Theta-function - Factbites

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Topic: Theta-function

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	Riemann-Siegel theta function - Wikipedia, the free encyclopedia
		In mathematics, the Riemann-Siegel theta function is the function
		The interest in the Riemann-Siegel theta function is in studying the Riemann zeta function and defining the Z function.
		The Riemann-Siegel theta function is an odd real analytic function for real values of t; it is an increasing function for values t
	en.wikipedia.org /wiki/Riemann-Siegel_theta_function (321 words)

	Theta function - Wikipedia, the free encyclopedia
		With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions (sometimes called quasi-periodicity, though this is not related to the use of that term for dynamical systems).
		The most common form of theta function is that occurring in the theory of elliptic functions.
		This theta function is a modular form of weight n/2 (on an appropriately defined subgroup) of the modular group.
	en.wikipedia.org /wiki/Theta_function (1143 words)

	d2dgauss.m
		function h = d2dgauss(n1,sigma1,n2,sigma2,theta) % Function "d2dgauss.m": % This function returns a 2D edge detector (first order derivative % of 2D Gaussian function) with size n1n2; theta* is the angle that % the detector rotated counter clockwise; and sigma1 and sigma2 are the % standard deviation of the Gaussian functions.
	www.bic.mni.mcgill.ca /~joubin/mtrr/MATLAB_CODES/d2dgauss.m (82 words)

	Brain wave Functions Alpha Beta Theta Brainwaves
		During this awakening cycle it is possible for individuals to stay in the theta state for an extended period of say, five to 15 minutes--which would allow them to have a free flow of ideas about yesterday's events or to contemplate the activities of the forthcoming day.
		A person who is driving on a freeway, and discovers that they can't recall the last five miles, is often in a theta state--induced by the process of freeway driving.
		It is well known that the brain is an electrochemical organ; researchers have speculated that a fully functioning brain can generate as much as 10 watts of electrical power.
	brain.web-us.com /brainwavesfunction.htm (1028 words)

	Theta Functions
		This computes the multidimensional theta function with characteristic char (a 2g x 1 matrix) at z (a g x 1 matrix) and tau, the small period matrix of the analytic Jacobian A.
		This computes the multidimensional theta function with characteristic char (a 2g x 1 matrix) at z (a g x 1 matrix) and tau (a symmetric g x g matrix with positive definite imaginary part).
		The vector c is called the characteristic of the theta function.
	magma.maths.usyd.edu.au /magma/htmlhelp/text583.htm (197 words)

	PlanetMath: Riemann $þeta$-function
		Riemann showed that the theta function satisfied a functional equation, which was the key step in the proof of the analytic continuation for the Riemann Xi Function; this has direct consequences of course with the Riemann Zeta function.
		The Riemann theta function is a number theoretic function which is only really used in the derivation of the functional equation for the Riemann Xi Function.
		Cross-references: Riemann zeta function, Riemann Xi function, analytic continuation, functional equation, exact form, domain, functional equation for the Riemann Xi function, derivation, function
	planetmath.org /encyclopedia/RiemannThetaFunction.html (128 words)

	IRAF help : images gauss (Jan91)
		Circularly Symmetric Gaussian Function ratio = 1 theta = 0.0 N = normalization factor G = N * exp (-0.5 * (r / sigma) ** 2) 2.
		Theta is measured counter-clockwise from the x axis and must be between 0 and 180 degrees.
		Convolve an image with an elliptical Gaussian function whose sigma in the major and minor axis direction is 2.0 and 1.5 respectively, and whose position angle is 45 degrees, using wrap around boundary extension.
	www.astro.uni-bonn.de /~webstw/cm/lfa_html/iraf/images.gauss.html (704 words)

	jinc.m
		function j=jinc(theta) % function j=jinc(theta) % % This function computes the jinc function as defined by % Bracewell's 2D imaging text, namely % % j=besselj(1,pi*theta)./(2*theta); % % The value at jinc(0) is set to pi/4 % Copyright 2002 Board of Trustees, Leland Stanford Jr.
	nova.stanford.edu /~curtis/research/matlabutils/matlab/util/jinc.m (64 words)

	Cwikel
		The arithmetic theta function is a modular form of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface attached to a Shimura curve of Q. This function can be used to define a theta lift from modular forms of weight 3/2 to the elements of the arithmetic Chow group.
		A conjectural analogue of a result of Waldspurger gives a characterization of the nonvanishing of this arithmetic theta lift in terms of (i) local obstructions and (ii) the nonvanishishing of the central derivative of the L-function.
	www.math.princeton.edu /~seminar/2002-03-sem/KudlaAbstract4-17-2003.html (88 words)

