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Topic: Cubic function

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	ROSTLAB - Welcome
		For those of you who prefer to continue using the previous layout for some time they will be available without support at http://rostlab.org/old_before2008/.
		Research goals of the lab involve using protein and DNA sequences along with evolutionary information to predict a protein's: overall function, interaction partners, secondary structure, disordered regions, subcellular localization, membrane spanning protein structure, intra-chain residue contacts, cell cycle control, and domain boundaries.
		Another significant research focus is to improve the effectiveness and efficiency of structural genomics projects' ability to determine the structures of proteins on a large scale.
	cubic.bioc.columbia.edu (414 words)

	CUBIC Overview
		The function grows much slower than binary increase (which is the logarithmic) near the origin (or plateau).
		Note that a response function of a protocol is the sending packet rate per RTT (or window size) in terms of packet loss rates.
		CUBIC borrows this idea; low utilization triggers CUBIC to increase its window growth rate by disabling the window clamping, and when there are competing traffic, it simply reverts to the regular CUBIC operation (which ensures fairness).
	www4.ncsu.edu /~rhee/export/bitcp/index_files/Page815.htm (1667 words)

	Econometric model
		In addition to a cubic function of income, the regression includes a time trend and population.
		While the cubic model in income levels provides a straightforward test for how the MPE varies with average income, it can be improved upon as a specification for the bivariate relationship.
		The loglikelihood function from the linear cubic model is -2978.82 and from the log quadratic model is -2500.69.
	www.worldbank.org /html/prddr/prdhome/peg/wps13/indexp4.htm (866 words)

	Cubic function - Wikipedia, the free encyclopedia
		In mathematics, a cubic function is a function of the form
		The derivative of a cubic function is a quadratic function.
		The integral of a cubic function is a quartic function.
	en.wikipedia.org /wiki/Cubic_function (217 words)

	Examples of Rational Function Graphing (Site not responding. Last check: )
		On dividing the numerator by the denominator, the polynomial quotient is a linear function.
		On dividing the numerator by the denominator, the polynomial quotient is a quadratic function.
		On dividing the numerator by the denominator, the polynomial quotient is a cubic function.
	www.webgraphing.com /examples_rationals.jsp (173 words)

	: cubic equation amounts to finding the roots of a cubic function. ,EXPLORE INDIA,India, Indian news, Indian Travel, ...
		Cubic equations were known to the ancient Indians and ancient Greeks since the 5th century BC, and even earlier to the ancient Egyptians, who dealt with the problem of doubling the cube, and attempted to solve it using compass and straightedge constructions.
		In an early paper he wrote regarding cubic equations, he discovered that a cubic equation can have more than one solution, that it cannot be solved using earlier compass and straightedge constructions, and found a geometric solution which could be used to get a numerical answer by consulting trigonometric tables.
		In fact, all cubic equations can be reduced to this form if we allow m and n to be negative, but negative numbers were not known at that time.
	www.indias.com /wiki-Cubic_equation (2645 words)

	A Catalog of Cubic Plane Curves
		This cubic plane curve is asymptotic to the semicubical parabola.
		This cubic curve is asymptotic to a line, and crosses itself at a node located at the origin.
		This cubic curve is asymptotic to a line, and has a cusp at the origin.
	staff.jccc.edu /swilson/planecurves/cubics.htm (905 words)

	BIC < Main < TWiki
		So the growing function after a window reduction will be most likely to be a linear one followed by a logarithmic one (marked as "additive increase" and "binary search" in the figure).
		Figure 2 shows a cubic function whose shape is similar to the BIC window curve [See Figure 1 in BIC overview page].
		CUBIC borrows this idea; low utilization triggers CUBIC to increase its window growth rate by disabling the window clamping, and when there are competing traffic, it simply reverts to the regular CUBIC operation (which ensures fairness).
	netsrv.csc.ncsu.edu /twiki/bin/view/Main/BIC (3011 words)

	Approximating Cubic Bezier Curves in Flash MX
		This technique doesn't really approximate a cubic bezier but it is a smart approach to draw a continuous curve with 4 control points (2 anchors and 2 handles), just like with a cubic bezier curve.
		Indeed we don't calculate any point on the cubic curve through a polynomial equation, we don't have to derive any new control points as they are already available to us, the only thing we need to do is to calculate the middle of a segment, which is straightforward.
		Since that point is on the cubic curve and since we know the formula for the cubic bezier, we can calculate the exact tangent to the bezier curve.
	www.timotheegroleau.com /Flash/articles/cubic_bezier_in_flash.htm (4207 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In mathematics, a cubic function is a function of the form
		The derivative of a cubic function is a quadratic function.
		The integral of a cubic function is a quartic function.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=cubic_function (192 words)

