science logarithmic.html Detailedlogarithmictimeline of the Universe http www.futuretimeline.net http www.futuretimeline.net a timeline of future history DEFAULTSORT DetailedLogarithmicTimeline ...Main logarithmictimeline This timeline allows one to see the whole history of the universe, the Earth, and mankind Humankind is a bastard word, half Latin, half Germanic. Its use is based on the mistaken idea that mankind is sexist. in one table. Each row is defined in years ago , that is, year s before the present calendar date date , with the earliest times at the top of the chart. In each table cell on the right, references to events or notable people are given, more or less in chronological order within the cell. Each row corresponds to a change in log time before present of about 0.1 using log base 10 , similar to Renard numbers . class wikitable style background silver abbr Interval Time interval, before the present time. a annum year style background silver abbr Period List of time periods Period style background silver abbr Event Event, Invention or Historical development align center 13.7 Gigaannum Ga &ndash 12.6 Ga Big Bang , Inflation cosmology Inflation , Galaxy formation and evolution Stars and galaxies , Earliest quasar s align center 12.6 Ga &ndash 10 Ga NGC 6522 star cluster forms, at least 12 Ga ago. Omega Centauri star cluster forms align center 10 Ga &ndash 8 Ga Gliese 876 and its planets form ref name saffe2005 cite journal last1 Saffe first1 C. last2 G mez first2 M. last3 Chavero ... 2011 Thailand floods . A logarithmictimeline can also be devised for events which should occur .... See also Timeline of the far future List of timelines Timeline of the Big Bang Geologic time scale Timeline of evolution Orders of magnitude time World history Technological singularity Logarithmictimeline Future of an expanding universe References Reflist External links http www.stanford.edu ... more details
comprehensive version similar to that of Sparks Histomap can be found at Detailedlogarithmictimeline . Example of a forward looking logarithmictimeline In this table each row is defined in seconds ... logarithmic.html Detailedlogarithmictimeline of the Universe http urss.ru cgi bin db.pl?cp &page Book&id ...Use dmy dates date April 2012 Unreferenced date April 2009 A logarithmictimeline is a timeline laid out according to a logarithmic scale . This necessarily implies a zero point and an infinity point , neither ... years 3 10 sup 12 sup years in the future. Example of a backward looking logarithmictimeline In this table ... that memories naturally fade in an exponential manner. Logarithmic timelines have also been used in future studies to justify the idea of a technological singularity . A logarithmic scale enables ... outline the nearer we approach modern times, and the logarithmic scale fulfills just this condition ... 10 sup 40 sup to 10 sup 35 sup Planck Epoch align center 10 sup 35 sup to 10 sup 30 sup Timeline of the Big .... Note that the logarithmic scale never actually gets to zero. class wikitable Years Ago List ... Web WWW , Biotechnology , Nanotechnology , Global warming , Timeline of historic inventions 2000s more... align center 10 sup 1 sup to 10 sup 2 sup 20th century Timeline of transportation ... , World war s, Timeline of historic inventions 20th century more... align center 10 sup 2 sup ... , Industrial Revolution , Colonialism , Firearms , Steam engine , Timeline of historic inventions ... , Major world religions Religions , Philosophy, Timeline of historic inventions 8th millennium ..., Ice age ends, Domestication Timeline of agriculture and food technology Agriculture and Animal husbandry ... , Timeline of cosmological eras Cosmology Timeline of the Big Bang Big Bang , Galaxy formation and evolution Stars and galaxies , Earth , Origin of Life Life See also Timeline of the Big Bang Geologic time scale Timeline of evolution Natural history Orders of magnitude time Technological singularity ... more details
Logarithmic can refer to Logarithm , a transcendental function in mathematics Logarithmic scale , the use of the logarithmic function to describe measurements Logarithmic growth Logarithmic distribution , a discrete probability distribution Natural logarithm mathdab ... more details
The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary ... , each elementary process should be equilibrated by its reverse process. History The principle of detailed ... introduced the principle of detailed balance for chemical kinetics. ref Wegscheider, R. 1911 http ... that follow from the principle of detailed balance. In 1931, Lars Onsager used these relations in his ... was awarded the 1968 Nobel Prize in Chemistry . Now, the principle of detailed balance is a standard ... equilibrium. This leads us immediately to the concept of detailed balance each process is equilibrated ... must be the same for the chain to be reversible. A Markov process satisfies detailed balance ... reversible Markov chain . ref name OHagan A Markov process is said to have detailed balance if the transition ... s P s,s ,. math The detailed balance condition is stronger than that required merely for a stationary distribution