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Topic: Additive function


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In the News (Tue 23 Apr 19)

  
  Additive function - Wikipedia, the free encyclopedia
In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime we have:
Outside number theory, the term additive is usually used for all functions with the property f(ab) = f(a) + f(b) for all arguments a and b.
An example of an arithmetic function which is additive but not completely additive is ω(n), defined as the total number of different prime factors of n.
en.wikipedia.org /wiki/Additive_function   (255 words)

  
 List of mathematical functions - Wikipedia, the free encyclopedia
A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.
Subadditive function: The value of a sum is less than or equal to the sum of the values of the summands.
Superadditive function: The value of a sum is greater than or equal to the sum of the values of the summands.
www.wikipedia.com /wiki/List+of+functions   (796 words)

  
 Additive function -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07)
The function Ω(n), defined as the total number of (A number that has no factor but itself and 1) prime factors of n, counting multiple factors multiple times.
An example of an arithmetic function which is additive but not completely additive is ω(n), defined as the total number of different (A number that has no factor but itself and 1) prime factors of n.
From any additive function f(n) it is easy to create a related (Click link for more info and facts about multiplicative function) multiplicative function g(n) i.e.
www.absoluteastronomy.com /encyclopedia/A/Ad/Additive_function.htm   (267 words)

  
 Additive - Wikipedia, the free encyclopedia
When used as a noun, additive refers to something that is introduced to a larger quantity of something else, usually to alter characteristics of the larger quantity.
For example, sweetener is used as an additive to alter the flavor of food.
Formally additive may also be contrasted with sectional, see repetition.
en.wikipedia.org /wiki/Additive   (248 words)

  
 Additive function   (Site not responding. Last check: 2007-11-07)
Outside number theory, the term additive is usually used for all functions with the propertyf(ab) = f(a) + f(b) for all arguments a and b.
An additive function f(n) is said to be completely additive if f(ab) =f(a) + f(b) holds for all positive integers a and b, even whenthey are not coprime.
An example of an arithmetic function which is additive but not completely additive is ω(n), defined as thetotal number of different prime factors of n.
www.therfcc.org /additive-function-151006.html   (242 words)

  
 Lebesgue-Stieltjes integration - Wikipedia, the free encyclopedia
We may now proceed to construct the Lebesgue-Stieltjes integral of a non-negative, measurable function in a similar fashion to the construction of the corresponding Lebesgue integral.
We are finally equipped to define the Lebesgue-Stieltjes integral of an arbitrary function f with respect to the measure associated with an arbitrary additive function of an interval, v, which is of bounded variation.
Where f is a real-valued function of a real variable and v is a non-decreasing real function, the Lebesgue-Stieltjes integral is equivalent to the Riemann-Stieltjes integral, in which case we often write
en.wikipedia.org /wiki/Lebesgue-Stieltjes_integration   (584 words)

  
 .:: General Purpose Hash Function Algorithms - By Arash Partow ::.
When algorithms which contain hash functions are analyzed it is generally assumed that hash functions have a complexity of O(1), that is why look-ups for data in a hash-table are said to be of O(1) complexity, where as look-ups of data in maps (Red-Black Trees) are said to be of O(logn) complexity.
Same as additive hashing in that every element in the data string is used to construct the hash, but unlike additive hashing the values are put through a process of bitwise shifting.
It is a simple hash function using a strange set of possible seeds which all constitute a pattern of 31....31...31 etc, it seems to be very similar to the DJB hash function.
www.partow.net /programming/hashfunctions   (1393 words)

  
 Liouville function - Wikipedia, the free encyclopedia
The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.
The Liouville function is related to the Riemann zeta function by the formula
Haselgrove, C.B. A disproof of a conjecture of Polya.
www.wikipedia.org /wiki/Liouville_function   (198 words)

  
 PlanetMath: additive   (Site not responding. Last check: 2007-11-07)
Cross-references: set function, properties, sequence, disjoint, algebra, real function
This is version 3 of additive, born on 2002-08-30, modified 2003-02-11.
Object id is 3400, canonical name is Additive.
planetmath.org /encyclopedia/Additive.html   (50 words)

  
 math lessons - Arithmetic function
In number theory, an arithmetic function (or number-theoretic function) f(n) is a function defined for all positive integers and having values in the complex numbers.
The most important arithmetic functions are the additive and the multiplicative ones.
An important operation on arithmetic functions is the Dirichlet convolution.
www.mathdaily.com /lessons/Arithmetic_function   (223 words)

  
 [No title]
additive +------------------------------------------------------------ A function f: G to H from a semigroup G to a semigroup H is additive if f(a+b) = f(a) + f(b).
For example, if G is the group of additive integers and N=k N with an integer k, then G/N = Z_k is finite group of integers modulo k.
function field +------------------------------------------------------------ A function field is a finite extension of the field C(z) of rational functions in the variable z.
www.math.harvard.edu /~knill/sofia/data/algebra.txt   (1599 words)

