a log b , where the base is unknown and the knowledge of the base of the logarithm is unnecessary it defers the choice of base. Definition The indefinitelogarithm operator Log ... See dimensional analysis . In the case of the quantities that result from the indefinitelogarithm ... indefinitelogarithm quantities, and can be represented with the same notation, e.g., math log n math for the logarithmic unit which is equal to the indefinitelogarithm of math n math . Mathematical ... fixes the number x , one obtains the indefinitelogarithm, which is a function of the base b . That is, math ... function of the argument x, while the indefinitelogarithm is a decreasing function of the base ... of our logarithms. Thus, replacing the indefinitelogarithm by a definite logarithm can be compared ... value math n math for indefinitelogarithm quantities math L mathrm Log n math . The concepts ... IndefiniteLogarithm Category Logarithms Category Special functions ...multiple issues original research August 2010 unreferenced December 2009 COI July 2010 The indefinitelogarithm of a positive number n variously denoted log n , Log n or even sometimes just log n is the logarithm without regard to any particular base it is a function of the base , not a number . This is as opposed to the ordinary, or definite logarithm , where there is always implicitly or explicitly a particular base to which the logarithm is being taken. In other words, an indefinitelogarithm of a number is a function that is known to have the properties of any logarithm function i.e. ... 0 to the logarithm of x base math b math . Using lambda calculus notation, we can express ... of indefinite logarithms and their multiplication by scalars, thereby forming a completeness complete vector space of indefinitelogarithm quantities. One way to understand the meaning of the indefinitelogarithm is to think of it as a dimensioned i.e., not dimensionless quantity . Any such quantity ... more details
Wiktionarypar indefiniteIndefinite may refer to In mathematics When talking about positive or negative indefinite forms in multilinear algebra, see definite bilinear form . Indefinite integral refers to the antiderivative . Indefinite is sometimes used to describe an unknowable quantity, with meaning similar to unlimited or undetermined . In grammar, see indefinite article and indefinite pronoun . See also Eternity NaN disambig ... more details
File Binary logarithm plot with ticks.svg right thumb upright 1.35 alt Graph showing a logarithm curves ... of a function graph of the logarithm to base 2 crosses the x axis x axis horizontal axis at 1 and passes ... axis, but asymptotic does not meet or intersect it . The logarithm of a number is the exponent by which .... For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3 nowrap 1000 10 ... end , then y is the logarithm of x to base b , and is written log sub b sub x , so nowrap ... to perform computations more easily, using slide rule s and Common logarithmlogarithm table s. These devices rely on the fact&mdash important in its own right&mdash that the logarithm of a product ... function in the 18th century. The logarithm to base nowrap begin b 10 nowrap end is called the common logarithm and has many applications in science and engineering. The natural logarithm ... in pure mathematics , especially calculus . The binary logarithm uses base nowrap begin b 2 nowrap ... , and can aid in forensic accounting . In the same way as the logarithm reverses exponentiation , the complex logarithm is the inverse function of the exponential function applied to complex numbers . The discrete logarithm is another variant it has applications in public key cryptography ... 8 is the product of three factors of 2 math 2 3 2 times 2 times 2 8. , math It follows that the logarithm ... for an elementary treatise. group nb Definition The logarithm of a number x with respect to base b is the exponent to which b has to be raised to yield x . In other words, the logarithm of x to base ... 2009 , chapter 1 ref math b y x. , math The logarithm is denoted log sub b sub x pronounced as the logarithm of x to base b or the nowrap base b logarithm of x . In the equation y log sub b sub x , the value y is the answer to the question To what power must b be raised, in order to yield x ? . For the logarithm ..., and root The logarithm of a product is the sum of the logarithms of the numbers being multiplied ... more details
The term integral logarithm may stand for Discrete logarithm in algebra , Logarithmic integral function in calculus . disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