	CLAS Cerenkov detector efficiency
		The plot of mean number of photoelectrons as a function of projective angles Theta, Phy for sector 1 were used to plot the number of electron candidates as a function of Nphe.
		Thereafter are the plots of the mean number of the detected photoelectrons as a function of Theta and Phy :
		Theta and Phy are accordingly polar and azimuthal angles of the entrance point on the surface of the Cerenkov detector in the sector reference system.
	www.jlab.org /~vlassov/cc/e_rec.html (908 words)

	CSE 291 Lecture Notes, January 20, 2004
		To show that a family is exponential, you may have to write theta as a function of the natural parameters, e.g.
		Hence for fixed x, the score function says which values of theta are best: the optimum score is zero and any non-zero score is less desirable.
		We can use the same t for many different functions g of the same theta.
	www-cse.ucsd.edu /users/elkan/291winter2004/jan20.html (910 words)

	trans_function.m
		function tf = trans_function(theta); % %**************************************************************** % This function performs the transformation from % theta** in [0, pi] to z in [L_END;R_END] using the transformation % % z=.5((R_END-L_END)cos(theta)+L_END+R_END); % % and returns the value f(z), where f is a user specified function.
		% % Input % % theta value in interval [0, pi] % % Global Variables % % f Function name.
		% The name of the function must be assigned to the string % variable f.
	amath.colorado.edu /courses/5600/2004fall/pa3/trans_function.m (101 words)

	CSE 250B Lecture Notes for May 22, 2000
		In M step we have a function of theta to maximize.
		X, theta' ] where the expectation is an integral over Y. Often we can simplify this by finding a single special y value such that the integral over Y is the same as evaluating the integrand for this special y value.
		In general, the expectation of a function is the function of the expectation if and only if the function is linear.
	www-cse.ucsd.edu /~elkan/250B/may22.html (758 words)

	Elliptic and Modular Functions
		Given a lattice L = [a, b] in the complex plane, this function returns the value of the elliptic j-invariant of L. This is the j-invariant of tau where tau = a/b or tau = b / a, whichever is in the upper half complex plane.
		Defined this way, theta satisfies theta(q, - z)= - theta(q, z), it is periodic with period 2pi in the second variable: theta(q, z + 2pi)= theta(q, z), and its zeroes are of the form m_1pi + m_2(log x/i) for any integers m_1, m_2.
		This is a modular function of weight 0 whose Fourier expansion starts with j(s)=e^(-2pi i s) + 744e(2pi i s) + 196884e(2pi i s) +...
	www.math.wisc.edu /help/magma/text467.html (1285 words)

	dis.mix.r
		###################################################################### # The main function # # x is the raw data, cut is a voector of cut-off pts # # max.comp is the maximal number of components # ###################################################################### dis.mix.em
	www.stat.psu.edu /~fxuan/research/dis.mix.r (116 words)

	Riemann Hypothesis in a Nutshell
		The functional equation of the zeta function is
		The function Z(t) is typically the object of study for locating zeros of the zeta function on the critical line and verifying the Riemann Hypothesis.
		Since there are infinitely many non-trivial zeros of the zeta function, there is no way you can verify computationally that they all lie on the critical line.
	www.math.ubc.ca /~pugh/RiemannZeta/RiemannZetaLong.html (1384 words)

	moments.m
		% % function [centroid, theta, roundness] = moments(im) % % Argument: im - a binary image containing values of 0 or 1 % % Returns: centroid - a 2 element vector % theta - the angle of axis of minimum inertia (radians) % roundness - ratio of minimum inertia/maximum inertia.
		% MOMENTS % % Function calculates the moments of a binary image and returns % the centroid, the angle of axis of minimum inertia, and a measure % of 'roundness'.
		The function assumes that there is only one object % in the binary image.
	www.csse.uwa.edu.au /~wongt/Documents/matlab/moments.m (137 words)

	Yorick - Basic Ideas
		The external variable theta determines the phase points at which the damped sine wave is evaluated; q_out will write two header lines, followed by two columns, with one line for each element of the theta array.
		This does no harm, since any functions or variables defined in the file will be replaced by their new definitions the next time you include the file, just as they would if you typed new definitions.
		As you use a function, you notice that the surrounding code is often the same, suggesting a savings if it were incorporated into the function.
	www.cgd.ucar.edu /cms/pjr/yorick/yorickstuff/yorick_1.html (6000 words)

	Exact Formulae for the Lovász Theta Function of Sparse Circulant Graphs
		The Lovász theta function has attracted much attention for its connection with diverse issues such as communicating without errors and computing large cliques in graphs.
		Exact Formulae for the Lovász Theta Function of Sparse Circulant Graphs: SIAM Journal on Discrete Mathematics Vol.
		Exact Formulae for the Lovász Theta Function of Sparse Circulant Graphs
	epubs.siam.org /sam-bin/dbq/article/41852 (160 words)

