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Topic: Beta function

Related Topics

Airy function

Theta function

Gamma function

Error function

Elliptic function

Method of steepest descent

Riemann zeta function

Exponential function

Hyperbolic function

Logarithmic integral

Gudermannian function

Falling factorial

Cousin problems

Schwarzian derivative

Dirichlet series

	Beta function - Wikipedia, the free encyclopedia
		The Nörlund-Rice integral is a contour integral involving the beta function.
		The incomplete beta function is a generalization of the beta function that replaces the definite integral of the beta function with an indefinite integral.
		The situation is analogous to the incomplete gamma function being a generalization of the gamma function.
	en.wikipedia.org /wiki/Beta_function (308 words)

	Alpha-Beta Search
		Beta is the worst-case scenario for the opponent.
		If a move results in a score that is greater than or equal to beta, this whole node is trash, since the opponent is not going to let the side to move achieve this position, because there is some choice the opponent can make that will avoid it.
		This caused the function to change its perspective with each recursion, to reflect the fact that the two players are in contention, and have opposite goals.
	www.seanet.com /~brucemo/topics/alphabeta.htm (1809 words)

	betapdf (Statistics Toolbox) (Site not responding. Last check: 2007-10-12)
		The beta probability density function for a given value x and given pair of parameters a and b is
		The uniform distribution on (0 1) is a degenerate case of the beta pdf where a = 1 and b = 1.
		A likelihood function is the pdf viewed as a function of the parameters.
	www-rohan.sdsu.edu /doc/matlab/toolbox/stats/betapdf.html (168 words)

	Beta distribution - Wikipedia, the free encyclopedia
		(α,β) is the incomplete beta function and I
		Beta distributions are used extensively in Bayesian statistics, since beta distributions provide a family of conjugate prior distributions for binomial distributions.
		For this reason, the Beta distribution - along with the triangular distribution - is used extensively in PERT, CPM and other project management / control systems to describe the time to completion of a task.
	en.wikipedia.org /wiki/Beta_distribution (603 words)

	NDEI.ORG :: Practical Diabetology > Beta-Cell Function, Dysfunction, and Preservation in Type 2 Diabetes
		Although beta cell function did not return to normal, the weight loss was associated with significant improvements in postchallenge insulin-secretory rates and in basal glucose levels and glucose tolerance.
		Various assessment techniques have demonstrated that beta-cell function is significantly compromised early in the course of impaired glucose tolerance and Type 2 diabetes.
		The relentless deterioration of beta-cell function in Type 2 diabetes is reflected by the progressive deterioration of glycemic control that is a hallmark of the disease.
	www.ndei.org /v2/website/content/index.cfm?MiscContent_ID=53 (1924 words)

	Beta
		The Beta function compares changes in a field to changes in a benchmark index over a given period of time.
		Beta values greater than 1 indicate that the price of the security changed by a larger percentage than the market as a whole.
		Beta values greater than 1 indicate that the price of the security has a tendency to move faster than that of the market.
	www.tradingsolutions.com /functions/Beta.html (429 words)

	CDr Wallach Beta-Carotene: use and function of
		Carotenoids generally contain a conjugated polyene structure which is efficient at absorbing light, and are the major yellow and red pigments in many fruits and vegetables.
		Beta Carotene is not toxic to the liver even in high doses in contrast to Vitamin A. Large doses of Beta Carotene will increase the body's demands for Vitamin E; therefore, those of you on 50,000 to 100,000 units of beta carotene per day.
		The definitive role of beta carotene/vitamin E is yet to be understood, but there is sufficient reason to use beta-carotene in a dose of 50,000 units per day.
	www.eagle-min.com /faq/faq66.htm (710 words)

	Scientific Research within the Beta Cell Biology Consortium
		This raises the exciting possibility that beta cells have a significant regenerative capacity that could be used to treat diabetes.
		The goal of this proposal is to advance technologies and understanding about the mechanism of pancreatic beta cell development in embryogenesis and adult islets, and to promote the application of such advances to islet regeneration and stem cell biology by other members of the Beta Cell Biology Consortium (BCBC).
		For instance, in that mouse, immune mediated destruction of the endogenous beta cells can be carefully regulated such that the killing takes place over weeks (to create an increasing need for new beta cell function) and such that new beta cells created from the progenitor would not be susceptible to the immune mediated killing.
	www.betacell.org /research (3631 words)

	NIH Guide: IMAGING PANCREATIC BETA CELL MASS, FUNCTION, OR INFLAMMATION
		Insulin is produced in the pancreatic islet beta cell and released in response to a meal, or to elevations in plasma glucose and certain amino acids.
		In the course of development of this technique, it would be of great clinical benefit to be able to identify the location, number, viability, growth and function of these grafts, and to noninvasively monitor their response to immune modulating therapy using imaging.
		These include tagged antibodies to the beta cell surface, ligands for receptors specific to the beta cell, or agents whose contrast properties are "unmasked" by beta cell enzymes.
	grants.nih.gov /grants/guide/rfa-files/RFA-DK-99-018.html (3754 words)