The term Napierian logarithm , or Naperian logarithm, is often used to mean the natural logarithm . However, as first defined by John Napier , it is a function given by in terms of the modern logarithm Image NapLog.png thumb 360px A plot of the Napierian logarithm for inputs between 0 and 10 sup 8 sup . math mathrm NapLog x frac log frac 10 7 x log frac 10 7 10 7 1 . math Since this is a quotient of logarithms, the base of the logarithm chosen is irrelevant. It is not a logarithm to any particular base in the modern sense of the term however, it can be rewritten as math mathrm NapLog x log frac 10 7 10 7 1 10 7 log frac 10 7 10 7 1 x math and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one. The Napierian logarithm is related to the natural logarithm by the relation math mathrm NapLog x approx 9999999.5 16.11809565 ln x math and to the common logarithm by math mathrm NapLog x approx 23025850 7 log 10 x . math References citation last1 Boyer first1 Carl B. last2 Merzbach first2 Uta C. isbn 9780471543978 page 313 publisher Wiley title A History of Mathematics year 1991 . citation last Edwards first Charles Henry page 153 publisher Springer Verlag title The Historical Development of the Calculus year 1994 . citation last Phillips first George McArtney isbn 9780387950228 page 61 publisher Springer Verlag series CMS Books in Mathematics title Two Millennia of Mathematics from Archimedes to Gauss volume 6 year 2000 . Category Logarithms math stub es Logaritmo neperiano ... more details
In mathematics , the indefinite product operator is the inverse operator of math Q f x frac f x 1 f x math . It is like a discrete version of the indefinite product integral . Some authors use term discrete multiplicative integration ref N. Aliev, N. Azizi and M. Jahanshahi 2007 http www.m hikari.com imf password2007 9 12 2007 jahanshahiIMF9 12 2007 1.pdf Invariant functions for discrete derivatives and their applications to solve non homogenous linear and non linear difference equations . ref Thus math Q prod x f x f x , . math More explicitly, if math prod x f x F x , math , then math frac F x 1 F x f x , . math If F x is a solution of this functional equation for a given f x , then so is CF x for any constant C . Therefore each indefinite product actually represents a family of functions, differing by a multiplicative constant. Period rule If math T , math is a period of function math f x , math then math prod x f Tx C f Tx x 1 , math Connection to indefinite sum Indefinite product can be expressed in terms of indefinite sum math prod x f x exp left sum x ln f x right , math Alternative usage Some authors use the phrase indefinite product in a slightly different but related way to describe a product in which the numerical value of the upper limit is not given. ref http www.risc.uni ... x , math List of indefinite products This is a list of indefinite products math prod x f x , math . Not all functions have an indefinite product which can be expressed in elementary functions. math prod ... math prod x cot x tan x 1 C tan x , math math prod x tan x cot x 1 C cot x , math See also Indefinite ... Product.html Indefinite products with Mathematica http www.math.rwth aachen.de MapleAnswers 660.html bug in Maple V to Maple 8 handling of indefinite product http www.math.tu berlin.de mueller HowToAdd.pdf ... like Identities DEFAULTSORT Indefinite Product Category Mathematical analysis Category Mathematics related lists Indefinite sums Category Mathematical tables Indefinite sums ... more details
TOCright Indefinite detention is the incarceration of an arrest ed person by a national government or law .... ref name hrw.org http www.hrw.org en news 2004 12 15 uk law lords rule indefinite detention breaches ... and human rights groups hold unfavorable views of indefinite detention. Australia In 19??, indefinite ..., Chinese, and Cambodian refugees previous laws had also allowed for the indefinite detention ... Al Kateb v Godwin that the indefinite detention of a statelessness stateless person is lawful. All states and territories except New South Wales allow for indefinite imprisonment indefinite detention ... since 1960 is a preventive detention law enforced in Malaysia which allows indefinite detention without ...?actno REVED 143 ref United Kingdom In 2004, the House of Lords ruled that indefinite detention ... 40 align right In the United States, indefinite detention has been used to hold terrorism terror ... www.boston.com news nation washington articles 2005 01 02 indefinite detention of suspects in terror ... PATRIOT act permits indefinite detention of immigrants ref http www.aclu.org natsec emergpowers 12483leg20011023.html ... title ref The International Red Cross has criticized the indefinite detention of prisoners at Guantanamo ... that it will rule on indefinite detention. ref http www.washingtonpost.com wp dyn content article 2008 ... amendment to the National Defense Authorization Act for Fiscal Year 2012 that would have banned indefinite ... been undermined. ref Khaki, Ategah, Senate Rejects Amendment Banning Indefinite Detention, ACLU Blog ... law authorizing indefinite military detention without trial or charge, World Socialist Web Site , 2 ... indefinite detention provision of the law was decried as a historic assault on American liberty ... is a blight on his legacy because he will forever be known as the president who signed indefinite detention ... indefinite detention bill law Press release, December 31, 2011 from American Civil Liberties Union . ref See also Administrative detention Habeas corpus Indefinite imprisonment Incapacitation penology ... more details
In mathematics , a logarithm of a matrix is another matrix mathematics matrix such that the matrix exponential ... logarithm and in some sense an inverse function of the matrix exponential . Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in a Lie group and the logarithm is the corresponding element of the Lie algebra . Definition A matrix B is a logarithm of a given matrix A if the matrix exponential of B is A math e B A. , math Example Logarithm ... 0 & 1 1 & 0 end pmatrix , math is a logarithm of A . Thus, the matrix A has infinitely many logarithms ... math is a generator of the Lie algebra so 2 . Existence The question of whether a matrix has a logarithm has the easiest answer when considered in the complex setting. A matrix has a logarithm if and only if it is invertible matrix invertible . ref harvtxt Higham 2008 , Theorem 1.27 ref The logarithm is not unique, but if a matrix has no negative real eigenvalues, then it has a unique logarithm whose eigenvalues lie all in the strip z C Im z . This logarithm is known as the principal logarithm ... matrix has a real logarithm if and only if it is invertible and each Jordan block belonging to a negative .... This can already be seen in the scalar case the logarithm of 1 is a complex number. The existence ... B . , math For any invertible matrix, math A 1 e ln A . , math Further example Logarithm of rotations in 3D space A rotation math R in rm SO 3 math in the 3D is given by a 3x3 orthogonal matrix The logarithm ... of rotation matrices. Calculating the logarithm of a diagonalizable matrix A method for finding ln ... each diagonal element of A&prime by its natural logarithm in order to obtain math ln A math . Then math ln A V ln A V 1 . , math That the logarithm of A might be a complex matrix even if A is real ... . The non uniqueness of the logarithm of a matrix follows from the non uniqueness of the logarithm ... more details
confusing date July 2010 Criminal procedure trial Indefinite imprisonment or indeterminate imprisonment .... ref name google1 cite web url http books.google.com books?id zcMJAAAAIAAJ&pg PA94&dq Indefinite ... for the life sentence remainder of his her natural life . In theory, an indefinite prison sentence ... of the indefinite sentence is one of the most effective, ref cite web url http books.google.com books?id F 0tAAAAIAAJ&pg PA369&dq indefinite prison sentence title Journal of the American Institute of ... Google ... Reform have defined indefinite sentences as fundamentally flawed . ref cite web url http news.bbc.co.uk 2 hi uk news 7004756.stm title UK & 124 Indefinite prison terms flawed publisher BBC News date ... for imposing indefinite as opposed to fixed sentences is to protect the community. An offender can ... Opinion date accessdate 2010 01 26 ref Uses by location In some places, indefinite sentences have ...&dq indefinite prison sentence title Prison methods in New York state, a ... Google Books publisher Books.google.com ... more recently. Australia Indefinite imprisonment was introduced in Queensland in 2003 under the Dangerous Prisoners Sexual Offenders Act 2003 . This allows indefinite detention to be imposed on dangerous ... 2008 Sentencing 2520Conference 25202008 papers Ronken 2520Johnson.pdf Indefinite prison sentence&hl en&ct clnk&cd 71&gl us&ie UTF 8 title Balancing Rights Arguments for indefinite detention of dangerous ... to the community. The indefinite sentence s must be reviewed by the court when the nominal sentence ..., and every three years after. Indefinite imprisonment has a minimum nominal sentence of ten years ... s of indefinite imprisonment is 30 years, currently being served by serial paedophile Geoffrey Robert ... Michael Roach Western Australia was sentenced to three consecutive indefinite terms with a nominal ... be given an indefinite prison sentence. This means the offender is at risk for causing a serious personal ... 2010 01 26 ref New Zealand In New Zealand, indefinite imprisonment is called preventive detention ... more details
File Graph of common logarithm.png right thumb 400px The common logarithm. The common logarithm is the logarithm with base 10. It is also known as the decadic logarithm , named after its base, and Briggsian logarithm , after Henry Briggs mathematician Henry Briggs , an English mathematician who pioneered ... . On calculators it is usually log , but mathematician s usually mean natural logarithm rather than common logarithm when they write log . To mitigate this ambiguity the ISO 31 11 ISO specification is that log ... tables of base 10 logarithm s were found in appendices of many books. Such a table of common logarithms gave the logarithm, often to 4 or 5 decimal places, of each number in the left hand column, which ... between 1 and 10, since if one wanted the logarithm of, for example, 120, one would know that. math ... the fractional part of the logarithm of 120, known as the mantissa of the common logarithm of 120 was found ... . The location of the decimal point in 120 tells us that the integer part of the common logarithm of 120, called the characteristic of the common logarithm of 120, is 2. Numbers between and excluding ... logarithm, characteristic, and mantissa of powers of 10 times a number number logarithm characteristic ... is common to all of the 5 10 sup i sup . A Logarithm Tables of logarithms table of logarithms will have ... x . Mathematicians, on the other hand, wrote log x when they mean log sub e sub x for the natural logarithm ..., that notation, according to which one writes ln x when the natural logarithm is intended, may ... common, electronic calculators. Numeric value The numerical value for logarithm to the base 10 can ... x frac log 2 x log 2 10 math as procedures exist for determining the numerical value for natural logarithmlogarithm base e and binary logarithmlogarithm base 2 . Natural logarithm Numerical value Binary logarithm Algorithm Algorithms for computing binary logarithms See also logarithm History History ... logarithm tables Category Logarithms als Logarithmentafel ar de Dekadischer Logarithmus ... more details
