From these data, the starting material or product concentration over time may be obtained by simply taking the integral of a polynomial fit to the experimental curve.
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From the concentration data, the rate of reaction over time may be obtained by taking the derivative of a polynomial fit to the experimental curve.
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An earlier scrambler used in Packet over SONET/SDH (RFC 1619, 1994) had a short polynomial with only 7 bits of internal state which allowed a malicious attacker to create a Denial-of-service attack by transmitting patterns in all 27-1 states, one of which was guaranteed to desynchronize the clock recovery circuits.
Using the LLL-algorithm, Frank, and his student, Éva Tardos developed a general method, which could transform some polynomial time algorithms into strongly polynomial.
, the polynomial x1d +...+ xnd given by Strassen and by Baur and Strassen.
In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A Horn, of The University of Utah, who proposed it in 1962.
In mathematics, in particular in computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus.
Brahmagupata's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta (598–668 CE) in the early 7th century CE.
However, one can combine these remainders recursively to reduce the cost, using the following trick: if we want to evaluate modulo two polynomials and , we can first take the remainder modulo their product , which reduces the degree of the polynomial and makes subsequent modulo operations less computationally expensive.
The AKS primality test, published in 2002, proves that primality testing also lies in P, while factorization may or may not have a polynomial-time algorithm.
More precisely, the problem is polynomial-time if the graph is 2-colorable, that is, it is bipartite, and is NP-complete otherwise.
D.Haussler, M.Kearns, N.Littlestone and M. Warmuth, Equivalence of models for polynomial learnability, Proc.
In cryptography, concrete security or exact security is a practice-oriented approach that aims to give more precise estimates of the computational complexities of adversarial tasks than polynomial equivalence would allow.
Variable elimination and the simplex algorithm are used for solving linear and polynomial equations and inequalities, and problems containing variables with infinite domain.
Efficient polynomial-time algorithms for the membership problem are the CYK algorithm and Earley's Algorithm.
However, this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for example, the complexity of the characteristic functions of an NP-complete problem and its co-NP-complete complement is exactly the same even though the underlying decision problems may not be considered equivalent in some typical models of computation.
The history of polynomial factorization starts with Hermann Schubert who in 1793 described the first polynomial factorization algorithm, and Leopold Kronecker, who rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.
The FKT algorithm, named after Fisher, Kasteleyn, and Temperley, counts the number of perfect matchings in a planar graph in polynomial time.
H. W. Lenstra, Jr. for using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.
This is because exact solution of the full CI determinant is NP-complete, so the existence of a polynomial time algorithm is unlikely.
Lenstra showed that a cyclic group does not have a generic polynomial if n is divisible by eight, and Smith explicitly constructs such a polynomial in case n is not divisible by eight.
In contrast, Shamir's secret sharing scheme represents the secret as the y-intercept of an n-degree polynomial, and shares correspond to points on the polynomial.
Lie Group Representations of Polynomial Rings by Bertram Kostant published in the American Journal of Mathematics Vol 85 No 3 (July 1963)
for some polynomial V(z) of degree at most N − 2, and if this has a polynomial solution S then V is called a Van Vleck polynomial (after Edward Burr Van Vleck) and S is called a Heine–Stieltjes polynomial.
in Invariant theory a finite set of invariant polynomials, such that every invariant polynomial may be written as a polynomial function of these basis elements
Hochbaum and Shmoys presented a polynomial-time approximation scheme in 1987 that finds an approximate solution to the offline makespan minimisation problem with atomic jobs to any desired degree of accuracy.
His interest in polynomial algebra was influenced by his belonging to the German combinatorial school of Carl Friederich Hindenburg, Christian Kramp and others.
In mathematics, a Lidstone series, named after George James Lidstone, is a kind of polynomial expansion that can expressed certain types of entire functions.
The Lindsey–Fox algorithm uses the FFT (fast Fourier transform) to very efficiently conduct a grid search in the complex plane to find accurate approximations to the N roots (zeros) of an Nth-degree polynomial.
In mathematics, an LLT polynomial is one of a family of symmetric functions introduced by Alain Lascoux, Bernard Leclerc, and Jean-Yves Thibon (1997) as q-analogues of products of Schur functions.
MPSolve (Multiprecision Polynomial Solver) is a package for the approximation of the roots of a univariate polynomial.
NC Graphics focused on developing a surface modelling software product that used polynomial mathematics and was driven by human-readable input commands based on the APT language.
The reciprocal-of-polynomial formulation is used for the same reason that computational boundedness is defined as polynomial running time: it has mathematical closure properties that make it tractable in the asymptotic setting.
When a language L is complete for some class B, then AL=AB provided that machines in A can execute reductions used in the completeness definition of class B. In particular, since SAT is NP-complete with respect to polynomial time reductions, PSAT=PNP.
According to the Oxford English Dictionary, polynomial succeeded the term binomial, and was made simply by replacing the Latin root bi- with the Greek poly-, which comes from the Greek word for many.
Polynomial systems maybe interpreted as conceptually straight forward extensions of linear systems to the non-linear case.
The paper is a joint work by Martin Dyer, Alan M. Frieze and Ravindran Kannan.
It is possible to determine the bounds of the roots of a polynomial using Samuelson's inequality.
The solutions to this equation are called the roots of the quadratic polynomial, and may be found through factorization, completing the square, graphing, Newton's method, or through the use of the quadratic formula.
German mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed that the polynomial is stable if and only if the sequence of determinants of its principal submatrices are all positive.
The first Jacobi-Trudi formula expresses the Schur polynomial as a determinant
Jerrum, Valiant, and Vazirani showed that every #P-complete problem either has an FPRAS, or is essentially impossible to approximate; if there is any polynomial-time algorithm which consistently produces an approximation of a #P-complete problem which is within a polynomial ratio in the size of the input of the exact answer, then that algorithm can be used to construct an FPRAS.
Sparse binary polynomial hashing (SBPH) is a generalization of Bayesian filtering that can match mutating phrases as well as single words.
Faulhaber's formula expresses as a polynomial in n.