
	Where results make sense

Topic: Monotonically increasing

Related Topics

Fatima Meer

Headlands and bays

13 Colonies

In the News (Wed 23 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	PlanetMath: monotonic
		Intuitively, this means that a monotone sequence can be thought of a “staircase” going either only up, or only down, with the stairs any height and any depth.
		Smooth (analytic) monotone functions are like “slopes,” either up or down at potentially varying steepnesess.
		This is version 2 of monotonic, born on 2002-02-18, modified 2005-08-16.
	planetmath.org /encyclopedia/Monotonically.html (93 words)

	PlanetMath: monotonically increasing
		``strictly increasing,'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
		This is version 7 of monotonically increasing, born on 2002-02-18, modified 2005-08-16.
		The definition in PlanetMath for 'monotonically nondecreasing' is NIST's definition for 'monotonically increasing' (http://www.nist.gov/dads/HTML/monotoncincr.html).
	planetmath.org /encyclopedia/MonotonicallyIncreasing.html (106 words)

	MonotonicExample.nb
		We say f is monotonically increasing (monotonically decreasing) on (a,b) if whenever a= f(y)).
		Given any countable subset E of (a,b), we can construct a function f that is monotonic on (a,b), discontinuous at every point of E, and continuous at every other point of (a,b) that is not in E.
		Both a monotonically increasing and monotonically decreasing function are constructed.
	www.bsu.edu /web/mkarls/MonotonicExample (279 words)

	Monotonic function - Wikipedia, the free encyclopedia
		However, the terms "increasing" and "decreasing" are avoided, since they lose their appealing pictorial motivation as soon as one deals with orders that are not total.
		A constant function is both monotone and antitone; conversely, if f is both monotone and antitone, and if the domain of f is a lattice, then f must be constant.
		Monotonicity of entailment is a property of many logic systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions.
	en.wikipedia.org /wiki/Monotonic_function (974 words)

	MATH debate: does X^3 increase? - SPSW
		I'd say it's constantly increasing because if you go a tiny bit to the right of zero it goes up, and if you go a tiny bit to the left it goes down (in other words, the secant lines always have positive slope).
		I'm sure we all agree as to an idea of increase, and the issue is to have we should define it in math.
		In my math classes, a prof has outlined what he will mean when he says 'increasing', and he only uses the word 'increasing' because it is a pain to say montonically increasing or strictly increasing every time.
	www.someplacesomewhere.com /index.php?showtopic=4231 (2081 words)

	Calculus/Sequences - Wikibooks, collection of open-content textbooks
		This sequence is neither increasing, nor decreasing, nor convergent.
		A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.
		If the terms of the sequence are a subset of an ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing.
	en.wikibooks.org /wiki/Calculus/Sequences (594 words)

	Re: 'monotonic increasing'
		In all cases monotonically is used to express that the sequence is non-decreasing which is in line both with the mathematical definition and the Merriam-Webster online dictionary #2 sense.
		In some of the cases the sequence required is actually strictly monotonically increasing but the other words make this clear, and since strictly monotonic sequences are also monotonic, it is not wrong.
		All these cases (either about timestamps or TCP sequence numbers) appear to use monotonically increasing in line with the mathematical definition although it is possible that a couple of them (e.g., RFC3571, s4) ought to use strictly monotonic, although the usage is clear from the additional words.
	www.mail-archive.com /ietf@ietf.org/msg25950.html (614 words)

	RFC 2747 - RSVP Cryptographic Authentication
		This memo discusses ways to relax the strictness of the in-order delivery of messages as well as techniques to generate monotonically increasing sequence numbers that are robust across sender failures and restarts.
		Sequence Number values may be any monotonically increasing sequence that provides the INTEGRITY object [of each RSVP message] with a tag that is unique for the associated key's lifetime.
		The ability to generate unique monotonically increasing sequence numbers across a failure and restart implies some form of stable storage, either local to the device or remotely over the network.
	members.tripod.com /rfc_archive/rfc_2747.html (6207 words)

	Riskiness
		In short, increasing risk is what risk-averters dislike (R.1), the movement of probability mass from center of a distribution to its tails (definition R.2) and the adding of noise to a random variable (definition R.3).
		However, instead of doing this, let us instead move to a point such as A. The movement from W to A is an increase in risk as we are moving away from the certainty line, but it is not a "mean-preserving" increase because the movement from W to A is not at angle -p/(1-p).
		Of course, from the perspective of agent v, the movement from W to A is a mean-utility decreasing increase in spread.
	cepa.newschool.edu /het/essays/uncert/increase.htm (3657 words)

	Methodology - Crime in Vancouver
		A monotonically increasing linear function was chosen because areas further away from landuse are the most suitable and suitability increases with distance, which is also applied to distance from boundaries, as suitability also increases further away from boundaries.
		A monotonically decreasing linear function was chosen, implying that the further away from road networks, accessibility decreases.
		The monotonically increasing J-shaped curve implies that neighbourhoods with a higher crime rate are more likely in need of a new police station.
	www.sfu.ca /geog/geog355fall04/ajlau/methodology.html (1109 words)

	[No title]
		This memo discusses ways to relax the strictness of the in-order delivery of messages as well as techniques to generate monotonically increasing sequence numbers that are robust across sender failures and restarts.
		Sequence Number values may be any monotonically increasing sequence that provides the INTEGRITY object [of each RSVP message] with a tag that is unique for the associated key's lifetime.
		The ability to generate unique monotonically increasing sequence numbers across a failure and restart implies some form of stable storage, either local to the device or remotely over the network.
	www.rfc-editor.org /rfc/rfc2747.txt (6207 words)

	[No title]
		The order of the values of x must be monotonically increasing.
		A third vector is needed to indicate the abscissas (x- coordinates) of the new points to be interpolated by the spline.
		Like the x vector, the vector of abscissas must be monotonically increasing.
	www.ibiblio.org /gferg/ldp/man/mann/spline.n.html (990 words)

	[No title]
		Monotonicity One way of classifying function is based on whether, and where, they go up and down.
		Here are some examples: (draw on the board a function that is monotonically increasing, monotonically decreasing, and constant) One obvious way these functions are different is that the first one always goes up as you go to the right, the second goes down, and the third is constant.
		We call functions of the first type increasing functions, those of the seconde type decreasing functions, and functions of the third type constant functions.
	www.astro.princeton.edu /~jgreene/gs_fall07/class5.txt (1483 words)

	Method for measuring selected frequencies of a coupled-dual resonator crystal - Patent 5594354
		determining the inflection points where the change in phase goes from monotonically decreasing to monotonically increasing and also where the change in phase goes from monotonically increasing to monotonically decreasing, wherein the critical frequencies correspond to the inflection points.
		In each of the three cases, each of the four critical frequencies corresponds to the zero phase crossing of the voltage phase response at or near the particular voltage amplitude maximum or minimum for the particular case in question.
		In addition, [d.O slashed./dω] goes from decreasing to increasing, therefore, time delay becomes T=-[d.O slashed./dω]=-[1/(2π)][d.O slashed./df] which shows that time delay T goes from increasing to decreasing which is a relative maxima at those points.
	www.freepatentsonline.com /5594354.html (5358 words)

	Tips on Performance Tuning SQL Server Database Clustered Indexes
		Generally, but not always, the clustered index should be on a column that monotonically increases--such as an identity column, or some other column where the value is increasing--and is unique.
		If you are inserting new rows into a table that has a clustered index as its primary key, and the key monotonically increases, this means that each INSERT will physically occur one after another on the disk.
		This is because SQL Server has the ability to determine if data being inserted into a table has a monotonically increasing sequence, and won't perform page splits when this happens.
	www.sql-server-performance.com /clustered_indexes.asp (1758 words)

	linint2_points
		A strictly monotonically increasing array that specifies the X [longitude] coordinates of the fi array.
		A strictly monotonically increasing array that specifies the Y [latitude] coordinates of the fi array.
		Assume fi is dimensioned time x lev x lat x lon as in example 2, where lat and lon are 1D strictly monotonically increasing coordinate variables.
	www.ncl.ucar.edu /Document/Functions/Built-in/linint2_points.shtml (1053 words)

	Methodology - West Nile Virus Risk Analysis for the City of Burnaby
		Wetland Factor: The control points were 600 meters and 2500 meters; monotonically increasing, sigmoidal curve was used to rescale the values of the image wetlanddist so that people living within 600 meters of wetland are in risk and suitability increases until it reaches 2500 meters.
		Water body Factor: The control points were 250 meters and 1500 meteres; monotonically increasing, sigmoidal curve was used to rescale the values of the image waterbodydist so that people living within 250 meters of lakes and so on are considered to be in risk.
		Wood Area Factor: The control points were 500 meters and 2000 meters; monotonically increasing, sigmoidal curve was used to rescale the values of the image woodareadist so that people living within 500 meters of woodland are considered to be in risk.
	www.sfu.ca /geog/geog355fall03/jimmyy/methodology.html (503 words)