For the theorem in probability theory Law of the iterated logarithm In computer science , the iterated logarithm of n , written log star n usually read log star , is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1. The simplest formal definition is the result of this recursive function math log n begin cases 0 & mbox if n le 1 1 log log n & mbox if n 1 end cases math On the positive real numbers, the continuous super logarithm inverse tetration is essentially equivalent math log n lceil text slog e n rceil math but on the negative real numbers, log star is 0, whereas math lceil text slog e x rceil 1 math for positive x , so the two functions differ for negative arguments. Image Iterated logarithm.png right 300px thumb Figure 1. Demonstrating lg 4 2 In computer science, lg star is often used to indicate the binary iterated logarithm, which iterates the binary logarithm instead. The iterated logarithm accepts any positive real number and yields an integer . Graphically, it can be understood as the number of zig zags needed in Figure 1 to reach the interval 0, 1 on the x axis. Mathematically, the iterated logarithm is well defined not only for base 2 and base e , but for any base greater than math e 1 e approx1.444667 math . The iterated logarithm is closely related to the generalized logarithm function used in symmetric level index arithmetic . It is also proportional to the additive persistence of a number , the number of times one must replace the number by the sum of its digits before reaching its digital root . Analysis of algorithms The iterated logarithm is useful in analysis of algorithms and computational ... to Algorithms 1 Section 30.5. ref The iterated logarithm grows at an extremely slow rate, much slower than the logarithm itself. For all values of n relevant to counting the running times of algorithms ... of particles in the known universe , the iterated logarithm with base 2 has a value no more ... more details
An indefinite pronoun is a pronoun that refers to one or more unspecified beings, objects, or places. List of English indefinite pronouns Note that many of these words can function as other parts of speech too, depending on context. For example, in many disagree with his views the word many functions as an indefinite pronoun, while in many people disagree with his views it functions as a quantifier a type of Determiner class determiner that qualifies the noun people . Example sentences in which the word functions as an indefinite pronoun are given. Singular wikt another another &ndash Thanks, I ll have another. wikt anybody anybody &ndash Anybody can see the truth. wikt anyone anyone &ndash Anyone can see this. wikt anything anything &ndash Anything can happen if you just believe. wikt each each &ndash From each according to his ability, to each according to his need . wikt either either &ndash Either will do. wikt enough enough &ndash Enough is enough. wikt everybody everybody &ndash Everybody was invited. wikt everyone everyone &ndash Everyone had a cup of coffee. wikt everything everything &ndash Everything is permitted wikt less less &ndash Less is known about this period of history. wikt little little &ndash Little is known about this period of history. wikt much much &ndash Much was discussed at the meeting. wikt neither neither &ndash In the end, neither was selected. wikt no one no one &ndash No one thinks that you are mean wikt nobody nobody &ndash Nobody wants to be one of the contestants. wikt nothing nothing &ndash Nothing is true. wikt one Pronoun one &ndash One might see it that way. wikt other other &ndash One was singing while the other played the piano. wikt ... usage, in the sense of one ref http www.bartleby.com 68 20 3220.html Indefinite you, indefinite ... Haspelmath, Martin . 1997. Indefinite pronouns . Oxford Clarendon Press. External links Wiktionary indefinite pronoun http englishplus.com grammar 00000027.htm Using Indefinite Pronouns lexical ... more details
