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Topic: Polynomial sequence

Related Topics

Fibonacci polynomials

Polynomial

Monic polynomial

Chebyshev polynomials

Bernoulli polynomials

Newtons difference method

Laguerre polynomials

Polynomial interpolation

Legendre polynomials

Bell polynomials

Monomial

Fibonacci number

Field (mathematics)

Real number

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	Binomial type - Wikipedia, the free encyclopedia
		In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by { 0, 1, 2, 3,...
		The set of all polynomial sequences of binomial type is a group in which the group operation is "umbral composition" of polynomial sequences.
		of coefficients of the first-degree terms in a polynomial sequence of binomial type may be termed the cumulants of the polynomial sequence.
	en.wikipedia.org /wiki/Binomial_type (1073 words)

	Sequence - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		In mathematics, a sequence is a list of objects (or events) arranged in a "linear" fashion, such that the order of the members is well defined and significant.
		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 a 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.
	www.peekskill.us /project/wikipedia/index.php/Sequence (676 words)

	Kids.net.au - Encyclopedia Polynomial - (Site not responding. Last check: 2007-10-21)
		Polynomials are important because they are the simplest functions: their definition involves only addition and multiplication (since the powers are just shorthands for repeated multiplications).
		The culmination of these efforts is Taylor's theorem, which roughly states that every differentiable function locally looks like a polynomial, and the Weierstrass approximation theorem, which states that every continuous function defined on a compact interval of the real axis can be approximated on the whole interval as closely as desired by a polynomial.
		Polynomials with coefficients in R can be added by simply adding corresponding coefficients and multiplied using the distributive law and the rules
	www.kids.net.au /encyclopedia-wiki/po/Polynomial (1464 words)

	Polynomial
		Note that the polynomials of degree ≤ n are precisely those functions whose (n''+1)st derivative is identically zero.
		Other related objects studied in abstract algebra are formal power series, which are like polynomials but may have infinite degree, and the rational function s, which are ratios of polynomials.
		Polynomial regression analysis applet - It calculate a calibration for a MALDI TOF (and possibly other) mass spectrometers using any kind of (semi-)repetitive peptide as the calibrant.
	www.nebulasearch.com /encyclopedia/article/Polynomial.html (1987 words)

	Sequence - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		In mathematics, a sequence is a list of objects (or events) which have been arranged in a linear fashion; such that each member comes either before, or after, every other member, and the order of members is important.
		Sequences can be finite, as in the example just given, or infinite, such as the sequence of all even positive integers (2,4,6,...).
		The elements in a sequence are also called terms, and the number of terms (possibly infinite) is called the length of the sequence.
	encyclopedia.worldsearch.com /sequence.htm (514 words)

	Spreading Codes for Direct Sequence CDMA and Wideband CDMA Cellular Networks
		A block diagram of the baseband model of a direct sequence (DS) CDMA modulator and demodulator is shown in Fig.
		The second sequence is said to be a decimation of the first, and the notation a´= a[q] is used to indicate that a´ is obtained by sampling every qth symbol of a.
		Kasami sequence sets are one of the important types of binary sequence sets because of their very low cross-correlation [4, 13].
	www.comsoc.org /~ci/private/1998/sep/Jabbari.html (4747 words)

	Robinson Polynomial Sequence (Site not responding. Last check: 2007-10-21)
		It first fails to be a polynomial at a(n) when the denominator a(n-k) = x+y+z or x(x+y+z)+y+z, and when k+1 <= n-k <= k+1+p.
		Comment: The Somos-4, Somos-5, Somos-6, Somos-7 sequences are all special cases of the Robinson sequence conjecture.
		After that, his sequences produce integers and mine don't.
	grail.cba.csuohio.edu /~somos/robinson.html (321 words)

	Polynomial (Site not responding. Last check: 2007-10-21)
		Splines are piecewise defined polynomials and provide more flexibility than ordinary polynomials when defining simple and smooth functions.
		In this article polynomials are written using the (canonical) monomial basis (i.e.
		As there is no general closed formula to calculate the roots of a polynomial of degree 5 and higher, root-finding algorithms are used in numerical analysis to approximate the roots.
	www.worldhistory.com /wiki/P/Polynomial.htm (1801 words)

	WebReports - Guess my Robot teacher guide
		It is a foundation activity, in the sense that it establishes tools, practices and base knowledge useful for a wide range of activities such as Convergence and Divergence, Coding and Fibonacci.
		The advantage of ToonTalk is that the sequences can be viewed not only as a product (a series of terms), but also as a process that can be observed and altered.
		By altering the parameters and number of chained robots, any polynomial sequence can in theory be generated.
	www.weblabs.org.uk /wlplone/Members/yish/my_reports/Report.2004-06-25.4000 (740 words)