that is, there are Markov processes with stationary distributions that do not have detailed balance. Detailed balance implies that, around any closed cycle of states, there is no net flow ... transition matrix, the no net flow condition implies detailed balance. Transition matrices that are symmetric ... detailed balance. In these cases, a uniform distribution over the states is an equilibrium distribution. For continuous systems with detailed balance, it may be possible to continuously transform the coordinates ... the Markov states into a degeneracy of sub states. Detailed balance and the entropy growth For many systems of physical and chemical kinetics, detailed balance provides sufficient conditions for the entropy ... states that, according to the Boltzmann equation, the principle of detailed balance implies positivity ... gas kinetics with detailed balance ref name Boltzmann1872 ref name Tolman1938 served as a prototype ... of steady states and for quasi steady state approximation. J. Math. Chem, 3 1 , 25 42. ref with detailed balance. Nevertheless, the principle of detailed balance is not necessary for the entropy growth ... more details
in statistics Palermo Technical Impact Hazard Scale Logarithmictimeline counting f stop s for ratios ...Refimprove date May 2009 Cleanup date August 2007 File Logarithmic Scales.svg thumb 400px Various scales ... . A logarithmic scale is a scale measurement scale of measurement using the logarithm of a physical ... spaced increments that are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4. Each unit increase on the logarithmic ... for the given base 10, in this case . Presentation of data on a logarithmic scale can be helpful ... the actual values reduces a wide range to a more manageable size. Some of our sense s operate in a logarithmic fashion Weber Fechner law , which makes logarithmic scales for these input quantities especially ... shown logarithmic scales to be the most natural display of numbers by humans. ref cite web url http ... Logarithmic scales are either defined for ratios of the underlying quantity, or one has to agree to measure the quantity in fixed units. Deviating from these units means that the logarithmic measure ... s value is considered to be a dimensional quantity expressed in generic indefinite base logarithmic units. Example scales On most logarithmic scales, small values or ratios of the underlying quantity correspond to negative values of the logarithmic measure. Well known examples of such scales ... theory . Particle Size Distribution curves of soil Some logarithmic scales were designed such that large values or ratios of the underlying quantity correspond to small values of the logarithmic measure ... . Absorbance of light by transparent samples. Logarithmic units Logarithmic units are abstract mathematical ... on a logarithmic scale, that is, as being proportional to the value of a logarithm function. In this article, a given logarithmic unit will be denoted using the notation log n , where n is a positive ... of logarithmic units include common units of information and entropy , such as the bit log 2 ... and bel log 10 , neper log e , and other logarithmic scale units such as the Richter scale ... more details
Unreferenced date December 2009 In mathematics , specifically in calculus and complex analysis , the logarithmic ... properties Many properties of the real logarithm also apply to the logarithmic derivative, even ... So for positive real valued functions, the logarithmic derivative of a product is the sum of the logarithmic ... that the logarithmic derivative of a product is the sum of the logarithmic derivatives of the factors when they are defined . Similarly in fact this is a consequence , the logarithmic derivative of the reciprocal of a function is the negation of the logarithmic derivative of the function math ... number is the negation of the logarithm of the number. More generally, the logarithmic derivative of a quotient is the difference of the logarithmic derivatives of the dividend and the divisor math ... of the logarithms of the dividend and the divisor. Generalising in another direction, the logarithmic derivative of a power with constant real exponent is the product of the exponent and the logarithmic ... rule compare the list of logarithmic identities each pair of rules is related through the logarithmic derivative. Computing ordinary derivatives using logarithmic derivatives Main Logarithmic differentiation Logarithmic derivatives can simplify the computation of derivatives requiring the product ... to compute Nowrap &fnof x . Instead of computing it directly, we compute its logarithmic derivative ... the logarithmic derivative of each factor, summing, and multiplying by . Integrating factors The logarithmic derivative idea is closely connected to the integrating factor method for first order ... rule as D M where M now denotes the multiplication operator by the logarithmic derivative ... f has neither a zero nor a Pole complex analysis pole . Further, at a zero or a pole the logarithmic ... sup with n an integer, n 0. The logarithmic derivative is then n z and one can draw the general conclusion that for f meromorphic, the singularities of the logarithmic derivative of f are all ... more details
