Ordered OLPS and CF Nth numerators

Generalised Hilbert Numerators Ii

Let K[〈X〉] denote the large polynomial ring (in the sense of Halter-Koch [7]) on the set X = {x1, x2, x3, . . . } of indeterminates. For each integer n, there is a truncation homomorphism ρn : K[〈X〉] → K[x1, . . . , xn]. If I is a homogeneous ideal of K[〈X〉], then the N-graded Hilbert series of K[x1,...,xn] ρn(I) can be written as gn(t) (1−t) ; it was shown in [13] that if in addition I is what...

Generalized Hilbert Numerators

Numerators of Differences of Nonconsecutive Farey Fractions

Abstract. An elementary but useful fact is that the numerator of the difference of two consecutive Farey fractions is equal to one. For triples of consecutive fractions the numerators of the differences are well understood and have applications to several interesting problems. In this paper we investigate numerators of differences of fractions which are farther apart. We establish algebraic ide...

Explicit BCJ Numerators from Pure Spinors

We derive local kinematic numerators for gauge theory tree amplitudes which manifestly satisfy Jacobi identities analogous to color factors. They naturally emerge from the low energy limit of superstring amplitudes computed with the pure spinor formalism. The manifestation of the color–kinematics duality is a consequence of the superstring computation involving no more than (n − 2)! kinematic f...

HSI based colour image equalization using iterative nth root and nth power

In this paper an equalization technique for colour images is introduced. The method is based on n th root and n th power equalization approach but with optimization of the mean of the image in different colour channels such as RGB and HSI. The performance of the proposed method has been measured by the means of peak signal to noise ratio. The proposed algorithm has been compared with convention...