Image Binary logarithm plot.png thumbnail right 200px Plot of log sub 2 sub n In mathematics , the binary logarithm log sub 2 sub n is the logarithm to the Binary numeral system base 2 . It is the inverse function of n 2 sup n sup . The binary logarithm of n is the power to which the number 2 must be raised to obtain the value n . This makes the binary logarithm useful for anything involving powers of 2 , i.e. doubling. For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, the binary logarithm of 8 is 3, the binary logarithm of 16 is 4 and the binary logarithm of 32 is 5. Applications Information theory The binary logarithm is often used in computer science and information theory because it is closely connected ..., the definition of the amount of self information and information entropy involves the binary logarithm ... an occurrence of one of two equally probable alternatives. Computational complexity The binary logarithm ... can also be said to run in, say, O log sub 13 sub n time. The base of the logarithm in expressions ..., the base of the logarithm needs to be specified. For example O 2 sup lb n sup is not the same ... logarithm ln or the common logarithm log functions, which are found on most scientific calculators . The specific Logarithm Change of base change of logarithm base formulae for this are log sub ... domain mathematics domain and range mathematics range , the binary logarithm can be computed rounding up or down. These two forms of integer binary logarithm are related by this formula math ... binary logarithm can be interpreted as the zero based index of the most significant 1 bit in the input ... support, and applications for the integer binary logarithm. Real number For a general positive number positive real number , the binary logarithm may be computed in two parts Compute the integer ... 2. Now the integral part of the logarithm is simply n , and the fractional part is lb 2 ... more details
In mathematics the indefinite sum operator also known as the antidifference operator , denoted by math sum x , math or math Delta 1 , math , ref PlanetMath urlname IndefiniteSum title Indefinite Sum ref ref http hostel6.ru books Papers Computer algebra Summation Man. 20Closed 20forms 20for 20symbolic 20summation. 20JSC 201993 20 22s .pdf On Computing Closed Forms for Indefinite Summations. Yiu Kwong Man. J. Symbolic Computation 1993 , 16, 355 376 ref ref If Y is a function whose first difference is the function y , then Y is called an indefinite sum of y and denoted sup 1 sup y http books.google.co.uk books?id 5rFOeE0zvY4C&pg PA41&dq 22indefinite sum 22 Introduction to Difference Equations , Samuel Goldberg ref is the linear operator , inverse of the difference operator forward difference operator math Delta , math . It relates to the difference operator forward difference operator as the indefinite ... equation for a given f x , then so is F x C for any constant C . Therefore each indefinite ... of discrete calculus Indefinite sums can be used to calculate definite sums with the formula ref ... summation Often the constant C in indefinite sum is fixed from the following equation math int 1 2 ... by parts main Summation by parts Indefinite summation by parts math sum t f t Delta g t f t g ... x , math then math sum x f Tx x f Tx C , math Alternative usage Some authors use the phrase indefinite ... of indefinite sums This is a list of indefinite sums of various functions. Not every function has an indefinite sum that can be expressed in terms of elementary functions. Antidifferences of rational ... See also Indefinite product Time scale calculus List of derivatives and integrals in alternative calculi .... Indefinite summation of rational functions with additional minimization of the summable part. Programmirovanie, 2008, Vol. 34, No. 2. DEFAULTSORT Indefinite Sum Category Mathematical analysis Category Mathematical tables Indefinite sums Category Finite differences Category Linear operators in calculus ... more details
primarysources date January 2009 Infobox Film name Time Indefinite image caption director Ross McElwee producer writer Ross McElwee starring music cinematography Ross McElwee editing distributor released runtime 114 min. language English budget Time Indefinite is an autobiographical 1993 documentary film directed by Ross McElwee and exploring themes of grief , mortality, and the convenient disconnection of watching life through a camera lens. The title comes from a passage from the Bible mentioned by a visiting Jehovah s Witness . McElwee is filming the interaction and focused on adjusting the exposure to try to catch the play of light over the man s face distracted, he hears the phrase about 30 seconds after the man says it and understands it to refer to the unpredictable imminence of death. Plot In the film, director Ross McElwee gets married, finally putting an end to his family s worrying his grandmother dies his wife Marilyn has a miscarriage and his father, a medical doctor, dies suddenly within a week of McElwee s wife s miscarriage. His mother had died of cancer ten years earlier and so McElwee returns to his father s house, where his father s housekeeper ministers to him about Christianity and faith . McElwee goes to visit his friend Charleen, who is now living alone in a new apartment. She had lived on an island in an old two story house abandoned by the U.S. Army she and her husband worked to restore it and lived together there for years before becoming estranged. Charleen then lived there alone, but on returning home from a trip she finds that her husband has set fire to the house and died downstairs at the grand piano in an arson suicide . Charleen has her husband s cremation cremated remains in a bag inside a box and tries to get rid of them but can t bring herself to do it. McElwee s brother is a successful doctor on a visit to his brother s practice, Ross ... s web page External links imdb title 108341 Time Indefinite Category 1993 films Category P.O.V. ... more details