Unreferenced date December 2009 Image Log.svg thumb A graph of logarithmic growth In mathematics , logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y C log x . Note that any logarithm base can be used, since one can be converted to another by a fixed constant. Logarithmic growth is the inverse of exponential growth and is very slow. A familiar example of logarithmic growth is the number of digits needed to represent a number, N , in positional notation , which grows as log sub b sub N , where b is the base of the number system used, e.g. 10 for decimal arithmetic. Another example is in cryptography , where the key cryptography key size needed to protect against a brute force attack for a certain period of time grows logarithmically with the desired protection interval. In the design of computer algorithm s, logarithmic growth, and related variants, such as log linear, or linearithmic , growth are very desirable indications of efficiency. Logarithmic growth can lead to apparent paradoxes, as in the martingale roulette system martingale roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler s bankroll. It also plays a role in the St. Petersburg paradox . In microbiology , the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing are proportional to the population. See also Iterated logarithm an even slower growth model DEFAULTSORT Logarithmic Growth Category Logarithms ... more details
In algebraic geometry , a logarithmic pair consists of a Algebraic variety variety , together with a divisor along which one allows mild logarithmic singularities. They were studied by harvtxt Iitaka 1976 . Definition A boundary Q divisor on a variety is a Q divisor D of the form &Sigma d sub i sub D sub i sub where the D sub i sub are the distinct irreducible components of D and all coefficients are rational numbers with 0&le d sub i sub &le 1. A logarithmic pair , or log pair for short, is a pair X , D consisting of a normal variety X and a boundary Q divisor D . The log canonical divisor of a log pair X , D is K D where K is the canonical divisor of X . A logarithmic 1 form on a log pair X , D is allowed to have logarithmic singularities of the form d log z d z z along components of the divisor given locally by z 0. References Citation authorlink Shigeru Iitaka last1 Iitaka first1 Shigeru title Logarithmic forms of algebraic varieties id MathSciNet id 0429884 year 1976 journal Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics issn 0040 8980 volume 23 issue 3 pages 525 544 Citation last1 Matsuki first1 Kenji title Introduction to the Mori program publisher Springer Verlag location Berlin, New York series Universitext isbn 978 0 387 98465 0 id MathSciNet id 1875410 year 2002 Category algebraic geometry ... more details
align right Image Logarithmic Spiral Pylab.svg 260px thumb Logarithmic spiral pitch 10 Image NautilusCutawayLogarithmicSpiral.jpg ... logarithmic spiral File Fractal Broccoli.jpg 200px thumb Romanesco broccoli , which grows in a logarithmic spiral Image Mandel zoom 04 seehorse tail.jpg thumb 200px A section of the Mandelbrot set following a logarithmic spiral Image Low pressure system over Iceland.jpg thumb 200px A low pressure area over Iceland shows an approximately logarithmic spiral pattern File Messier51 sRGB.jpg thumb 200px The arms of Spiral galaxy spiral galaxies often have the shape of a logarithmic spiral, here the Whirlpool Galaxy Image Polygon spiral.svg thumb 300px A logarithmic spiral , equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic ... math r, theta math the logarithmic curve can be written as ref cite book title Divine Proportion ... mirabilis , Latin for miraculous spiral , is another name for the logarithmic spiral. Although ... 1952 , Evolutes. p. 206 ref Properties The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression , while in an Archimedean spiral these distances are constant. Logarithmic ... maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic ... to the lines, the mapping of all lines to all logarithmic spirals is onto . The pitch angle of the logarithmic ... the real line to a logarithmic spiral in the complex plane. One can construct a golden spiral , a logarithmic ... pitch about 17.03239 degrees , or approximate it using Fibonacci number s. Logarithmic spirals in nature In several natural phenomena one may find curves that are close to being logarithmic spirals ... Gilbert J. last Chin date 8 December 2000 title Organismal Biology Flying Along a Logarithmic Spiral ... a logarithmic spiral with pitch of about 12 degrees. ref cite book title The universal book of mathematics ... more details