  
 Institute of Mathematics of National Academy of Sciences of Armenia   (Site not responding. Last check: 2007-11-07)
It is proved, if the distribution function of majorant of dyadic derivative ratio satisfies to some necessary condition and almost everywhere there exists dyadic derivative, then the additive function may be restored by its derivative.
For functions of several variables we estimate the difference between certain Riemann integral means and similar means for cubic partial sums of their Fourier series.
The paper is devoted to investigation of functions of several variables with finite essential variation in the sense of Vitali.
math.sci.am /Journal/1995_5.html   (359 words)

  
 Multi-function additive for lubricating oils - Patent 4978464   (Site not responding. Last check: 2007-11-07)
As is known in the art, some lubricant additives function as antiwear agents, some as antioxidants, some as antifriction agents, and some as extreme pressure agents.
As was indicated previously, the solubility of the additive depends upon the number of carbon atoms in the ligands.
Concentrates of the additive of the present invention in a suitable diluent hydrocarbon carrier provide a convenient means of handling the additives before their use.
www.freepatentsonline.com /4978464.html   (2324 words)

  
 Features Item : COATINGS R&DNOTEBOOK

  (Site not responding. Last check: 2007-11-07)

The enhanced performance of a coating additive can be supported by the greater control of the specific in-application function of the additive.
When additives are incorporated into the molecular cavity of these solids and formulated into an applied coating, their release is based on the selective aqueous extraction of the additive from the porous microsphere.
In cases where additives such as biocides are employed, the controlled release mechanism not only provides sustained protection from microorganisms, but also contributes to minimizing the negative impact to the surrounding ecosystem.
www.ippmagazine.com /CDA/ArticleInformation/features/BNP__Features__Item/0,6897,110301,00.html   (554 words)

  
 [No title]   (Site not responding. Last check: 2007-11-07)
When the utility is additively separable, this means that there exists some kind of independence between the attributes, and this independence makes the elicitation of the utility much easier to perform.
Another advantage of additive utility functions lies in their computation: thanks to the additive separability, they are usually very simple mathematical functions and therefore they can be usually computed very quickly, especially when using parallel algorithms.
The major disadvantage of these structural conditions is that they prevent the use of additive utilities in many applications, for instance in fields like medical decision making (where the set of states of health usually satisfies neither restricted solvability nor connectedness); or economics, where some consumer goods may not be infinitely divisible.
www-poleia.lip6.fr /~gonzales/research/tutoriel_utilite.php   (4024 words)

  
 Hwang dataset detail
According to the paper by Hwang, et al, each of the functions was defined with a scaling factor incorporated so that the standard deviation of its values over a 2,500-point grid would be one, and with values translated so that they are all non-negative over the domain.
The detailed forms of the five functions can be found in the paper by Hwang, et al, or by examining the source of the generation program used to create the DELVE dataset (gen.c).
The figure in the paper shows the function defined by the formula in terms of reals, and this is the form used in generating the DELVE dataset.
www.cs.toronto.edu /~delve/data/hwang/hwangDetail.html   (1282 words)

  
 An Additive Model of Test Anxiety: Role of Exam-Specific Expectations - Questia Online Library   (Site not responding. Last check: 2007-11-07)
The study tested a hypothesis whereby anxiety concerning examinations covering different subjects is an additive function of dispositional test anxiety and the anticipated results of individual tests.
The authors of that review concluded that mathematics anxiety is functionally similar to test anxiety, relating to individual differences in the tendency to appraise test items involving the manipulation of numbers as threatening.
Alternatively, an additive model of test anxiety would specify that each individual has some stable disposition (i.e., TA-trait), and the level of anxiety associated with different tests is expected to deviate from that level, depending on situational factors as appraised by that individual.
www.questia.com /PM.qst?a=o&d=96407004   (848 words)

  
 The Joint Distribution Of q-Additive Functions - Drmota (ResearchIndex)   (Site not responding. Last check: 2007-11-07)
A real-valued function f, de ned on the nonnegative...
3: additive functions on polynomial sequences (context) - Bassily, atai et al.
8 additive functions on polynomial sequences (context) - Bassily, atai et al.
citeseer.ist.psu.edu /387129.html   (719 words)

  
 Abstracts
-differentiable function can be represented as the sum of an additive mapping and a continuously differentiable function.
Functional equations have many interesting applications in the characterization problems of probability theory (e.g.
The main goal of this work is to call attention to hypergroups and to the possibility of studying functional equations on hypergroups.
www.math.klte.hu /analizis/conferences/debkat/2001/abstracts.html   (1213 words)

