BCJ numerators from differential operator of multidimensional residue

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...

Multidimensional wavefront estimation from differential delays

The propagating wavefield measured by complex sources-receivers arrangements can be characterized by a delayed waveform in the n-dimensional (n-D) space of measurements. In this paper, we propose a method for the nonparametric estimation of the time of delay function (also referred to as wavefront) that do not require the knowledge of the waveform. The n-D wavefront is estimated by using a leas...

Discretizing Laplace–Beltrami Operator from Differential Quantities

The Laplace–Beltrami operator (LBO) is the fundamental geometric object associated with manifold surfaces and has been widely used in various tasks in geometric processing. By understanding that the LBO can be computed by differential quantities, we propose an approach for discretizing the LBO on manifolds by estimating differential quantities. For a point on the manifold, we first fit a quadra...

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