In mathematics, the logarithmic norm is a real valued Functional mathematics functional on Operator mathematics ..., or its induced operator norm . The logarithmic norm was independently introduced by Germund Dahlquist ... unbounded operators as well. ref Gustaf S derlind, The logarithmic norm. History and modern theory ... matrix norm. The associated logarithmic norm math mu math of math A math is defined math mu A lim limits ... equals math mu A math , and is in general different from the logarithmic norm math mu A math , as math ... 0 math , but the logarithmic norm math mu A math may also take negative values, e.g. when math A math is Positive definite matrix negative definite . Therefore, the logarithmic norm does not satisfy the axioms of a norm. The name logarithmic norm, which does not appear in the original reference, seems ... d mathrm dt math is the Dini derivative upper right Dini derivative . Using logarithmic differentiation ... If the vector norm is an inner product norm, as in a Hilbert space , then the logarithmic norm ... to be unbounded. Thus Differential operator differential operators too can have logarithmic norms, allowing the use of the logarithmic norm both in algebra and in analysis. The modern, extended theory ... norm and the logarithmic norm are then associated with extremal values of Quadratic form quadratic ... x neq 0 frac real langle x, Ax rangle langle x,x rangle math Properties Basic properties of the logarithmic ... e t mu A , math for math t geq 0 math math mu A 0 , Rightarrow , A 1 leq 1 mu A math Example logarithmic norms The logarithmic norm of a matrix can be calculated as follows for the three most common ... sum limits j, j neq i a ij math Applications in matrix theory and spectral theory The logarithmic norm ... A leq real , lambda k leq mu A math . More generally, the logarithmic norm is related to the numerical ... , R A leq 1. math Thus the matrix norm and logarithmic norms may be viewed as generalizing the modulus ... theory and numerical analysis The logarithmic norm plays an important role in the stability analysis ... 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
Probability distribution name Logarithmic type mass pdf image Image Logarithmicpmf.svg 300px center Plot of the logarithmic PMF small The function is only defined at integer values. The connecting lines are merely guides for the eye. small cdf image Image Logarithmiccdf.svg 300px center Plot of the logarithmic CDF parameters math 0 p 1 math support math k in 1,2,3, dots math pdf math frac 1 ln 1 p frac p k k math cdf math 1 frac Beta p k 1,0 ln 1 p math mean math frac 1 ln 1 p frac p 1 p math median mode math 1 math variance math p frac p ln 1 p 1 p 2 , ln 2 1 p math skewness exists, but too complex kurtosis exists, but too complex entropy exists, but too complex mgf math frac ln 1 p , exp t ln 1 p text for t ln p , math char math frac ln 1 p , exp i ,t ln 1 p text for t in mathbb R math pgf math frac ln 1 pz ln 1 p text for z frac1p math In probability and statistics , the logarithmic distribution also known as the logarithmic series distribution or the log series distribution is a discrete probability distribution derived from the Maclaurin series expansion math ln 1 p p frac p 2 2 frac p 3 3 cdots. math From this we obtain the identity math sum k 1 infty frac 1 ln 1 p frac p k k 1. math This leads directly to the probability mass function of a Log p distributed random variable math f k frac 1 ln 1 p frac p k k math for k 1, and where 0 p 1. Because of the identity above, the distribution is properly normalized. The cumulative distribution function is math F k 1 frac Beta p k 1,0 ln 1 p math where B is the incomplete beta function . A Poisson mixture of Log p distributed random variables has a negative binomial distribution . In other words, if N is a random variable with a Poisson distribution , and X sub i sub , i 1, 2, 3, ... is an infinite ... the logarithmic distribution in a paper that used it to model relative species abundance . ref ... discrete distributions publisher John Wiley & Sons year 2005 edition 3 chapter Chapter 7 Logarithmic ... more details
Dablink Logarithmic derivative is a separate article. Calculus In calculus , logarithmic differentiation or differentiation by taking logarithms is a method used to derivative differentiate function mathematics function s by employing the logarithmic derivative of a function , ref cite book title Calculus demystified pages 170 first Steven G. last Krantz publisher McGraw Hill Professional year 2003 isbn 0071393080 ref math ln f frac f f math The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself. Logarithmic differentiation relies on the chain rule as well as properties of logarithms in particular, the natural logarithm , or logarithmic to the base e mathematics e to transform products into sums and divisions into subtractions, and can also applied to functions raised to the power of variables or functions. ref cite book title Golden Differential Calculus pages 282 author N.P. Bali publisher Firewall Media year 2005 isbn 8170081521 ref ref name Bird cite book title Higher Engineering Mathematics first John last Bird pages 324 publisher Newnes year 2006 isbn 0750681527 ref However, the principle can be implemented, at least in part, in the differentiation of almost all differentiable function s, providing that these functions are non zero. Overview For a function math y f x , math logarithmic differentiation typically begins by taking the natural logarithm, or the logarithm to the base e constant e , on both sides, remembering to take absolute values ref cite book title Schaum s Outline of Theory ... Differentiation Rules Logarithmic differentiation extratext see for textbook examples of logarithmic ... Lie group s List of logarithm topics List of logarithmic identities Notes references External ... web url http www.math.ucdavis.edu kouba CalcOneDIRECTORY logdiffdirectory LogDiff.html title Logarithmic ... LogDiff.aspx title Calculus I Logarithmic differentiation accessdate 2009 03 10 DEFAULTSORT Logarithmic ... more details