	BIBLIOGRAPHY
		On the theorems of Watson and Dragonette for Ramanujan's mock theta functions.
		Ramanujan's "Lost Notebook." IX the partial theta function as an entire function.
		On a conjecture of Guinand for the plane partition function.
	www.math.psu.edu /andrews/biblio.html (2521 words)

	estim_CEVb.m
		function [THETA,THETA_sum,elapsed_time,Yb,Ypred,Ypred_sum] = estim_CEVb(Y,m,R,hor,beta,flag_beta) % ESTIM_CEVe estimates the parameters of the CEV model using % Bootstrap.
		% % OUTPUT VARIABLES % 'THETA' is the (R x cT) matrix of estimates from parameter bootstrap samples.
	galton.uchicago.edu /~artigas/Research/estim_CEVb.m (247 words)

	[Tutor] nested functions
		Notice we use a function with theta as an argument.
		Recall that zmatrix is a function, which expects and angle as its argument.
		To rotate point around the x-axis in the XYZ coordinate system, we use the rotation matrix: def xmatrix(theta): return [[1,0, 0], [0, cos(theta),-sin(theta)], [0, sin(theta), cos(theta)]] where theta is the angle you want to rotate by.
	mail.python.org /pipermail/tutor/2002-April/013688.html (523 words)

	ass4
		The arguments # are the function to integrate, the bounds of integration, which may be # -Inf or +Inf, the number of points to evaluate the function at, and any # additional arguments to the function.
		The arguments are the # function to integrate, the low and high bounds, and the number of points # to use.
		Additional arguments to pass to the function being integrated # can follow.
	www.utstat.utoronto.ca /~radford/sta2102.S03/ass4 (206 words)

	Theta functions
		That the zeta function ought to come into the scheme of things somehow is not surprising - the Poisson and related summation formulae are special cases of the Jacobi theta function.
		This counterpart to Poisson's summation formula is shown to be essentially 'equivalent' to the famous functional equation of Riemann's zeta-function, to the 'modular relation' of the theta-function, to the Nielsen-Doetsch summation formula for Bessel functions and to the partial fraction expansion of the periodic Hilbert kernel."
		Additionally, the properties of the zeta function are automatically connected to the theory of prime numbers.
	www.maths.ex.ac.uk /~mwatkins/zeta/thetafunctions.htm (559 words)

	Riemann Theta Function
		Then the Riemann theta function is defined by
	www.math.sdu.edu.cn /mathency/math/r/r313.htm (559 words)

	theta.py
		As the theta module requires the atmqty package (in order to access the AtmConst class) and theta is distributed as part of the atmqty package, the parent directory to the atmqty directory is added to sys.path for this module testing case to enable doctest to work on theta.
		TypeError: theta: Args not Numeric floating """ } #- Execute doctest if module is run from command line: if __name__ == "__main__": """Test the module.
		TypeError: theta: p0 not floating >>> p = [400., 410., 308.2] >>> a = theta.theta(p, T) Traceback (most recent call last):...
	www.johnny-lin.com /py_pkgs/atmqty/lib/theta.py (477 words)

	On Extracting Maximum Stable Sets in Perfect Graphs Using Lovasz's Theta Function
		Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set.
		We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function.
		We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly.
	www.optimization-online.org /DB_HTML/2003/10/757.html (247 words)

	Mathematics of Computation
		Abstract: The Riemann theta function is a complex-valued function of
		First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision.
		Keywords: Riemann theta function, pointwise approximation, uniform approximation
	www.ams.org /mcom/2004-73-247/S0025-5718-03-01609-0/home.html (440 words)

	Theta.java
		This is true because * the estimates, which lead to the approximation of the oscillating part of the Riemann* theta function, are rather weak, and therefore the error for the actual values often falls low * of the tolerance.
		* Evaluating the theta function may easily lead to overflows or numerical * instabilities, which should be avoid.
		of the Riemann theta function can be factored * out and the remaining oscillatory part can be approximated with a prescribed error * tolerance.
	www-sfb288.math.tu-berlin.de /~jtem/riemann/src/riemann/theta/Theta.java (1166 words)

	ACE (3.0, 1997): Theta-SYMF package
		function realizes a certain multiplicative automorphism of the ring of symmetric functions.
		It is defined on power-sum functions as follows:
		Whenever there is a conflict between the function name
	phalanstere.univ-mlv.fr /~ace/ACE/3.0/SYMF/Theta.html (70 words)

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