Other people2 Alan Baker disambiguation Alan Baker Infobox scientist name Alan Baker Commented out because image was deleted image alanbakerfields.gif 200px image AlanBakerFrame.jpg image size 250px caption Alan Baker birth date Birth date and age 1939 08 19 df y birth place London , England death date death place nationality United Kingdom British field Mathematics work institutions University of Cambridge alma mater University College London br University of Cambridge doctoral advisor Harold Davenport doctoral students John Coates mathematician John Coates br Yuval Flicker br Roger Heath Brown br David Masser br Robert Odoni br Cameron Leigh Stewart Cameron Stewart known for Number theory br Diophantine equations prizes Fields Medal 1970 br Adams Prize 1972 footnotes Alan Baker , Royal Society FRS born on 19 August 1939 is an England English mathematician . He was born in London . He is known for his work on effective methods in number theory , in particular those arising from transcendence theory . He was awarded the Fields Medal in 1970, at age 31. His academic career started as a student of Harold Davenport , at University College London and later at Cambridge. He is a fellow of Trinity College, Cambridge . His interests are in number theory, Transcendence theory transcendence , logarithmic form , Effective results in number theory effective methods , Diophantine geometry and Diophantine analysis . Selected publications Citation last1 Baker first1 Alan title Linear forms in the logarithms of algebraic numbers. I doi 10.1112 S0025579300003971 mr 0220680 year 1966 journal Mathematika issn 0025 5793 volume 13 pages 204 216 Citation last1 Baker first1 Alan title Linear forms in the logarithms of algebraic numbers. II doi 10.1112 S0025579300008068 mr 0220680 year 1967a journal Mathematika issn 0025 5793 volume 14 pages 102 107 Citation last1 Baker first1 Alan title Linear forms in the logarithms of algebraic numbers. III doi 10.1112 S0025579300003843 mr 0220680 year ... more details
A product distribution is a probability distribution constructed as the distribution of the Product business product of random variable s having two other known distributions. Given two statistically independent random variables X and Y , the distribution of the random variable Z that is formed as the product math Z XY math is a product distribution . Algebra of random variables main Algebra of random variables The product is one type of algebra for random variables Related to the product distribution are the ratio distribution , sum distribution and difference distribution . More generally, one may talk of combinations of sums, differences, products and ratios. Many of these distributions are described in Melvin D. Springer s book from 1979 The Algebra of Random Variables . ref name SpringerM1979Algebra Cite book author Melvin Dale Springer title The Algebra of Random Variables publisher John Wiley & Sons Wiley year 1979 isbn 0 471 01406 0 ref Derivation A way of deriving the product distribution of Z from the joint distribution of the two other random variables, X and Y , is by integration of the following form ref Rohatgi, V.K., 1976. An Introduction to Probability Theory Mathematical Statistics. Wiley, New York. ref math p Z z int infty infty frac 1 x , p X,Y left x, frac z x right , dx. math This is not always straightforward. Special cases The distribution of the product of two random variables which have lognormal distribution s is again lognormal. This is itself a special case of a more general set of results where the logarithm of the product can be written as the sum of the logarithms. Thus, in cases where a simple result can be found in the list of convolutions of probability distributions , where the distributions to be convoluted are those of the logarithms of the components of the product, the result might be transformed to provide the distribution of the product. However this approach is only useful where the logarithms of the components of the produc ... more details