In contexts including complex manifold s and algebraic geometry , a logarithmic differential form is a meromorphic differential form with pole s of a certain kind. Let X be a complex manifold, and math D subset X math a divisor and math omega math a holomorphic p form on math X D math . If math omega math and math d omega math have a pole of order at most one along D , then math omega math is said to have a logarithmic pole along D . math omega math is also known as a logarithmic p form. The logarithmic p forms make up a Sheaf mathematics subsheaf of the meromorphic p forms on X with a pole along D , denoted math Omega p X log D math . In the theory of Riemann surfaces , one encounters logarithmic one forms which have the local expression math omega frac df f left frac m z frac g z g z right dz math for some meromorphic function resp. rational function math f z z mg z math , where g is holomorphic and non vanishing at 0, and m is the order of f at 0 .. That is, for some open covering , there are local representations of this differential form as a logarithmic derivative modified slightly with the exterior derivative d in place of the usual differential operator d dz . Observe that math omega math has only simple poles with integer residues. On higher dimensional complex manifolds, the Poincar residue is used to describe the distinctive behavior of logarithmic forms along poles. Holomorphic Log Complex By definition of math Omega p X log D math and the fact that exterior differentiation d satisfies math d 2 0 math , one has math d Omega p X log D U subset Omega p 1 X log D U ... dx partial g partial y D frac 1 2 frac dx y D math . Vital to the residue theory of logarithmic forms ... on logarithmic p forms, produces filtrations on cohomology math W mH k X mathbb C text Im mathbb H k ... . Classically, for example in elliptic function theory, the logarithmic differential forms were recognised ... s on S , can be identified more concretely with a vector space of logarithmic differentials. External ... more details
x ln y ln x end array math The area interpretation allows to easily derive basic properties of the logarithmic ... mean which is related to logarithms is the geometric mean . The logarithmic mean is a special case of the Stolarsky mean . References http www.everything2.com index.pl?node id 801020 Logarithmic mean Everything2.com http jipam old.vu.edu.au v4n4 088 03.html Oilfield Glossary Term logarithmic mean mathworld Arithmetic Logarithmic GeometricMeanInequality Arithmetic Logarithmic Geometric Mean Inequality ... 3B2 6 Generalizations of the logarithmic mean , Mathematics Magazine, Vol. 48, No. 2, Mar., 1975 ... more details
refimprove date February 2012 Cleanup date February 2008 Logarithmic decrement , , is used to find the damping ratio of an underdamped system in the time domain. The logarithmic decrement is the natural logarithm natural log of the ratio of the amplitudes of any two successive peaks math delta frac 1 n ln frac x t x t nT , math where x t is the amplitude at time t and x t nT is the amplitude of the peak n periods away, where n is any integer number of successive, positive peaks. The damping ratio is then found from the logarithmic decrement math zeta frac 1 sqrt 1 frac 2 pi delta 2 . math The damping ratio can then be used to find the undamped natural frequency sub n sub of vibration of the system from the damped natural frequency sub d sub math omega d frac 2 pi T , math math omega n frac omega d sqrt 1 zeta 2 , math where T, the period of the waveform, is the time between two successive amplitude peaks. The damping ratio can also be found using a slightly simplified variation on these equations for two adjacent peaks. This method is identical to the above, but simplified for the case of n equal to 1 math zeta frac 1 sqrt 1 frac 2 pi ln x 0 x 1 2 , math where x sub 0 sub is the left peak and x sub 1 sub is the first peak to its right. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5 it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped. The method of fractional overshoot can be useful for damping ratios between about 0.5 and 0.8. The fractional overshoot OS is math OS frac x p x f x f , math where x sub p sub is the amplitude of the first peak of the step response and x sub f sub is the settling amplitude. Then the damping ratio is math zeta frac 1 sqrt 1 frac pi ln OS 2 . math See also Damping Damping factor Q factor References reflist cite book last Inman first Daniel J. title Engineering Vibrations year 2008 publisher Pearson Education, Inc. location Upper ... more details