	Noncommutative Case: Gelfand-Kirillov dimension
		consisting of polynomials that are homogeneous of degree
		After staring at this sequence for a while, one sees that every other term is a square and the intermediate terms are products of sucessive integers after the 6th term.
		This sequence came from a gradation, so to get the sequence coming from the filtration we simply take the partial sums.
	math.ucsd.edu /~ncalg/NCBIGDOC02/node355.html (522 words)

	Interleaving Fibonacci Numbers
		For example, given the even-ordered sequence 0, 1, 3, 8, 21, 55, 144, … we could simply apply the “greedy algorithm” by expressing each term as the sum of the maximum number of the immediately preceding terms.
		This shows that another way of arriving at the recurrence for the kth Fibonacci numbers is to solve for the (k-2)th degree polynomial that gives, when multiplied by the characteristic polynomial of the Fibonacci sequence, a polynomial whose only non-zero coefficients are for powers that are multiples of k.
		This implies that f is a root of the characteristic polynomial, as expected.
	www.mathpages.com /home/kmath285/kmath285.htm (514 words)

	Aitken's and Neville's Methods
		are examples of how iteration is used to construct a sequence of polynomial approximating of increasing order.
		Since the polynomial constructions are unique the following theorem applies for the Lagrange Polynomial, Newton polynomial and the polynomials constructed with both Aitken's method and Neville's method too.
		It is also useful to use a sequence of polynomial approximations with increasing degree.
	math.fullerton.edu /mathews/n2003/NevilleAlgorithmMod.html (600 words)

	Using Local Optimality Criteria for Efficient Information Retrieval (Site not responding. Last check: 2007-10-21)
		Hence sequence 1-2-3 is preferable to sequence 2-3; that is, redundant filter 1 should not be deleted from the sequence 1-2-3.
		And with a sequence of filters, the setup cost need only be incurred for the sequence once because each processor applies the data to each filter in turn, so its cost can be amortized; and the final union of results is just a disjoint union, easy to accomplish.
		If both sequences had the same filters just after the entailed filters, then all the other filters would have to precede those entailed filters in interchange-sorted order, and the two sequences would have to be identical.
	www.nps.navy.mil /Content/CS/ncrowe/marie/discap.html (13700 words)

	Functions for Scientific WorkPlace
		The extent to which the expressions in the return are computed is commensurate with the specificity of the parameters that are passed to fourier_series.
		Then B(g,10,2..8,x) is the degree 10 polynomial in x that approximates g(x) over the interval [2,8] as constructed in S. Bernstein's constructive proof of the Uniform Approximation by Polynomials Theorem.
		The return is a sequence of twentyone points on the graph of f.
	artsci.wustl.edu /~bblank/swp (2625 words)

	Next Number in a Sequence Lesson - III
		This sequence is actually related to the previous one.
		If you try common differences on this sequence, you'll see that it doesn't work, so this does not appear to be a polynomial sequence.
		Whenever a sequence is not obviously generated by a polynomial, it is generally (though not always) generated by a recursion.
	www.purplemath.com /modules/nextnumb3.htm (613 words)

	Polynomial sequence - Encyclopedia, History, Geography and Biography
		Polynomial sequence - Encyclopedia, History, Geography and Biography
		In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3,..., in which each index is equal to the degree of the corresponding polynomial.
		The article about Polynomial sequence contains information related to Polynomial sequence and See also.
	www.arikah.net /encyclopedia/Polynomial_sequence (90 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-21)
		You can find the degree of this polynomial sequence by making so-called "sequences of differences." You make a sequence of differences by subtracting the consecutive numbers of the original sequence.
		To see that this holds for the general case, suppose we have a sequence defined by P(n) = a*n^t + Q(n), where Q(n) is of lower degree than P(n).
		But for the sequence of differences (SoD(n)) of P(n) this means: SoD(n) = P(n+1) - P(n) = = an^t + R(n) + Q(n+1) - (an^t + Q(n)) = R(n) + Q(n+1) - Q(n).
	mathforum.org /library/drmath/view/56383.html (914 words)

	Remote operating system having secure communication of encoded messages and automatic re-synchronization (US5191610)
		A PRBN generator (170) in the receiver (150) produces a sequence of reference numbers that is identical to the sequence of identification numbers.
		The receiver (150) responds to the transmitted message when there is not identity between the reference number and the identification number provided that a reference number identical to the identification number is generated within a search length in the sequence of reference numbers, thereby providing automatic re-synchronization of the transmitter and receiver.
		PRBN generating means comprising a generator polynomial derived from a prime polynomial for generating a sequence of reference numbers, said receiving means PRBN generating means generator polynomial being identical to said transmitting means PRBN generating means generator polynomial, said sequence of reference numbers being identical to said sequence of identification numbers,
	www.delphion.com /details?pn=US05191610__ (522 words)