	Beta-Carotene
		It is unclear whether beta-carotene has any biological function for humans other than as a precursor for vitamin A. There is some evidence that beta-carotene may play a beneficial role in human nutrition beyond its provitamin A function.
		Ultraviolet light suppression of one type of immune function was significantly inhibited in a randomized trial of healthy older men taking 30 milligrams of beta-carotene daily for 47 days while simultaneously consuming a low-carotenoid diet.
		Effect of vitamin E and beta carotene on the incidence of primary nonfatal myocardial infarction and fatal coronary heart disease.
	www.pdrhealth.com /drug_info/nmdrugprofiles/nutsupdrugs/bet_0032.shtml (5202 words)

	Minimax with Alpha-Beta Cutoff
		As the algorithm evolves, the alpha and beta values of a node may change, but the alpha value will never decrease, and the beta value will never increase.
		The MINIMAX-AB function is called with as parameters the root of the game tree, -infinity (-I) as alpha value, and +infinity (+I) as beta value.
		And here is a C (yes C) program that tests the alpha-beta function on a couple of examples.
	www.cis.temple.edu /~ingargio/cis587/readings/alpha-beta.html (861 words)

	beta function (Site not responding. Last check: 2007-10-12)
		As the gamma function is defined as an integral, the beta function can also be written in an integral form
		So that the curve is also called the Euler beta function or the first Euler function.
		The beta function comes into picture when calculating the total density by performing convolutions of classical state densities which have a power law form.
	www.2dcurves.com /gamma/gammab.html (143 words)

	Dave Jewitt: Beta Pictoris Star (Site not responding. Last check: 2007-10-12)
		The models are used to constrain the range of disk parameters (inclination, radial gradient, vertical scale height, flare factor, phase function) in Beta Pictoris.
		From the Figure, we conclude that highly inclined (face-on) disks are difficult to distinguish from the circular halo of light scattered from the central star.
		The perpendicular spike (due to forward scattering from the near-side of the disk) seen in the middle column could easily be confused with a stellar jet.
	www.ifa.hawaii.edu /faculty/jewitt/beta.html (288 words)

	Complex Log Beta Function
		Compute the log beta function with complex arguments.
		The complex beta function is simply the natural log of the above function.
		This syntax computes the complex component of the complex log beta function.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/clnbeta.htm (347 words)

	RFA-DK-05-007: Beta Cell Regeneration for Diabetes Therapy
		The purpose of this RFA is to invite and support applications characterizing the regenerative potential of human beta cells, including studies to define signals and cellular targets required to regenerate pancreatic function in the diabetic microenvironment, and experiments to identify ways to enhance beta cell regeneration in vivo.
		The overall objective of this RFA is to support studies that will characterize the regenerative potential of human beta cells and/or islets in vivo, define cellular and molecular factors regulating pancreatic regeneration in normal and diabetic adults, and identify mediators and cellular targets capable of enhancing recovery of endogenous beta cell function in diabetic patients.
		Basic research to enhance our understanding of the life cycle of human beta cells and their regenerative capacity in vivo, including studies of signals required to maintain human beta cell mass and viability in normal and diabetic in vivo microenvironments.
	grants.nih.gov /grants/guide/rfa-files/RFA-DK-05-007.html (5261 words)

	Beta Function -- from Wolfram MathWorld (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-12)
		which are an immediate consequence of the analogous identities for gamma functions.
		"Beta Function" and "Incomplete Beta Function." §6.2 and 6.6 in
		Jeffreys, H. and Jeffreys, B. "The Beta Function." §15.02 in Methods of Mathematical Physics, 3rd ed.
	mathworld.wolfram.com.cob-web.org:8888 /BetaFunction.html (383 words)

	BETA
		The BETA function returns the value of the beta function B(This routine is written in the IDL language.
		If one argument is a scalar and the other argument is an array, the function uses the scalar value with each element of the array, and returns an array with the same dimensions as the input array.
		The point at which the beta function is to be evaluated.
	www.astro.princeton.edu /~esirko/idl_html_help/B7.html (213 words)