begin log sub 10 sub 1000 3. nowrap end Logarithms were introduced by John Napier in the early 17th ... mathematics product is the sum of the logarithms of the factors math log b xy log b x log b y . , math The present day notion of logarithms comes from Leonhard Euler , who connected them to the exponential ... . Logarithms are commonplace in scientific formula s, and in measurements of the Computational complexity ... . Motivation and definition The idea of logarithms is to reverse the operation of exponentiation ... , see exponentiation or ref Citation last1 Shirali first1 Shailesh title A Primer on Logarithms publisher ... , since nowrap 2 sup 4 sup 2&thinsp 2&thinsp &thinsp 2&thinsp &thinsp 2 16. Logarithms can also be negative ... called logarithmic identities or log laws , relate logarithms to one another. ref All statements ..., and root The logarithm of a product is the sum of the logarithms of the numbers being multiplied the logarithm of the ratio of two numbers is the difference of the logarithms. Therefore, the logarithm ... is linked from Mathematica The logarithm log sub b sub x can be computed from the logarithms of x and b ... math log b x frac log k x log k b . , math cite Typical scientific calculators calculate the logarithms ... series isbn 978 0 07 005023 5 year 1999 , p. 21 ref Logarithms with respect to any base b can be determined using either of these two logarithms by the previous formula math log b x frac log 10 x log ... properties explained below. On the other hand, nowrap base 10 logarithms are easy to use for manual ... is ubiquitous. The following table lists common notations for logarithms to these bases and the fields ... introduced integer logarithms in base 3 trakacheda and base 4 caturthacheda . ref citation contribution ... lookups. However logarithms are more straightforward and require less work. It can be shown using ... of logarithms alt A baroque picture of a sitting man with a beard. The method of logarithms ... Descriptio Description of the Wonderful Rule of Logarithms . ref Citation author Ernest William Hobson ... more details
DIT is a three letter abbreviation that can mean Defining Issues Test a quantitative test of moral reasoning by James Rest Dehradun Institute of Technology , Dehradun a premier engineering college of India Delhi Institute of Technology Detroit Institute of Technology Dublin Institute of Technology Diversified Information Technologies of Scranton, PA Digital Imaging Technician DigiPen Institute of Technology Directory Information Tree in implementations of Lightweight Directory Access Protocol LDAP and X.500 Dual inheritance theory Development Integration Test Software testing done at the conclusion of system development, which can include both manual and automated testing. Diiodotyrosine Drug induced thrombocytopenia dit can mean Institute of Dit A form of Dance that Adam Malone does, called the dit a synonym for Ban information , a logarithmic unit which measures information or entropy based on base 10 logarithms and powers of 10, referring to it as a decimal numerical digit digit . a particle in French language French names indicating a surname that the person used as a family name the shorter of the two symbols used in Morse code a French language French narrative poetic form of the Middle Ages most famously associated with Guillaume de Machaut the word literally means spoken , i.e. a poem meant to be spoken and not sung . See Medieval French literature . Doctor in Training Details in Thread a remote control . disambig de DIT fr Dit it DIT ja DIT ... more details
In statistics , given a set of data, math X x 1,x 2 dots,x n math and corresponding weight function weights , math W w 1, w 2, dots,w n math the weighted geometric mean is calculated as math bar x left prod i 1 n x i w i right 1 sum i 1 n w i quad exp left frac sum i 1 n w i ln x i sum i 1 n w i quad right math Note that if all the weights are equal, the weighted geometric mean is the same as the geometric mean . Weighted versions of other means can also be calculated. Probably the best known weighted mean is the weighted arithmetic mean, usually simply called the weighted mean . Another example of a weighted mean is the weighted harmonic mean . The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. See also average central tendency summary statistics Weighted mean Category Means Category Mathematical analysis statistics stub cs V en geometrick pr m r eo La peza geometria meznombro fr Moyenne g om trique pond r e ru ta ... more details
Orphan date November 2006 The quantitative insulin sensitivity check index QUICKI is derived using the inverse of the sum of the logarithms of the fasting insulin and fasting glucose math 1 log fasting insulin U mL log fasting glucose mg dL This index correlates well with glucose clamp technique glucose clamp studies r 0.78 , and is useful for measuring insulin sensitivity IS , which is the inverse of insulin resistance IR . It has the advantage of that it can be obtained from a fasting blood sample, and is the preferred method for certain types of clinical research. Source Katz A, Nambi SS, Mather K, Baron AD, Follmann DA, Sullivan G, Quon MJ. Quantitative insulin sensitivity check index a simple, accurate method for assessing insulin sensitivity in humans. J Clin Endocrinol Metab. 2000 Jul 85 7 2402 10. PMID 10902785 Values typically associated with the QUICKI calculation for insulin resistance in humans fall broadly within a range between 0.45 for unusually healthy individuals and 0.30 in diabetics. So lower numbers reflect greater insulin resistance. Source as above Katz et al. Also data for unusually healthy individuals derived from those practicing caloric restriction. See CR Society for details. treatment stub Category Diabetes ... more details