with computer software. See also Chronology Detailedlogarithmictimeline List of timelines Living graph Logarithmictimeline Sequence of events SIMILE Synchronoptic view Timeline of world history ChronoZoom ... in the timeline. A timeline of evolution can be over millions of years, whereas a timeline about the September 11, 2001 timeline for the day of the attacks September 11, 2001 can take place over minutes. While most timelines use a linear timescale, for very large or small timespans, logarithmictimeline s use a logarithmic scale to depict time. Types of timelines File Minard.png 250px thumb ...Other uses Selfref For Wikipedia s timeline and related tools, see Wikipedia Timeline . File Tidslinje 1.JPG thumb right 240px The bronze timeline Fifteen meters of History with background information board, rebro , Sweden . A timeline is a way of displaying a list of events in chronological order, sometimes ... events and trends for a particular subject. A timeline is related to, Clarify date April 2012 ... biographies . Examples include Chronology of Shakespeare s plays Timeline of the African American Civil Rights Movement Timeline of European exploration Timeline of Solar System exploration Timeline of United States history 1930 1949 World War I timeline Natural sciences Timelines are also used in the natural ... timeline 2009 H1N1 Flu Pandemic Timeline Geologic time scale Timeline big bang Timeline of the Big Bang Timeline of evolution Timeline of Evolution Project management Another type of timeline is used ... timeline in the implementation phase of the life cycle of a computer system. Time scale Timelines ... timeline that also uses geography as part of the visualization. Timelines, no longer constrained ... first2 Daniel title Cartographies of Time A History of the Timeline publisher Princeton Architectural Press year 2010 pages 272 isbn 978 1 56898 763 7 9000 External links Commons Timeline Wiktionary timeline http www.bl.uk timeline Timelines sources from history a British Library interactive history ... more details
refimprove date April 2011 Orphan date April 2011 Detailed division of labor , one of the two aspects of the division of labor , is where the labor required for one product is distributed between many people, each producing a part of the final product. So instead of each worker making a product piece by piece, each worker specializes in making one piece of the product, and all of the workers pieces come together to make the final product. This enhances productivity by increasing workers dexterity in performing a simple operation repeatedly and Saving time that is generally lost in passing from one type of work to the next. ref http www.faculty.rsu.edu users f felwell www Theorists Braverman Presentation Braverman.pdf Harry Braverman and the Working Man ref The most common example of this is Henry Ford s assembly line . The reason Ford Motor Company became so successful in the early 20th century is because Henry Ford was the first to master the assembly line, which uses detailed division of labor. Detailed division of labor can be seen on a larger scale where multiple companies will work together, each making interchangeable parts for a final product. Detailed division of labor is very profitable for capitalistic companies, but can be disadvantageous for workers. Resulting jobs are mind numbing, devoid of variety, human initiative and thought, and any sort of skill save. ref http www.faculty.rsu.edu users f felwell www Theorists Braverman Presentation Braverman.pdf Harry Braverman and the Working Man ref This can drive workers insane, as well as lowering the value of the worker s job because their labor becomes unskilled. This gives power to managers because they potentially could give jobs away to anyone who would do it for cheaper, while retaining the same production. This ability to take advantage of workers makes it very easy for economists to critique capitalism, because workers become just another factor of production. ref http www.faculty.rsu.edu users f felwell ... more details
In theoretical physics , a logarithmic conformal field theory is a generalization of the concept of usually two dimensional conformal field theory in which the correlator s of the basic fields are allowed to be multiply valued and be functions of the logarithm of the separation of the operators. References http xstructure.inr.ac.ru x bin theme3.py?level 1&index1 59186 Logarithmic conformal field theory on arxiv.org V. Gurarie, http dx.doi.org 10.1016 0550 3213 93 90528 W Logarithmic operators in conformal field theory , Nucl. Phys. B410 1993 535 549. M. R. Gaberdiel, H. G. Kausch, http dx.doi.org 10.1016 0550 3213 96 00364 1 Indecomposable fusion products , Nucl. Phys. B477 1996 293 318. M. Reza Rahimi Tabar, A. Aghamohammadi and M. Khorrami, The logarithmic conformal field theories , Nucl. Phys. B497 1997 555 566. Category Conformal field theory quantum stub ... more details