	Simulation with beta response function
		Beta response function is defined by k * (x-a)^alpha * (b-x)^gamma.
		This is not a direct parameter in beta response function, but program finds the parameter k from other parameters so that the response has the desired height, since it is difficult to guess a nice value directly for k.
		It seems that it is impossible to obtain reliable estimates of parameters of beta response function from observed community data.
	cc.oulu.fi /~jarioksa/softhelp/betasimu.htm (2658 words)

	beta, betainc, betaln (MATLAB Function Reference) (Site not responding. Last check: 2007-10-12)
		computes the beta function for corresponding elements of the complex arrays
		computes the natural logarithm of the beta function,
		function can range over very large or very small values, its logarithm is sometimes more useful.
	www.cs.berkeley.edu /titan/sww/software/matlab/techdoc/ref/beta.html (81 words)

	The Gamma Function
		This is why we thought it would be a good idea to have a page on this function with its basic properties.
		Historically the search for a function generalizing the factorial expression for the natural numbers was on.
		Euler's first integral or the Beta function: In studying the Gamma function, Euler discovered another function, called the Beta function, which is closely related to
	www.sosmath.com /calculus/improper/gamma/gamma.html (608 words)

	2004 Nobel Laureates Lecture Stockholm - Question on Beta function! - SciForums.com
		They mentioned that one step in their work was calculating the Beta function for some configuration and they showed their result, and that it was important for it to be negative.
		what Gross discovered is that the beta function of QCD is negative, meaning that the coupling constant gets smaller at larger energies, as compared with QED where it gets larger, which means that perturbation theory can work for QCD if you crank up the energy beams high enough.
		The action is a functional, this means for every possible path through phase space that a system can take, it assigns a real number (phase space is the space of all possible coordinates and their derivatives.
	www.sciforums.com /showthread.php?t=43140 (3899 words)

	TGF-beta
		Other researchers believe that cells that are resistant to TGF-beta, such as those in colon cancer, “spit” the protein out, where it then functions in the tumor microenvironment to stimulate cancer progression.
		Understanding the molecular events involved in TGF-beta function in normal cells and its lack of function in tumor cells is now a focus of basic research as well as drug development.
		Because of their key role in controlling growth, components of the TGF-beta pathway are considered to be major tumor suppressor genes; absence or malfunction of one or more receptors or signaling proteins is believed to have an impact on loss of growth regulation.
	www.aacr.org /page5569.aspx (1025 words)

	PlanetMath: beta function
		The beta function was first defined by L. Euler in 1730, and the name was given by J. Binet.
		This is version 17 of beta function, born on 2003-02-09, modified 2006-10-02.
		(Special functions :: Elementary classical functions :: Gamma, beta and polygamma functions)
	planetmath.org /encyclopedia/BetaFunction.html (49 words)

	Beta Function (Site not responding. Last check: 2007-10-12)
		The beta function forms part of the definition of several distributions:
		It is convenient to define the beta function in terms of the gamma function:
		The graph below shows the range of values of the Beta function for the values of a and b used in the documentation for the Beta distribution.
	www.brighton-webs.co.uk /maths/beta.asp (52 words)

	Mathematica Documentation: Beta
		, a, b] gives the generalized incomplete beta function
		• Note that the arguments in the incomplete form of Beta are arranged differently from those in the incomplete form of Gamma.
		• In TraditionalForm, Beta is output using \[CapitalBeta].
	documents.wolfram.com /mathematica/functions/Beta (72 words)

	Beta-function - Wikipedia, the free encyclopedia
		For the mathematical function see Euler beta function.
		In theoretical physics, specifically quantum field theory, a beta-function β(g) encodes the dependence of a coupling parameter, g, on the energy scale, μ of a given physical process.
		In this case, the non-zero beta function tells us that the classical scale invariance is anomalous.
	en.wikipedia.org /wiki/Beta-function (458 words)

	FAQ: Calculating the beta function
		The beta function can be defined in terms of the gamma function and thus calculated using the Stata functions exp() and lngamma().
		On the latter, see help on math functions.
		Given arguments a and b, the beta function
	www.stata.com /support/faqs/stat/beta.html (81 words)

	[No title]
		Calculates any one parameter of the beta distribution given values for the others.
		Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.
		Note The beta density is proportional to t^(A-1) * (1-t)^(B-1) Arguments P -- The integral from 0 to X of the chi-square distribution.
	www.zend.com /manual/function.stats-cdf-beta.php (369 words)

	Strings and beta function.
		I watched the elegant universe and one scienetist noticed the euler beta function seemed to explain what he was doing and it had properties of a vibrating string.
		It was asserted that physics should be symmetric with respect to this dual explanation; neither "channel" should be preferred.
		Veneziano then found that the symmetric mathematical model was defined by the beta function.
	www.physicsforums.com /showthread.php?p=920481 (372 words)

	Beta function : Integration
		Involving only one direct function with respect to a (2 formulas)
		Involving one direct function and elementary functions with respect to a (1 formula)
		Involving one direct function and elementary functions with respect to b (1 formula)
	functions.wolfram.com /GammaBetaErf/Beta/21/ShowAll.html (48 words)

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