Merge to Closed form expression discuss Talk Closed form expression Proposed merger from Analytical expression date May 2011 Unreferenced date December 2009 In mathematics , an analytical expression or expression in analytical form is a mathematical expression constructed using well known operations that lend themselves readily to calculation. As is true for closed form expression s, the set of well known functions allowed can vary according to context but always includes the Arithmetic Arithmetic operations basic arithmetic operations addition, subtraction, multiplication, and division , extraction of nth root n th roots , exponentiation, logarithms, and trigonometric functions. However, the class of expressions considered to be analytical expressions tends to be wider than that for closed form expressions. In particular, special functions such as the Bessel functions and the gamma function are usually allowed, and often so are Series mathematics Infinite series infinite series and continued fraction s. On the other hand, Limit of a sequence limits in general, and integral s in particular, are typically excluded. If an analytic expression involves only the algebraic operations, which are addition, subtraction, multiplication, division and exponentiation with integral or fractional exponents hence including the extraction of n th roots , then it is more specifically referred to as an algebraic expression . math stub DEFAULTSORT Analytical Expression Category Special functions ja zh ... more details
unreferenced date October 2010 The scale convolution of two functions math s t math and math r t math , also known as their logarithmic convolution is defined as the function br math s l r t r l s t int 0 infty s left frac t a right r a frac da a math when this quantity exists. Results The logarithmic convolution can be related to the ordinary convolution by changing the variable from math t math to math v log t math math s l r t int 0 infty s left frac t a right r a frac da a int infty infty s left frac t e u right r e u du math math int infty infty s left e log t u right r e u du. math Define math f v s e v math and math g v r e v math and let math v log t math , then math s l r v f g v g f v r l s v . , math PlanetMath attribution id 5995 title logarithmic convolution Category Logarithms ... more details
orphan date November 2009 Steiner s problem is the problem of finding the maxima and minima maximum of the function mathematics function math f x x 1 x . , math ref cite web url http mathworld.wolfram.com SteinersProblem.html title Steiner s Problem author Eric W. Weisstein publisher MathWorld accessdate 12 08 2010 ref It is named after Jakob Steiner . The maximum is at math x e math , where e denotes the e mathematical constant base of natural logarithms . One can determine that by solving the equivalent problem of maximizing math g x ln f x frac ln x x . math The derivative of math g math can be calculated to be math g x frac 1 ln x x 2 . math It follows that math g x math is positive for math 0 x e math and negative for math x e math , which implies that math g x math and therefore math f x math increases for math 0 x e math and decreases for math x e. math Thus, math x e math is the unique global maximum of math f x . math References references DEFAULTSORT Steiner s Problem Category Functions and mappings Category Mathematical optimization bs Steinerov problem he ... more details
Margaret Brisbane, 5th Lady Napier died 1706 was a Peerage of Scotland Scottish peer . Family Margaret Brisbane Married and maiden names n e Napier was a member of the Clan Napier Napier family of Merchiston , Scotland , and was the great granddaughter of John Napier , the inventor of logarithms. She was the daughter of Archibald Napier, 2nd Lord Napier and Lady Elizabeth Erskine, daughter of John Erskine, 19th Earl of Mar . Upon the death of her brother, Archibald Napier, 3rd Lord Napier , the title passed through her sister Jean to her nephew Thomas Nicolson, 4th Lord Napier . When he, too, died unmarried and without heir, the title passed to her. She married John Brisbane, Secretary to the Admiralty in the reign of Charles II http heraldry.celticradio.net search.php?id 125 , and they had a daughter, Elizabeth Napier, Mistress of Napier, who in turn married Sir William Scott, 2nd Baronet of Thirlestane. When she died in 1706, the title passed to her grandson, Francis Napier, 6th Lord Napier , who was 4 years old. start box s reg sct succession box before Thomas Nicolson, 4th Lord Napier Thomas Nicholson title Lord Napier after Francis Napier, 6th Lord Napier Francis Napier years end box DEFAULTSORT Brisbane, Margaret, 5th Lady Napier Category Clan Napier Category 1706 deaths Scotland noble stub ... more details