Multiple issues refimprove December 2007 tone December 2009 Indefinite lifespan or, indefinite life extension, is a term used in the life extension movement to refer to the longevity of humans, and other life forms, under conditions in which aging can be effectively and completely prevented and treated. Such individuals would still be susceptible to accidental or intentional death by physical trauma trauma or infectious diseases, but not death from aging. Their lifespans would be Wikt indefiniteindefinite , because protection from the effects of aging on health does not guarantee survival. Some life extension ists consider the term indefinite lifespan technically more correct than immortality which, especially in religious contexts, implies an inability to die. Actuarial escape velocity Life expectancy increases slightly every year as treatment strategies and technologies improve. At present, more than one year of research is required for each additional year of expected life. Actuarial escape velocity occurs when this ratio reverses, so that life expectancy increases faster than one year per one year of research, as long as that rate of advance is sustainable. ref name mattersnow Citation last de Grey first Aubrey D. N. J. title Escape Velocity Why the Prospect of Extreme Human ... Immortality The terms immortality and eternal youth are often used as synonyms for indefinite lifespan ... s, slain in war s, suicide choosing to die, etc. The term indefinite lifespan represents this more ... of indefinite lifespans , like the point of birth control , is to gain the opportunity to lead ... of indefinite lifespan if medical science is curtailed significantly, or if aging turns out to be massively ... near future, it may be conceivable for some of those now alive to attain indefinite lifespans. Citation needed date November 2011 According to biogerontologist Marios Kyriazis , indefinite ... in Mice, Science, Vol. 308, page 518. Life extension DEFAULTSORT Indefinite Lifespan Category Aging ... more details
Indefinite Monism is a philosophical conception of reality that asserts that only Awareness is real and that the wholeness of Reality can be conceptually thought of in terms of immanent and transcendent aspects. The immanent aspect is denominated simply as Awareness, while the transcendent aspect is referred to as Omnific Awareness. Awareness in this system is not equivalent to consciousness . Rather, Awareness is the venue for consciousness, and the transcendent aspect of Reality, Omnific Awareness, is what consciousness is of. In this system, what is real is distinguished from that which exists by showing that everything that we are conscious of exists but is not real since it is contingent upon awareness for its existence. Awareness is the source of its own energetic display its omneity. Rather than leading to a solipsistic account of reality, it is claimed through an analysis of consciousness that it is an error on our part to conceive of individuated awareness. That error being found in a conflation of the objects of consciousness with the subject of consciousness within an assumed form of reality of separate physical things. Proceeding from the one necessarily true and unquestionable fact that we are present to our experiences an understanding of reality is developed that is neither a materialist nor an idealist conceptualization. This way of viewing the world is referred to as surjective , a metaphorical use of a concept found in mathematical set theory that means a function that works upon every member of a set, where Awareness is the function and Omnific Awareness is the set, in order to distinguish this position from both subjectivity and objectivity. Within this system anything whatsoever can arise from Omnific Awareness, thus the use of the term indefinite in labeling this monism. What does arise as the existents that we are conscious of is conditioned by the affections ... Anaximander posited a monism which he described as apeiron , meaning boundless, unlimited, or indefinite ... more details
to the height, As the number of times a logarithm must be iterated function iterated to get to 1 the Iterated logarithm , As a generalization of Robert Munafo s http www.mrob.com pub math largenum.html large number class system , The precise definition of the super logarithm depends on a precise ... on the super logarithm for non integer range mathematics range . Definitions The super logarithm ... of the super logarithm from this sparse set to the real numbers, several approaches have been pursued ... are suggested. Linear approximation The linear approximation to the super logarithm is math mathrm ... like Holmes recognize that the super logarithm would be a great use to the next evolution of computer ... on a super logarithmic scale. Quadratic approximation The quadratic approximation to the super logarithm ... . This version of the super logarithm allows for basic calculus operations to be performed on the super logarithm, without requiring a large amount of solving beforehand. Using this method, basic investigation of the properties of the super logarithm and tetration can be performed with a small ... x c math . Thus given that the super logarithm is defined by math mathrm slog b 1 0 math and the third ... could be uniquely determined. Properties Other equations that the super logarithm satisfies are math ... tetrationforum index.php ref See also Iterated logarithm Tetration References references Ioannis ... logarithm , published online accessed Nov 2007 . George Szekeres, http projecteuclid.org DPubS ... showthread.php?threadid 579 Hyper operations Thread 2 DEFAULTSORT Super Logarithm Category ... more details