	Cyclic Redundancy Check
		F(x) A degree k-1 polynomial that is used to represent the k bits of the packet covered by the CRC.
		L(x) A degree 31 polynomial with all of the coefficients equal to one, i.e.,
		A sending device applies a 16- or 32-bit polynomial to a block of data that is to be transmitted and appends the resulting cyclic redundancy code (CRC) to the block.
	www.geocities.com /hodmas/crc.htm (1335 words)

	Linear Complexity: A Literature Survey
		The linear complexity (LC) of a sequence is the size in bits of the shortest linear feedback shift register (LFSR) which can produce that sequence.
		Application: Rueppel and Staffelbach show how to compute the linear complexity of a resulting sequence when the LC of each constituent sequence is known.
		However, some applications may be imagined where prior knowledge of neither a sequence border nor the size of the sequence are available.
	www.ciphersbyritter.com /RES/LINCOMPL.HTM (2349 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		One way to define a polynomial is as an ordered sequence of Terms where the ordering is from high to low based on the value of the exponents of the Terms.
		An ordered sequence is a collection of Terms of a polynomial.
		An ADT Ordered Sequence is a Sequence whose elements occur in order from high to low based on the value of the exponent of its term.
	www.cbu.edu /~yanushka/j1/l.7 (466 words)

	Using a parity-sensitive sieve to count prime values of a polynomial -- Friedlander and Iwaniec 94 (4): 1054 -- ...
		Using a parity-sensitive sieve to count prime values of a polynomial
		and that are applicable to an infinite class of polynomials to
		sequence is close to positive density and has extremely good regularity
	www.pnas.org /cgi/content/full/94/4/1054 (2789 words)

	Calculating the Sturm sequence of a polynomial (Site not responding. Last check: 2007-10-21)
		Calculating the Sturm sequence of a squarefree polynomial
		The polynomial coefficients a[0],...,a[n] (n > 1) are entered, separated by spaces.
		The number of sign-changes in the evaluated sequence is also printed.
	www.numbertheory.org /php/sturm.html (50 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Only the generator polynomial // for the main m-sequence is specified through the arguments.
		// The sub-sequence polynomial is calculated internally based on the // main polynomial.
		The relative shift of the subsequence is controlled // by the subsequence 'seed' argument.
	www-mobile.ecs.soton.ac.uk /bjc97r/pnseq/kasami.c (184 words)

	A Polynomial-Order Algorithm For Optimal Phrase Sequence Selection From A Phrase Lattice And Its Parallel Layered ... (Site not responding. Last check: 2007-10-21)
		Abstract: This paper (leais with a problem of selecting an optimal phrase sequence from a phrase lattice, which is often encountered in language processing such as word processing and post-processing for speech recognition.
		The problem is formulated as one of combinatorial optimization, and a polynomial order algorithm is derived.
		This algorithm finds an optimal phrase sequence and its dependency structure simultaneously, and is therefore particularly suited for an interface between speech recognition...
	citeseer.ist.psu.edu /586490.html (365 words)

	Finding the polynomial formula for a sequence on a TI-86 (Site not responding. Last check: 2007-10-21)
		Given a sequence such as 10, -1, -6, -5, 2, 15; we can check to see if it is a polynomial sequence by finding the difference of successive terms.
		If there is a polynomial function that exactly fits the sequence, list arithmetic on the calculator will help us find the coefficients.
		Since the second differences are constant, we know that the sequence is quadratic.
	d.w.gillette.home.att.net /conf3/Seq86.htm (333 words)

	Learn more about Polynomial in the online encyclopedia. (Site not responding. Last check: 2007-10-21)
		Learn more about Polynomial in the online encyclopedia.
		Hint: Play with putting spaces before and after your words to see the different results you get.
		From the definition of O-notation above, the polynomial is in O(x
	www.onlineencyclopedia.org /p/po/polynomial.html (1534 words)

	Functions
		Integral polynomial greatest common divisor and cofactors.
		L <- MUPSFF(p,A) Modular univariate polynomial squarefree factorization.
		Given a primitive polynomial A, of positive degree in the main variable, computes the squarefree factorization of A.
	www.mcs.drexel.edu /~krandick/saclib/node51.html (681 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		If that is the case divide it by its GCD with its derivative to obtain a square-free polynomial having the same roots.
		Then work with the new polynomial (of lower degree) instead.
		The leading terms of the Sturm polynomial sequence for f(x) are (up to positive factors): x^3, x^2, -Hx, D The number of roots between -oo and +oo i.e., the number of real roots is C(-oo)-C(+oo) where C(t) counts the sign changes in the Sturm polynomial* sequence evaluated at t.
	www.math.niu.edu /~rusin/known-math/94/sturm.seq (306 words)

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