File Manhattan Plot.png thumb 300px An illustration of a Manhattan plot depicting several strongly associated risk loci A Manhattan plot is a type of scatter plot , usually used to display data with a large number of data points many of non zero amplitude, and with a distribution of higher magnitude values, for instance in Genome wide association study genome wide association studies GWAS . ref name East cite journal pmid 20581876 doi 10.1038 ng0710 558 year 2010 last1 Gibson first1 Greg title Hints of hidden heritability in GWAS volume 42 pages 558 560 journal Nature Genetics issue 7 ref In GWAS Manhattan plots, genomic coordinates are displayed along the X axis, with the negative logarithm of the association P value for each single nucleotide polymorphism displayed on the Y axis. Because the strongest associations have the smallest P values e.g., 10 sup 15 sup , their negative logarithms will be the greatest e.g., 15 . It gains its name from the similarity of such a plot to the Manhattan skyline a profile of skyscrapers towering above the lower level buildings which vary around a lower height. References Reflist Category Statistical charts and diagrams Category Genetic epidemiology Category Bioinformatics statistics stub ... more details
refimproveBLP date January 2011 Stephen Pohlig is an electrical engineer currently working at MIT Lincoln Laboratory . As a graduate student of Martin Hellman s at Stanford University in the mid 1970 s, he helped develop the Pohlig Hellman exponentiation cipher and the Pohlig Hellman algorithm for computing discrete logarithm s. Bibliography S. Pohlig and M. Hellman, An improved algorithm for computing logarithms over GF p and its cryptographic significance Corresp. , Information Theory, IEEE Transactions on 24, no. 1 1978 106 110. Martin E. Hellman and Stephen C. Pohlig, http patft.uspto.gov netacgi nph Parser?Sect2 PTO1&Sect2 HITOFF&p 1&u 2Fnetahtml 2FPTO 2Fsearch bool.html&r 1&f G&l 50&d PALL&RefSrch yes&Query PN 2F4424414 United States Patent 4424414 Exponentiation cryptographic apparatus and method , January 3, 1984. References http purl.umn.edu 107353 Oral history interview with Martin Hellman , 2004, Palo Alto, California. Charles Babbage Institute , University of Minnesota, Minneapolis. Persondata Metadata see Wikipedia Persondata . NAME Pohlig, Stephen ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Pohlig, Stephen Category American electrical engineers Category Living people US engineer stub ... more details
Webster Wells 1851 Boston 1916 was a United States mathematician known primarily for his authorship of a series of mathematical textbooks. Wells graduated in 1873 at the Massachusetts Institute of Technology , where he was an instructor from 1873 to 1880, and later became successively an assistant professor 1883 , an associate professor 1885 , and a full professor 1893 of mathematics. Wells textbooks were used in many schools and colleges in the United States. Among the titles were Logarithms 1878 University Algebra 1878 Plane and Spherical Trigonometry 1884 Plane and Solid Geometry 1887 Higher Algebra 1889 College Algebra 1890 Academic Arithmetic 1893 Complete Trigonometry 1900 References Cite NIE Wells, Webster year 1905 Cite web url http name.umdl.umich.edu ACV1962.0001.001 title New plane geometry publisher University of Michigan Library author Webster Wells year 1909, 2005 accessdate 4 March 2011 Persondata Metadata see Wikipedia Persondata . NAME Wells, Webster ALTERNATIVE NAMES SHORT DESCRIPTION American mathematician DATE OF BIRTH 1851 PLACE OF BIRTH DATE OF DEATH 1916 PLACE OF DEATH DEFAULTSORT Wells, Webster Category 1851 births Category 1916 deaths Category American writers Category American mathematicians Category Massachusetts Institute of Technology faculty Category Massachusetts Institute of Technology alumni Category People from Massachusetts US writer stub US mathematician stub ... more details