	LAB #8: Piecewise Polynomial Interpolation (Site not responding. Last check: )
		The comb function is 0 and 1 and 0 and 1 and...
		Second, although the function is nice and smooth within each pair of intervals, there's an obvious "kink" in the derivative at the odd numbered data points, where the form of the parabola changes.
		There is just one cubic function that can be defined on this interval, and which has the appropriate function and derivative values at the two endpoints.
	www.math.pitt.edu /~troy/math2070/lab_08.html (2223 words)

	Design Documents for Explore Math
		Cubic functions are a component of the class curriculum.
		This example models a cubic function because solids are three-dimensional objects, and cubic functions have a degree equal to three.
		Drag another coefficient of the cubic function and predict the functions or relations that are modeled by the locus.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/Glazer/designdoc.html (6141 words)

	Cubic function (Site not responding. Last check: )
		A cubic function is very similar to a quadratic function, except the general formula is to an odd power, rather than an even power.
		The shape of a cubic function is in the shape of an S. The general formula of the cubic function is y=ax
		The parent function of a cubic function is y=x
	www.wisheights.k12.wi.us /math/Precalc/students/bachshane/Cubic.htm (194 words)

	A Catalog of Cubic Plane Curves
		This cubic plane curve is asymptotic to the semicubical parabola.
		This cubic curve is asymptotic to a line, and crosses itself at a node located at the origin.
		This cubic curve is asymptotic to a line, and has a cusp at the origin.
	staff.jccc.net /swilson/planecurves/cubics.htm (905 words)

	unit03-sect03-les03-lessond (Site not responding. Last check: )
		To write the equation or function notation for a particular cubic function using this method, we need its real zeros and some way of determining the value of a.
		The function notation for the graph is thus: f(x) = -
		We saw in the previous lessons that it is possible for a cubic to have two complex roots and hence its graph will not have three x-intercepts.
	www.cdli.ca /courses/math3103/unit03/section03/lesson03/3-lesson-d.htm (528 words)

	Enzyme function less conserved than anticipated (Site not responding. Last check: )
		Similarity of enzymatic function is measured by the identity of the first EC number (thick lines with circles), the first two EC numbers (thin lines with crosses and '+'), the first three (thin lines with triangles), and all four EC numbers (thick lines with diamonds).
		In fact, the theoretical transition function marking the line between signal and noise depends on the particular details of the alignment algorithm, in particular on the substitution matrix chosen [29].
		However, the surprising correlation between conservation of enzyme function and structure may indicate that conservation of structure drives function to a larger extend than we may have expected [19].
	cubic.bioc.columbia.edu /papers/2002_enzyme_cons/paper.html (8164 words)

	Parametric Cubic Curves
		In a slope-intercept form function, the slope of a curve is defined by the infamous three words: "rise over run." When the "run" is zero, a dimensional vortex opens and sucks you away to the outer limits.
		The simplest of the cubic curves, the Hermite form, is defined by two endpoints and the tangent vectors at these endpoints.
		Like the two cubic curves discussed in the previous sections, segments of the nonrational uniform B-spline are defined by four control points.
	spec.winprog.org /curves (2373 words)

	Assignment7
		Thus, whether a cubic function has one, two, or three zeros will have a huge impact on what its reciprocal looks like.
		Notice that the function f(x) is continuous for values of x less than pi/2.
		In all of the cases we have examined, a function being continuous of an interval does not imply that the reciprocal of that function is also continuous over that same interval.
	web.pdx.edu /~pconnor/Assignment7.html (976 words)

	Cubic Equation Solver
		Algebraic theory on polynomials says that there should be three roots for a cubic equation; complex roots, when exist, will appear in complex conjugate pairs.
		There is no "cubic_root" function in FORTRAN; you do it by raising a number to a factional power, e.g., 0.333...
		Problem Statement: Re-do the cubic equation solver with MATLAB by following the same approach as in FORTRAN, including the use of the function structure.
	www.glue.umd.edu /~nsw/ench250/cubiceq.htm (389 words)

	Cubic Equations
		This WorkBook is a gentle introduction to abstract algebra, and theory of equations, written in homage to Gerolimo Cardano, who, with Tartaglia, established procedures for solving cubic equations.
		The aim is to give a self-contained exposition of the basic facts about cubic equations within the context of abstract algebra, and at the same time to provide many opportunities to explore.
		For those of you familiar with matrix representations, the symbolic cubic numbers that we introduce are simply the elements of the algebra of 3x3 circulant matrices.
	www.mathwright.com /library/oldcardanox3.html (838 words)

