...that the converse is also true (Skolem's theorem): Let $f$ be a primitive polynomial with coefficients in $\widetilde{\bf Z}$. Then there exists an $x \in \wide
11 KB (1,771 words) - 16:57, 1 July 2020
...ory formulation of knot invariants [[#References|[a5]]], such as the Jones polynomial [[#References|[a6]]]. Flat connections also play a distinguished part in th
<TR><TD valign="top">[a6]</TD> <TD valign="top"> V.F.R. Jones, "A polynomial invariant for knots via von Neumann algebras" ''Bull. Amer. Math. Soc.'' ,
8 KB (1,229 words) - 08:30, 26 March 2023
...ant particular case where $K$ is a point, one can always choose the Taylor polynomial of order $k$ (centered at this point) as the representative in the equivale
3 KB (555 words) - 09:11, 12 December 2013
is the polynomial of best approximation. Analogues of this theorem exist for arbitrary Banach
4 KB (553 words) - 14:03, 17 March 2020
ii) for every [[additive polynomial]] (cf. [[#References|[a5]]]) $f$ with coefficients in $Kv$ and every $a\in
3 KB (523 words) - 19:54, 1 January 2015
is a polynomial of degree $ n $(
is a polynomial of odd degree $ d $,
12 KB (1,769 words) - 08:31, 26 March 2023
...s are defined correctly). As a consequence, the notions of logspace and/or polynomial time computability become mathematically well-defined machine-independent n
...exists an equivalence between polynomial time on the parallel machine and polynomial space in the sequential world. This equivalence does not hold for all paral
18 KB (2,656 words) - 04:11, 6 June 2020
where the denominator is an entire function that does not reduce to a polynomial.
4 KB (580 words) - 08:21, 6 January 2024
...igonometric polynomials (cf. also [[Trigonometric polynomial|Trigonometric polynomial]]), splines (see [[Spline approximation|Spline approximation]]), etc. An ap
9 KB (1,258 words) - 07:37, 4 November 2023
be a complex polynomial of non-zero degree having zero as an isolated singularity and let $ f ( 0
is the Alexander polynomial. In this case there thus arises a knot $ ( S ^ {2q+1} , k ) $.
13 KB (1,934 words) - 19:26, 17 January 2024
...ng $c[V_i]$, and from an algebraic point of view, one wants to know if the polynomial rings $c[V_1][x_1]$ and $c[V_2][x_2]$ being isomorphic forces the coordinat
3 KB (541 words) - 07:33, 13 November 2023
...the smallest strong witness for $n$, grows sufficiently slowly, there is a polynomial-time algorithm for primality. It is known that $W(n)$ is not bounded [[#Ref
3 KB (516 words) - 17:58, 8 November 2014
functions, $f:X \to {\bar k}$, for which there exists a polynomial $F\in k[T]$ such that $f(x)=F(x)$
4 KB (616 words) - 21:49, 30 March 2012
The first polynomial $ \Delta _ {1} ( t _ {1} \dots t _ \mu ) $
is called the Alexander polynomial. The Alexander module also defines the Steinitz–Fox–Smythe class of ide
37 KB (5,595 words) - 17:15, 18 May 2024
...ased, with it, e.g., the degrees of the polynomials increase. An algebraic polynomial of degrees $ n _ {1} \dots n _ {m} $
of the polynomial is fixed; then the summation in (1) is carried out over all indices satisfy
21 KB (3,060 words) - 20:29, 10 January 2021
is a polynomial, the corresponding dispersion relation is $ P ( - i \omega , ik _ {1} , i
4 KB (559 words) - 08:24, 16 March 2024
...of the dependence of the spectrum of the mass operator on the form of the polynomial, and the existence of the $ S $-matrix has been established. Fermion and sc
15 KB (2,298 words) - 22:02, 7 November 2017
that is representable as a homogeneous quadratic polynomial in the elements of $ \mathfrak g $.
4 KB (568 words) - 10:08, 4 June 2020
...lar'', if solutions of the equation loose analyticity, but exhibit at most polynomial growth at this point.
5 KB (815 words) - 21:42, 31 July 2015
of the [[chromatic polynomial]] $ \chi ( G;k ) $ (computing this number is $ \# P $-complete [[#Refer
...p"> R.P. Stanley, "A symmetric function generalization of the chromatic polynomial of a graph" ''Adv. Math.'' , '''111''' (1995) pp. 166–194</TD></TR>
10 KB (1,497 words) - 06:32, 26 March 2023