Image Complex log.jpg 200px right thumb A single branch of the complex logarithm. The hue of the color is used to show the Arg mathematics arg polar coordinate angle of the complex logarithm. The saturation ... logarithm. The page with the large version of this picture has an image that shows the encoding of colors as a function of their complex values. In complex analysis , a complex logarithm function is an inverse function inverse of the complex exponential function , just as the natural logarithm ln x is the inverse of the exponential function real exponential function e sup x sup . Thus, a logarithm ... books.google.com books?id FUWPyHM XK0C&pg PA40&dq logarithm intitle Complex intitle function intitle ... , then w ln r i is one logarithm of z adding integer multiples of 2 i gives all ... that single out one logarithm of each number in their domains. This is analogous to the definition ... the logarithm as a function whose domain is not a region in the complex plane , but a Riemann ... z , the principal value Log z is the logarithm whose imaginary part lies in the interval , ... value of the logarithm ref name Sarason can be defined by math text Log z text ln r i theta ln z i ... the notation log z appears without any particular logarithm having been specified, it is generally ... z 0 this is what it means for Log z to be a logarithm of z , but the identity ... of the complex logarithm Is there a different way to choose a logarithm of each nonzero complex ..., the answer is no. To see why, imagine tracking such a logarithm function along the unit circle , by evaluating ... L 1 0. To obtain a continuous logarithm defined on complex numbers, it is hence ... subset U of the complex plane such that L z is a logarithm of z for each z in U . ref name Sarason ... z if no confusion can result. Different branches can give different values for the logarithm of a particular ... logarithm Each branch L z of log z on an open set U is an inverse of a restriction of the exponential ... more details
logarithm to base b . The familiar base change formula for ordinary logarithms remains valid If c ... discrete logarithm records unsolved computer science Can the discrete logarithm be computed in polynomial .... Popular choices for the group G in discrete logarithm cryptography are the cyclic groups Z sub ... edition 3rd isbn 978 1 58488 508 5 year 2006 Number theoretic algorithms DEFAULTSORT Discrete Logarithm ... more details
This is a list of logarithm topics , by Wikipedia page. See also the list of exponential topics . Acoustic power antilogarithm Apparent magnitude Baker s theorem Bel Benford s law Binary logarithm Bode plot Henry Briggs mathematician Henry Briggs Cologarithm Common logarithm Complex logarithm Discrete logarithm e mathematical constant El Gamal discrete log cryptosystem Harmonic series mathematics Iterated logarithm Law of the iterated logarithm Linear form in logarithms Linearithmic List of integrals of logarithmic functions Logarithmic growth Logarithmic timeline Log likelihood ratio Log log Log log graph Log normal distribution Log periodic antenna Log Weibull distribution Logarithmic algorithm Logarithmic derivative Logarithmic differential Logarithmic differentiation Logarithmic distribution Logarithmic form Logarithmic graph paper Logarithmic identities Logarithmic scale Logarithmic spiral Logarithmic timeline Logit Mantissa is a disambiguation page see common logarithm for the traditional concept of mantissa see significand for the modern concept used in computing. Mel scale Mercator projection Moment magnitude scale John Napier Natural logarithm Neper Offset logarithmic integral pH Polylogarithm Polylogarithmic Richter magnitude scale Schnorr signature Significand Slide rule Sound intensity level Table of logarithms Weber Fechner law Category Exponentials Category Logarithms Category Indexes of mathematics topics Logarithm topics ... more details