Ueli Maurer born 26 May 1960 in Leimbach AG Leimbach , Switzerland is a professor for cryptography at the ETH Zurich Swiss Federal Institute of Technology Zurich ETH Zurich . Maurer studied electrical engineering at ETH Zurich and obtained his PhD in 1990. Afterwards, he joined Princeton university as a postdoc. In 1992 he became part of the computer science faculty of ETH Zurich. In a seminal work he showed that the Diffie Hellman problem is under certain conditions Equivalence relation equivalent to solving the discrete log problem. ref name MAURER Ueli Maurer Towards the equivalence of breaking the Diffie Hellman protocol and computing discrete logarithms. In Advances in Cryptology Crypto 94. Springer Verlag, 1994, S. 271 281. ref From 2002 until 2008 Maurer also served on the board of Tamedia Tamedia AG . ref name TAMEDIA http www.tamedia.ch de mediencorner medienmitteilungen Seiten Jahresabschluss2007Medienmitteilung.aspx Tamedia AG Medienmitteilung 23. April 2008 Jahresabschluss 2007 ref Maurer is editor in chief of the Journal of Cryptology . Links DNB Portal 114320357 http www.crypto.ethz.ch maurer Website of Ueli Maurer at ETH Zurich References Reflist Persondata Metadata see Wikipedia Persondata . NAME Maurer, Ueli ALTERNATIVE NAMES SHORT DESCRIPTION Swiss cryptographer DATE OF BIRTH 26 May 1960 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Maurer, Ueli Category 1960 births Category Living people Category Swiss cryptographers computer science stub ... more details
Refimprove date March 2007 Jainism ch rya Virasena was an 8th century India n Indian mathematics mathematician and Jainism Jain philosopher and scholar. He was a student of the Jain sage El ch rya. ref name Indranandi He is also known to be a famous orator and an accomplished poet. ref name Jinasena His most reputed work is the Jain treatise Dhavala . Late Dr. Hiralal Jain places the completion of this treatise in 816 AD. ref cite book last Nagrajji first Acharya Shri title Agama and Tripitaka Language and Literature publisher Concept Publishing Company series year 2003 page 530 isbn 8170227305, 9788170227304 ref Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ardhaccheda the number of times a number could be divided by 2 effectively logarithms to base 2. He also worked with logarithms in base 3 trakacheda and base 4 caturthacheda . ref citation contribution History of Mathematics in India title Students Britannica India Select essays editor1 first Dale editor1 last Hoiberg editor2 first Indu editor2 last Ramchandani first R. C. last Gupta page 329 publisher Popular Prakashan year 2000 contribution url http books.google.co.uk books?id xzljvnQ1vAC&pg PA329&lpg PA329&dq Virasena logarithm v onepage&q Virasena 20logarithm&f false ref Virasena gave the approximate formula C 3 d 16 d 16 113 to relate the circumference of a circle, C , to its diameter, d . For large values of d , this gives the approximation 355 113 3.14159292..., which is more accurate than the approximation 3.1416 given by Aryabhata in the Aryabhatiya . ref Citation last Mishra first V. author link last2 Singh first2 S. L. author2 link title First Degree Indeterminate Analysis in Ancient India and its Application by Virasena journal Indian Journal of History of Science volume 32 issue 2 pages 127 133 date February 1997 origyear 1995 month Nove ... more details
The generic group model ref cite conference author Victor Shoup title Lower bounds for discrete logarithms and related problems conference Advances in Cryptology Eurocrypt 97 booktitle Lecture Notes in Computer Science volume 1233 pages 256 266 publisher Springer Verlag date 1997 url http www.shoup.net papers dlbounds1.pdf format pdf accessdate 2010 04 09 ref ref cite conference author Ueli Maurer title Abstract models of computation in cryptography conference 10th IMA Conference On Cryptography and Coding booktitle Lecture Notes in Computer Science volume 2796 pages 1 12 publisher Springer Verlag date 2005 url ftp ftp.inf.ethz.ch pub crypto publications Maurer05.pdf format pdf accessdate 2007 11 01 ref is an idealised cryptographic model, where the adversary is only given access to a randomly chosen encoding of a group mathematics group , instead of efficient encodings, such as those used by the finite field or Elliptic curve cryptography elliptic curve groups used in practice. The model includes an oracle machine oracle that executes the group mathematics group binary operation operation . This oracle takes two encodings of group elements as input and outputs an encoding of a third element. If the group should allow for a pairing operation this operation would be modeled as an additional oracle. One of the main uses of the generic group model is to analyse computational hardness assumptions . An analysis in the generic group model can answer the question What is the fastest generic algorithm for breaking a cryptographic hardness assumption . A generic algorithm is an algorithm that only makes use of the group operation, and does not consider the encoding of the group. This question was answered for the discrete logarithm problem by Victor Shoup using the generic group model. ref Victor Shoup Lower Bounds for Discrete Logarithms and Related Problems. EUROCRYPT 1997 256 266 ref Other results in the generic group model are for instance. ref Ueli M. Maurer, Stefan Wolf ... more details