	1.5 - Shifting, Reflecting, and Stretching Graphs (Site not responding. Last check: )
		A translation in which the size and shape of the graph of a function is changed.
		You know the basic function is the sqrt(x) and you know the domain and range of the sqrt(x) are both [0,+infinity).
		You know this because you know those six common functions on the front cover of your text which are going to be used as building blocks for other functions.
	www.richland.edu /james/lecture/m116/functions/translations.html (2142 words)

	unit03-sect03-les02-lessonb (Site not responding. Last check: )
		Recall: A local maximum is the largest value of the function in a particular region and a local minimum is the smallest value of the function in a particular region.
		Also note that unlike the quadratic function, the local maxima and minima of a cubic does not occur exactly halfway between the zeros.
		All cubic functions with three distinct real zeros have that same "basic shape".
	www.cdli.ca /courses/math3103/unit03/section03/lesson02/3-lesson-b.htm (448 words)

	EDN Access -- 02.16.95 cubic interpolation hikes table's accuracy
		You can obtain very accurate approximations of a function from only a few data points contained in a look-up table, trading storage space for calculation time.
		Cubic interpolation takes into account the curvature of a function by using the beginning and ending slopes of a curve segment to approximate the missing curve with a cubic polynomial.
		Be sure to wait until you have completed a computation before throwing away the lower half of a double-precision integer calculation because the fractions could easily sum to more than 1 LSB.
	www.edn.com /archives/1995/021695/04di2.htm (268 words)

	cubic function factored with zeroes
		if you have any polynomial function with any x intercepts then each intercept is a solution to the equation when y=0.
		No, the fact that f is cubic means that there are no more that 3 intercepts- which is what is needed here.
		This is directly related to (or can be shown by, depending on how you want to look at it) the fact that if you divide your polynomial by x - x1 you MUST get a zero remainder if x1 is a zero of the polynomial.
	www.physicsforums.com /showthread.php?t=116627 (749 words)

	B-Splines
		These end conditions are specially crafted to form either a natural cubic spline or a clamped cubic spline.
		They are often times referred to as the knots because this is where we join the piecewise cubics, like pieces of string "knotted" together to form a larger piece of string.
		If you have unequally spaced points, then this is construction does not apply and construction of the cubic spline require a more cumbersome algorithm because each piecewise cubic will need to be individually crafted in order to meet all the conditions for a cubic spline.
	math.fullerton.edu /mathews/n2003/B-SplinesMod.html (512 words)

	SLATEC4 (DSBMV through RD) UCID-19631,19632,19633
		Evaluates a single cubic Hermite function and its first derivative at an array of points.
		Computes the definite integral of a piecewise cubic Hermite function when the integration limits are data points.
		Converts a PCH function to B-representation, so that it can be used with other elements of the B-spline package (see BSPDOC).
	www.llnl.gov /LCdocs/slatec4/index.jsp?show=s2.159 (852 words)

	Lab for Hermite Polynomial Interpolation
		The Hermite polynomial is referred to as a "clamped cubic," where "clamped" refers to the slope at the endpoints being fixed.
		A clamped cubic spline is obtained by forming a piecewise cubic function which passes through the given set of knots
		The clamped cubic spline forces the slope at the endpoints to be prescribed values.
	mathews.ecs.fullerton.edu /numerical/hp.htm (381 words)

	Cubic curve and graph display - Math Open Reference
		Equations of this form and are in the cubic "s" shape, and since a is positive, it goes up and to the right.
		Changing b alters the curvature of the parabolic element, and changing a changes the steepness of the cubic "s" curve.
		While it is running, move the sliders for b, c and d and observe the effects.
	www.mathopenref.com /cubicexplorer.html (568 words)

	flash menus - dreamweaver menu extensions, free
		The free version is a fully functional web menu with the first button label "f-source.com".
		Your website can be listed in the "Cubic Menu users".
		the function will get in a pressed button link, so it can be used to identify which button is pressed.
	f-source.com /buy/cubicMenu (1013 words)

	[No title]
		C C The interpolation scheme is a modified Cubic Shepard C method: C C C = [W(1)C(1)+W(2)C(2)+..+W(N)C(N)]/[W(1)+W(2)+..+W(N)] C C for bivariate functions* W(k) and C(k).
		C C Thus, C(k) is a cubic function which interpolates the data C value at node k.
		The transpose of the augmented regression C matrix is stored in B with columns (rows of B) defined C as follows: 1-4 are the cubic terms, 5-7 are the quad- C ratic terms, 8 and 9 are the linear terms, and the last C column is the right hand side.
	scicomp.ewha.ac.kr /netlib/toms/792 (3825 words)

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