Expert subject Mathematics date February 2009 In mathematics , in the field of functional analysis , an indefinite ... complex vector space math K math equipped with both an definite bilinear form indefinite inner product ... of math K math obeying math J 3 J. , math The indefinite inner product space itself is not necessarily ... of interest in typical applications fall into this quotient space. An indefinite inner product ... Consider a complex vector space math K math equipped with an indefinite hermitian form math langle ... form an indefinite inner product . The following subsets are defined in terms of the square norm induced by the indefinite inner product math K 0 stackrel mathrm def x in K langle x, ,x rangle 0 math ... may be called semi definite , and any subspace that is not semi definite is called indefinite . Let our indefinite inner product space also be equipped with a decomposition into a pair of subspaces ... K subset K 0 math and math K subset K 0 math , then math K math is called an indefinite ... of the indefinite inner product as a Hermitian form implies that math langle x, ,y rangle frac 1 4 langle x y, ,x y rangle langle x y, ,x y rangle math Therefore the indefinite inner product of any ... where the indefinite inner product has an analytically useful property such as Lorentz invariance ... the indefinite one, to be globally defined on a manifold and the other to be coordinate dependent ... indefinite inner product on math K math result in Hilbert spaces math tilde K math and math tilde ... or math Pi kappa math space . Conventionally, the indefinite inner product is given the sign that makes ... . Pesonen operator A symmetric operator A on an indefinite inner product space K with domain ... operators in spaces with an indefinite metric , John Wiley & Sons, Chichester, 1989, ISBN 0 471 92129 7. Bogn r, J. Indefinite inner product spaces , Springer Verlag, Berlin Heidelberg New York ... space with an indefinite metric first N.K. last Nikol skii first2 B.S. last2 Pavlov eom id p p073800 ... more details
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation g sup x sup h given elements g and h of a finite cyclic group G . The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie Hellman key agreement, ElGamal encryption , the ElGamal signature scheme , the Digital Signature Algorithm , and the elliptic curve cryptography analogs of these. Common choices for G used in these algorithms include the multiplicative group of integers modulo p , the multiplicative group of a finite field , and the group of points on an elliptic curve modulo p or over a finite field . Integers modulo p On 18 Jun 2005, Antoine Joux and Reynald Lercier announced the computation of a discrete logarithm modulo a 130 digit 431 bit strong prime in three weeks, using a 1.15 GHz 16 processor HP AlphaServer GS1280 computer and a number field sieve algorithm. ref Antoine Joux, Discrete logarithms in GF p &ndash 130 digits, June 18, 2005, http listserv.nodak.edu cgi bin wa.exe?A2 ind0506&L nmbrthry&T 0&P 20. ref On 5 Feb 2007 this was superseded by the announcement by Thorsten Kleinjung of the computation of a discrete logarithm .... They used the function field sieve to compute a discrete logarithm in a field of 2 sup 613 sup elements ... et al., who computed a discrete logarithm in the field of 3 sup 6 · 71 sup elements ... Discrete Logarithm Problem in GF 3 sup 6 n sup , 2010, http eprint.iacr.org 2010 090. ref This also ... logarithm on a Koblitz curve over a field of 2 sup 108 sup elements. The prize was awarded on 4 April ... logarithm on a curve over a field of 2 sup 109 sup elements. The prize was awarded on 8 April 2004 .... ECCp 109, involving taking a discrete logarithm on a curve modulo a 109 bit prime. The prize was awarded ... announced that they had carried out a discrete logarithm computation on an elliptic curve ... more details
British subjects Indefinite leave to remain ILR is an immigration status granted to a person who does not hold Right of Abode United Kingdom right of abode in the United Kingdom UK , but who has been admitted to the UK without any time limit on his or her stay and who is free to take up employment or study, without restriction. When indefinite leave is granted to persons outside the United Kingdom it is known as indefinite leave to enter ILE . A person who has indefinite leave to remain, the right of abode , or is an Republic of Ireland Irish citizen, has settled status if resident in the United Kingdom all British citizens have the right of abode . Settled status is central to British nationality law , as the most usual route to naturalisation or registration as a British citizen requires that the applicant be settled in the UK. Settled status is also important where a child of non British citizen parents is born in the UK, as unless at least one parent has settled status the child will not automatically be a British citizen. Benefits Holders of indefinite leave to remain may apply for British citizenship if they have held this status for twelve months or longer, are over 18 and have been living in the United Kingdom for the last five years or three years if married to or a civil partner of a British citizen . Other people aged over 18, who hold another form of British nationality ... parents has indefinite leave to remain or other settled status at the time of the child s birth. Prior ... , they pay Home Student rates. Costs Prior to 2003, Indefinite Leave to Remain in the UK ... from 3 April 2006, the period of time required to obtain Indefinite Leave to Remain increases ... leave to enter other than for an indefinite period. Citation needed date December 2009 This may be because ... may reapply for indefinite leave to enter the UK. British Overseas citizen s, British subject s and British ... nationality law Use dmy dates date September 2010 DEFAULTSORT Indefinite Leave To Remain Category ... more details
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