Orphan date February 2009 A logarithmic spiral beach is a type of beach which develops in the direction under which it is sheltered by a headland, in an area called the shadow zone. It is characterized as a logarithmic spiral because if you look at it in plan view or aerially, it represents the same shape that is created from the logarithmic spiral function. These beaches are also commonly referred to as zeta cure bays , half heart or crenulate shaped bays, or headland bays . Logarithmic spiral function Image Logarithmic Spiral Pylab.svg thumb Logarithmic Spiral The logarithmic spiral can be determined using the equation written in polar coordinates r e sup cot sup where the angle of rotation, is located between two lines drawn from the origin to any two points on the spiral. r the ratio of the lengths between two lines that extend out from the origin. The two lines are given as R sub O sub and R. So r also equals the ratio R R sub O sub . the angle between any line R from the origin and the line tangent to the spiral which is at the point where line R intersects the spiral. is a constant for any given logarithmic spiral. Spiral development This type of beach forms due to the refraction of approaching waves and their diffraction by an upcoast headland . The approaching wave front curves as a result of wave diffraction at the headland, which in turn causes the shoreline to bend and yield a log spiral shape. Log spiral beaches are often on swell dominated coasts where waves .... Famous logarithmic spiral beaches Image Half Moon Bay State Beach 1.jpg thumb Half Moon Bay ... of Logarithmic Spiral Beach. Australian Geographer 14.1 1978 44 45. Kimberley, M. M. Fitting a Logarithmic Spiral to the Shoreline of a Headland Bay Beach Computers & Geoscience 15 No. 7 1989 1089 1108. LeBlond, Paul H. An Explanation of the Logarithmic Spiral Plan Shape of HeadlandBay Beaches .... Logarithmic Spiral Coastlines The Northern Zululand Coastline. The South African Geographical Journal ... more details
complex date August 2011 A logarithmic barrier function is a type of barrier function . Formal definition minimize math bold c Tx math subject to math bold a i T x le b i, i 1, ldots,m math assume strictly feasible math bold x A x b ne0 math define logarithmic barrier math Phi x begin cases sum i 1 m log b i a i Tx & text for Ax b infty & text otherwise end cases math References Commons category Newton Method http www.ee.ucla.edu ee236a lectures barrier.pdf lecture on barrier method. Category Types of functions ... more details
In mathematics , the logarithmic integral function or integral logarithm li x is a special function . It occurs in problems of physics and has number theory number theoretic significance, occurring in the prime number theorem as an estimate of the number of prime number s less than a given value. Image Logarithmic integral.png thumb right Logarithmic integral function plot Integral representation The logarithmic integral has an integral representation defined for all positive real number s math x ne 1 math by the integral definite integral math rm li x int 0 x frac dt ln t . math Here, math ln math denotes the natural logarithm . The function math 1 ln t math has a mathematical singularity singularity at t 1, and the integral for x 1 has to be interpreted as a Cauchy principal value math rm li x lim varepsilon to 0 left int 0 1 varepsilon frac dt ln t int 1 varepsilon x frac dt ln t right . math Offset logarithmic integral The offset logarithmic integral or Eulerian logarithmic integral is defined as math rm Li x rm li x rm li 2 , math or math rm Li x int 2 x frac dt ln t , math As such, the integral representation has the advantage of avoiding the singularity in the domain of integration. This function is a very good approximation to the number of prime numbers less than x. Series representation The function li x is related to the exponential integral Ei x via the equation math hbox li x hbox Ei ln x , , math which is valid for x 1. This identity provides a series ... title Logarithmic Integral ref is math rm li x gamma ln ln x sqrt x sum n 1 infty frac 1 n 1 ... expansion for the exponential integral . Infinite logarithmic integral Clarify date November 2009 math int infty infty frac M t 1 t 2 dt math and discussed in Paul Koosis, The Logarithmic Integral ... The logarithmic integral is important in number theory , appearing in estimates of the number of prime ... 6 title Exponential, Logarithmic, Sine, and Cosine Integrals first N. M. last Temme Category Special ... more details
A logarithmic resistor ladder is an electronic circuit composed of a series of resistor s and switch es, designed to create an attenuation from an input to an output signal, where the logarithm of the attenuation ratio is proportional to a digital code word that represents the state of the switches. The logarithmic behavior of the circuit is its main differentiator in comparison with digital to analog converter s in general, and traditional Resistor ladder R 2R Ladder networks specifically. Logarithmic attenuation is desired in situations where a large dynamic range needs to be handled. The circuit described in this article is applied in Preamplifier audio devices , since human dynamic range audio perception of sound level is properly expressed on a logarithmic scale. Logarithmic input output behavior As in digital to analog converter s, a Binary numeral system binary word is applied to the ladder network, whose N bits are treated to represent an integer value according the relation math