	Polynomials with Distinct
		He went on to show that this property is not true in general for polynomials of degree 5 and higher, but that polynomials with equally spaced zeros always have monotonically increasing ratio vectors.
		In 2001, GVSU student Matthew Wells and I proved that for the famous class of orthogonal Chebyshev polynomials, they, too, have a monotonically increasing ratio vector.
		Indeed, families of orthogonal polynomials are natural to study in this setting, as one famous result on such functions is that they will always have real, distinct zeros.
	faculty.gvsu.edu /boelkinm/reu2003.htm (662 words)

	spline(n) manual page
		A third vector is needed to indicate the abscissas (x-coordinates) of the new points to be interpolated by the spline.
		Like the x vector, the vector of abscissas must be monotonically increasing.
		The order of the components of sx must be monotonically increasing.
	www-bio3d-igbmc.u-strasbg.fr /doclib/blt/spline.html (932 words)

	Sequence - Wikipedia, the free encyclopedia
		A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.
		If the terms of the sequence are a subset of an ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing.
		Any sequence fulfilling the monotonicity property is called monotonic or monotone.
	en.wikipedia.org /wiki/Sequential (898 words)

	Look-Up Table (Fixed-Point Blockset)
		data vector must be strictly monotonically increasing after conversion to the input's fixed-point data type, except in the following case.
		Also, the input values vector must be strictly monotonically increasing after conversion to the input's fixed-point data type, except in the following case.
		Note that due to quantization, the input values vector may be strictly monotonic in doubles format, but not so after conversion to a fixed-point data type.
	www.eecs.umich.edu /dco/faq/matlab-6.5/help/toolbox/fixpoint/lookuptable.html (1004 words)

	( ESNUG 366 Item 6 ) --------------------------------------------- [02/23/01]
		Developers and users must: * increase simulator accuracy * reduce the range of load and slew sweeps * pay close attention to how cells are designed and extracted * and know which cells will exhibit non-monotonic behavior anyway.
		If this output capacitance is increased, > then it will take more time to charge up, and the delay and slew times > will both increase as well.
		Just call me "The Librarian." Delay and slew times will not always increase with capacitance; if the capacitance is low enough and the input ramp large enough, you get the DC transfer curve you remember from your undergrad days.
	www.deepchip.com /items/0366-06.html (1045 words)

	Longest Increasing Sequence
		Finding the longest increasing run in a numerical sequence is straightforward, indeed you should be able to devise a linear-time algorithm fairly easily.
		The length of the longest increasing sequence in
		The length of the longest increasing subsequence of the entire permutation is given by
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK2/NODE47.HTM (562 words)

	CS4112 Tutorial Exercises 5 Week 8
		The function f is strictly monotonically increasing if whenever a>b then f(a)>f(b).
		Define a function is-ascending which returns T for all values that for values of k between 1 and (N-1) (inclusive), the value of f(k+1)>f(k), otherwise it returns F. That is it establishes whether f is a strictly monotonically increasing function.
		Define a similar function is-descending that establishes if f is a strictly monotonically decreasing function.
	www.csis.ul.ie /Modules/CS4112/exercises5.htm (195 words)

	Instructors' Notes -- Building Your Own Models
		Some students might suggest supply functions that are not monotonically increasing and some might suggest demand functions that are not monotonically decreasing.
		If so, be sure that they give supporting arguments -- for example, a supply function might not be monotonically increasing because with increasing profits per unit suppliers might no longer find it necessary to work long hours to make enough money.
		If the demand function is strictly monotonically decreasing and the supply function is strictly monotonically increasing then there is at most one equilibrium point.
	www.dean.usma.edu /math/MRCW/modeling/discreteModels/building/instructor.html (1025 words)

	Part 1
		The qualification of it being an isolated system is needed because increases in the entropy of a system can easily occur by the transfer of heat to-from something outside the system (this is how heat engines work, although it depends on where you draw your system boundaries), unless it is isolated.
		An ergodic process or system is inherently incapable of having a monotonically increasing (or decreasing) state function, such as entropy.
		) was a strictly monotonically increasing function, we would question his sanity, or at least the quality of his education.
	paias.org /Science/Entropy/entropy1.htm (4990 words)

Try your search on: Qwika (all wikis)