Examples of using Polynomials in English and their translations into Vietnamese
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All polynomials of order k are O(Nk).
Routh- Hurwitz criterion for second, third, and fourth-order polynomials.
Compute the polynomials and such that where y is a real number.
During the 1990s, Khavinson extended the FTA to polynomials of more than one variable.
One can ask for all polynomials in A, B, and C that are unchanged by the action of SL2;
This image shows sin( x){\displaystyle\sin(x)}and its Taylor approximations, polynomials of degree 1, 3, 5, 7, 9, 11 and 13.
Similarly, quadratic polynomials with three or more variables correspond to quadric surfaces and hypersurfaces.
The higher moments of the Poisson distribution are Touchard polynomials in λ, whose coefficients have a combinatorial meaning.
Next, we divide those polynomials to obtain the generalized Sturm chain: yields yields and the Euclidean division stops.
It was here that, for the first time,the fundamental theorem of algebra was stated for polynomials with complex coefficients, rather than just real coefficients.
What one sees is that among polynomials, repeated differentiation annihilates it, sends it to zero and then keeps it there.
The adjective real in this context was introduced in the 17th century by René Descartes,who distinguished between real and imaginary roots of polynomials.
A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm.
Where ζ{\displaystyle\zeta} denotes the Riemann zeta function; one approach to prove this inequality is to obtainthe Fourier series for the polynomials B k( x){\displaystyle B_{k}(x)}.
His book Fourier Series and Orthogonal Polynomials(dated 1941) was reprinted in 2004.
Subtraction(-), multiplication(×), and division(÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices,vectors, and polynomials.
With the advent of computer graphics, Bernstein polynomials, restricted to the interval[0, 1], became important in the form of Bézier curves.
An area of study in mathematics referred to broadly as Galois theory involves proving that no closed-form expression exists in certain contexts,based on the central example of closed-form solutions to polynomials.
Surprisingly, the classical Euclid's algorithm turned out to be inefficient for polynomials over infinite fields, and thus new algorithms needed to be developed.
Certain polynomials might have similar bending laminations, and that would tell us all these polynomials have something in common, even if on the surface they don't look like they have anything in common,” Lindsey said.
So if we viewed a squared as kind of the independent variable or the x term,so now this kind of has the shape of polynomials that hopefully you're used to factoring a little bit.
Several polynomial sequences like Lucas polynomials(Ln), Dickson polynomials(Dn), Fibonacci polynomials(Fn) are related to Chebyshev polynomials Tn and Un.
In 1986, geometer Sheldon Katz proved that the number of curves, such as circles,that are defined by polynomials of degree two and lie entirely in the quintic is 609,250.
Today algebra includes section 08-General algebraic systems,12-Field theory and polynomials, 13-Commutative algebra, 15-Linear and multilinear algebra; matrix theory, 16-Associative rings and algebras, 17-Nonassociative rings and algebras, 18-Category theory; homological algebra, 19-K-theory and 20-Group theory.
Noether's advisor, Paul Gordan, was known as the"king of invariant theory", and his chief contribution to mathematics was his 1870 solution of thefinite basis problem for invariants of homogeneous polynomials in two variables.
In mathematics, the Ax-Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck.[ 1][ 2][ 3][ 4].
DeMarco and Lindsey have found a systematic way to think about polynomials in 3-D terms, but whether that perspective will answer important questions about those polynomials is unclear.
There are many different kinds of products in mathematics:besides being able to multiply just numbers, polynomials or matrices, one can also define products on many different algebraic structures.
Imaginary number Isogonal Isogonal trajectory Orthogonal complementOrthogonal group Orthogonal matrix Orthogonal polynomials Orthogonalization Gram- Schmidt process Orthonormal basis Orthonormality Orthogonal transform Pan-orthogonality occurs in coquaternions Surface normal Orthogonal ligand-protein pair.
Note that this usage of the term linear is not the same as in the section above,because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity.