We sketch the architecture of O’Mega, a new optimizing compiler for tree amplitudes in quantum field theory, and briefly describe its usage. O’Mega generates the most efficient code currently available for scattering amplitudes for many polarized particles in the Standard Model and its extensions. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]

It is known that extremal doubly-even self-dual codes of length n ≡ 8 or 0 (mod 24) yield 3or 5-designs respectively. In this paper, by using the generator matrices of bordered double circulant doubly-even self-dual codes, we give 3-(n, k; m)-SEEDs with (n, k, m) ∈ {(32, 8, 5), (56, 12, 9), (56, 16, 9), (56, 24, 9), (80, 16, 52)}. With the aid of computer, we obtain 22 generator matrices of bor...

We describe the results of a computer-based search for 5 and 6dimensional lattice rules of specified trigonometric degree. In this search only lattice rules that can be generated by a circulant or skew-circulant generator matrix are considered, which makes this approach significantly faster than earlier approaches. The drawback is that we do not necessarily obtain optimal lattice rules. We also...

Abstract—Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be nonzero, has found many recent applications, including in distributed coding and storage, multiple access networks, and weakly secure data exchange. The dual problem, where the parity check matrix has a support constra...

Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length sl with index s over the finite field F are F[y]-submodules of the ring F[x, y]/< x − 1, y − 1 >. The aim of the present paper, is to study QC codes of length sl with index s over the finite field F and find generator polynomials and generator matrix for these codes. To achieve this...

The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of power matrices, and the coefficients are entire functions of finitely many coefficients of the infinitesimal generator. Furthermore coefficients of the solution...

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular, these functions include all the homogeneous polynomials that are reproducible by the generator, which links this representation to the accuracy of the space. We completely characterize the class of homogeneous fun...

In this paper, the reactive power control of a variable speed permanent-magnet synchronous wind generator with a matrix converter at the grid side is improved. A generalized modulation technique based on singular value decomposition of the modulation matrix is used to model different modulation techniques and investigate their corresponding input reactive power capability. Based on this modulat...

The authors would like to hereby acknowledge the support of StatDisT group. This work is based upon research supported by National Research foundation South Africa, Reference: SRUG 190308422768 grant number 120839, IFR170227223754 109214 and SARCHI Chair UID: 71199. opinions expressed conclusions arrived at are those not necessarily be attributed NRF.