other persons Peter Gray Peter Gray 1807? 1887 , was a Scottish writer on life contingencies. Gray was born at Aberdeen about 1807, was educated at Gordon s Hospital , now Gordon s College , in that city, from which he was sent on account of his promise and industry for two years to Aberdeen University . Here he developed a taste for mathematics, and, with the sole desire to assist the studies of a friend, afterwards took a special interest in the study of life contingencies. He became an honorary member of the Institute of Actuaries , and his contributions to the Journal of that society were numerous and valuable. He undertook, purely as a labour of love, the task of organising and preparing for publication the tables deduced from the mortality experience issued by the institute. Gray specially constructed for Part I. of the Institute Text Book an extensive table of values of log 10 1 i , appending thereto an interesting note on the calculations. He was a fellow of the Royal Astronomical and Royal Microscopical Societies , and was distinguished by his knowledge of optics and of applied mechanics. Gray died on 17 Jan. 1887, in his eightieth year. With Henry Ambrose Smith and William Orchard he published Assurance and Annuity Tables, according to the Carlisle Rate of Mortality , at three per cent., 8vo, London, 1851, and contributed a preliminary notice to William Orchard s Single and Annual Assurance Premiums for every value of Annuity, 8vo, London, 1856. His separate writings are 1. Tables and Formul for the Computation of Life Contingencies with copious Examples of Annuity, Assurance, and Friendly Society Calculations, 8vo, London, 1849. 2. Remarks on a Problem in Life Contingencies, 8vo, London, 1850. 3. Tables for the Formation of Logarithms and Anti Logarithms to twelve Places with explanatory Introduction, 8vo, London, 1865 another edition, 8vo, London, 1876. References reflist DNB wstitle Gray, Peter Persondata Metadata see Wikipedia Persondata . NAME Gray, ... more details
one equation to a system of linear equations in r unknowns, namely the discrete logarithms of the r ... discrete logarithms efficiently in elliptic curve groups. However For special kinds of curves ... Hellman and J.M. Reyneri, Fast computation of discrete logarithms in GF q ,Advances in Cryptology ... logarithms in finite fields and their cryptographic significance , by Andrew Odlyzko http www.cs.toronto.edu ... more details
and Discrete Logarithms , Journal of Cryptology, Volume 13, pp 437 447, 2000 ref that this analogy ... of another of Pollard s discrete logarithm algorithms, Pollard s rho algorithm for logarithms Pollard ... theoretic algorithms Category Computer algebra Category Logarithms nl Pollards lambda algoritme ... more details
the first example of mathematical problem where the solution is expressed in terms of super logarithms ... ,k 5 math require super super logarithms, super super super logarithms etc. slog as inverse of tetration ... Logarithms ru tr Tetrasyon S per logaritma S per logaritma ... more details
Sang, Five Place Logarithms , Edinburgh, 1859 Edward Sang, Life assurance and annuity tables with copious ... of Edinburgh, volume 26 Edward Sang, A New table of seven place logarithms of all numbers continuously ... of Actuaries Journal 16, 1872, 253 265. Edward Sang, Account of the new table of logarithms to 200,000 ... of a Table of the Logarithms of all Numbers up to One Million , 1872 constructed in the http locomat.loria.fr ... place errors in Vlacq s table of logarithms , Proceedings of the Royal Society of Edinburgh 8, 1875 ... logarithms of all numbers continuously up to 200000 , Edinburgh, 1878 second edition Edward Sang ... more details
math log b a log d a over log d b math This identity is needed to evaluate logarithms on calculators ... 1 over x b log a x 0 quad mbox if b 0 math The last limit is often summarized as logarithms grow ... right ,dx frac x left n 1 right n 1 C math Approximating large numbers The identities of logarithms ... × 10 sup 9,808,357 sup . Similarly, factorials can be approximated by summing the logarithms ... rules for logarithms. However a multivalued function can be defined which satisfies most of the identities ... www.mathwords.com l logarithm.htm Logarithm in Mathwords Category Logarithms Category Mathematical ... more details
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