alphabet that represents this sound. However, the symbol for a palatal lateral approximant may be used with a Extra short phonetics breve as an ad hoc symbol, placed under the letter to avoid the ascender, IPA &thinsp . ref This subscript placement is recommended by the typographers at SIL International . ref Features Features of the alveolar lateral flap flap palatal voiced oral lateral pulmonic Found in The Iwaidja language Iwaidja and Ilgar language s of Australia have a palatal lateral flap as well as alveolar lateral flap alveolar and retroflex lateral flap s. However, the palatal flap has not been shown to be phoneme phonemic it may instead be an underlying sequence IPA j . An example from Ilgar is the personal name IPA mi ar u . Notes Reflist IPA navigation DEFAULTSORT Palatal Lateral Flap Category Lateral consonants phonetics stub br Kensonenn staon a gostez dre stlakat fr Consonne battue lat rale palatale vois e ...   more details



  1. Stationary sequence

    In probability theory &ndash specifically in the theory of stochastic process es, a stationary sequence is a random sequence whose joint probability distribution is Invariant mathematics invariant over time. If a random sequence X sub   j sub is stationary then the following holds math begin align & qquad F X n,X n 1 , dots,X n N 1 x n, x n 1 , dots,x n N 1 & F X n k ,X n k 1 , dots,X n k N 1 x n, x n 1 , dots,x n N 1 , end align math where F is the joint cumulative distribution function of the random variable s in the subscript. If a sequence is stationary then it is wide sense stationary . If a sequence is stationary then it has a constant mean which may not be finite math E X n mu quad text for all n . math See also Stationary process References Probability and Random Processes with Application to Signal Processing Third Edition by Henry Stark and John W. Woods. Prentice Hall, 2002. Category Sequences and series Category Stochastic processes Category Time series analysis probability stub ...   more details



  1. Protomer

    In structural biology , a protomer is the structural unit of an oligomeric protein . A protomer can be a protein subunit or several different subunits, that assemble in a defined stoichiometry to form an oligomer . The protomer is the smallest subset of different subunits that form the oligomer. The protomers usually arrange in cyclic symmetry to form closed point group symmetries . Protomers are the main subunit in a viral capsid . br Examples br Different polypeptide chains protein subunits are conventionally designated by Greek letters. The number of each subunit in the oligomeric complex is indicated by the subscript number, similar to a chemical formula of a compound consisting of elements. Hemoglobin consists of two chains and two chains. The oligomer stoichiometry is thus sub 2 sub sub 2 sub . Hemoglobin is a heterotetramer consisting of four subunits two and two . It is a dimer of two protomers. Aspartate carbamoyltransferase has a sub 6 sub sub 6 sub subunit composition. The six protomers are arranged in D sub 3 sub symmetry. enzyme stub Category Structural biology Category Polymer chemistry es Prot mero fr Protom re ...   more details




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