  
 Project No C98-S01   (Site not responding. Last check: 2007-11-07)
Depending on the additive and the constituent fibers of the fabric, it is often difficult to deliver the additive to the fabric in sufficient quantity or with sufficient fastness to achieve longterm additive function.
When an additive is delivered in the form of its CD-IC crystals, it is protected from the environment encountered both during and after embedding into the carrier polymer fibers.
The ability of CD-ICs to function as stable, solid additive containers means that volatile liquid and gaseous additives can be incorporated into and delivered by and to solid polymer fibers, films, and fabrics, with their delivery tailored to on-demand exposure to various environmental conditions such as temperature, solvents, and gases.
www.ntcresearch.org /current/year9/C98-S01.htm   (1657 words)

  
 article2   (Site not responding. Last check: 2007-11-07)
If we can identify regions in the image where the image intensity is approximately uniform, for instance the sky, it may be possible to estimate the power spectrum or the probability density function of the random background noise from the intensity fluctuations in the uniform background regions.
Additive random noise degradation includes electronic circuit noise and in some cases amplitude quantization noise.
When the blurring function is assumed to be known, one approach to deblurring is Inverse Filtering.
www.iis.ee.ic.ac.uk /~frank/surp00/article2/cfcs98   (1113 words)

  
 The Additive Value of Combined Assessment of Myocardial Perfusion and Ventricular Function Studies -- Meine et al. 45 ...   (Site not responding. Last check: 2007-11-07)
Effects of maximal exercise stress on left ventricular function in patients with coronary artery disease using first pass radionuclide angiocardiography: a rapid, noninvasive technique for determining ejection fraction and segmental wall motion.
Incremental value of simultaneous assessment of myocardial function and perfusion with technetium-99m sestamibi for prediction of extent of coronary artery disease.
Functional assessment with electrocardiographic gated single-photon emission computed tomography improves the ability of technetium-99m sestamibi myocardial perfusion imaging to predict myocardial viability in patients undergoing revascularization.
jnm.snmjournals.org /cgi/content/full/45/10/1721   (2419 words)

  
 Cosmetics Unmasked Ingredients S
Origin: A waxy substance extracted from shellac, a yellow resin extracted from insects of the Lac family.
Function: Thickener and strengthener for some brands of mascara and nail polish.
Origin: A chemically modified naturally occurring polysaccharide similar to starch that is produced by the action of bacteria on cane sugar (sucrose).
www.gina.antczak.btinternet.co.uk /CU/IS.HTM   (5426 words)

  
 Journal of the American Statistical Association : Variable selection and function estimation in additive nonparametric ...   (Site not responding. Last check: 2007-11-07)
Start / J / Journal of the American Statistical Association / September 01, 1999 / Variable selection and function estimation in additive nonparametric regression using a data-based prior.
For the binary model, the probit link function is considered in detail, but other link functions can be used in place of the probit link function, as outlined in some earlier work (Wood and Kohn 1998).
The regression functions are estimated by their posterior means taking into account the hierarchical structure of the model.
static.highbeam.com /j/journaloftheamericanstatisticalassociation/september011999/variableselectionandfunctionestimationinadditiveno/index.html   (278 words)

  
 Additive function   (Site not responding. Last check: 2007-11-07)
In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime we have:f(ab) = f(a) + f(b).
All is still licensed under the GNU FDL.
Thence I down to the Hall, and shew, and let me take a copy of, all the articles against my Lord to make them good, of which I was mighty glad, and so away home, and to joyner to come to work at my office, and so back home and to my letters.
www.termsdefined.net /ad/additive-function.html   (363 words)

  
 Kolekcja matematyczno-fizyczna   (Site not responding. Last check: 2007-11-07)
Functions of an interval that are additive and of bounded variation
Measure defined by a non-negative additive function of an interval
Ward's theorems on derivation of additive functions of an interval
matwbn.icm.edu.pl /kstresc.php?tom=7&wyd=10   (148 words)

  
 Results
So it needs to be shown what types of function are additive.
The next theorem shows that there is only one type of additive function.
It is left to show that these are all the possible additive functions.
www-math.cudenver.edu /~rrosterm/gq/node6.html   (320 words)

  
 The following problem can be found on page 14 of the text:   (Site not responding. Last check: 2007-11-07)
As stated previously, the graph of the absolute value function is symmetric about the y-axis.
The absolute value function is continuous but not differentiable.
A function f is additive if for x and y in its domain, f(x + y) = f(x) + f(y).
jwilson.coe.uga.edu /EMAT4500/AssignmentPages/ChristyJenkins/CJ_ass1_abs.htm   (289 words)

  
 SMIL Boston Animation   (Site not responding. Last check: 2007-11-07)
The functional representation of the animation's definition is independent of this model, and may be expressed as a sequence of discrete values, a keyframe based function, a spline function, etc. In all cases, the animation exposes this as a function of time.
All other timing functions, including synchronization and time manipulations such as repeat, time scaling, etc. are provided (transparently) by the timing model.
When the animation is also additive, as composite animations typically are, they compose just as straight additive animations do (using the cumulative value).
www.w3.org /1999/08/WD-smil-boston-19990803/Animation/smil-animation   (4015 words)

  
 Fourier Series Applet   (Site not responding. Last check: 2007-11-07)
This java applet demonstrates Fourier series, which is a method of expressing an arbitrary periodic function as a sum of cosine terms.
In other words, Fourier series can be used to express a function in terms of the frequencies (harmonics) it is composed of.
The function is displayed in white, with the Fourier series approximation in red.
www.falstad.com /fourier   (117 words)

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