CodeValue sum i 1 N sw i cdot 2 i 1 math where math sw i math represents a value 0 or 1 depending ... publisher Analog Devices inc. accessdate 29 March 2012 ref . In contrast, the logarithmic ladder network ... math V in math is a b variable b input signal. Circuit implementation File Circuit diagram of logarithmic ... if sw i text then alpha 2 i 1 text else 1 math For logarithmic scaled attenuators, it is common practice ... sub load sub . The value of R sub source sub does not influence the logarithmic behavior Constant ... source sub . The value of R sub load sub does not influence the logarithmic behavior Circuit variations ... in 1955. Multiplying DA converters with logarithmic behavior were not known for a long time after that. An initial approach was to map the logarithmic code to a much longer code word, which could be applied ... inc. ref LOGDAC CMOS Logarithmic D A Converter, http www.analog.com static imported files data ... Online calculator to configure logarithmic ladder networks Category Articles created via the Article ... more details
In theoretical physics , the logarithmic Schr dinger equation sometimes abbreviated as LNSE or LogSE is one of the nonlinear modifications of Schr dinger equation Schr dinger s equation . It is a classical wave equation with applications to extensions of quantum mechanics , ref I. Bialynicki Birula and J. Mycielski, Annals Phys. 100, 62 1976 Commun. Math. Phys. 44, 129 1975 Phys. Scripta 20, 539 1979 . ref quantum optics , ref H. Buljan, A. iber, M. Solja i , T. Schwartz, M. Segev, and D. N. Christodoulides, Phys. Rev. E 68, 036607 2003 . ref nuclear physics , ref E. F. Hefter, Phys. Rev. A 32, 1201 1985 . ref ref V. G. Kartavenko, K. A. Gridnev and W. Greiner, Int. J. Mod. Phys. E 7 1998 287. ref transport and diffusion phenomena, ref S. De Martino, M. Falanga, C. Godano and G. Lauro, Europhys. Lett. 63, 472 2003 S. De Martino and G. Lauro, in Proceed. 12th Conference on WASCOM, 2003. ref ref T. Hansson, D. Anderson, and M. Lisak, Phys. Rev. A 80, 033819 2009 . ref open quantum systems and information theory , ref K. Yasue, Quantum mechanics of nonconservative systems , Annals Phys. 114 1978 479. ref ref N. A. Lemos, Phys. Lett. A 78 1980 239. ref ref J. D. Brasher, Nonlinear wave mechanics, information theory, and thermodynamics , Int. J. Theor. Phys. 30 1991 979. ref ref D. Schuch, Phys. Rev. A 55, 935 1997 . ref ref M. P. Davidson, Nuov. Cim. B 116 2001 1291. ref ref J. L. Lopez .... G. Zloshchastiev, Logarithmic nonlinearity in theories of quantum gravity Origin of time and observational ... ref K. G. Zloshchastiev, Vacuum Cherenkov effect in logarithmic nonlinear quantum theory , Phys ..., Spontaneous symmetry breaking and mass generation as built in phenomena in logarithmic nonlinear ..., Quantum Bose liquids with logarithmic nonlinearity Self sustainability and emergence of spatial ... . ref It is an example of an integrable model . The equation The logarithmic Schr dinger equation ... Logarithmic Schrodinger Equation Category Theoretical physics Category Quantum mechanics ... more details
Image Gaussian logarithm.svg thumb 300px right The math s b z math and math d b z math functions. A logarithmic number system LNS is an arithmetic system used for representing real numbers in computer and digital hardware , especially for digital signal processing . Theory In LNS, a number, math X math , is represented by the logarithm , math x math , of its absolute value as follows math X rightarrow s,x log b X , math where math s math is a bit denoting the sign of math X math math s 0 math if math X 0 math and math s 1 math if math X 0 math . The number math x math is represented by a binary word which usually is in the two s complement format. LNS can be considered as a floating point number with the significand being always equal to 1. This formulation simplifies the operations of multiplication, division, powers and roots, since they are reduced down to addition, subtraction, multiplication and division, respectively. On the other hand, the operations of addition and subtraction are more complicated and they are calculated by the formula math log b X Y x s b z math math log b X Y x d b z , math where math z y x math is the difference between the logarithms of the operands, the sum function is math s b z log b 1 b z math , and the difference function is math d b z log b 1 b z ... of floating point math operations. History Logarithmic number systems have been independently invented ... Kingsbury and Rayner introduced logarithmic arithmetic for digital signal processing in 1971. ref cite journal author N. G. Kingsburg and P. J. W. Rayner title Digital filtering using logarithmic arithmetic ... Systems 22 logarithmic&q logarithmic search ref that won the Gordon Bell Prize in 1999. LNS is commonly ... is described in the context of the European Logarithmic Microprocessor ELM . ref cite journal author ... title The European Logarithmic Microprocessor journal IEEE Transactions on Computers volume ... title Comparing Floating point and Logarithmic Number Representations for Reconfigurable Acceleration ... more details
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