Massless scattering at special kinematics as Jacobi polynomials

We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two-parameter family of kinematics. We present explicit and compact formulas for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Palindromic and perturbed polynomials: zeros location

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Producing xylan/Eudragit (R) S100-based microparticles by chemical and physico-mechanical approaches as carriers for 5-aminosalicylic acid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Rumen microbial diversity under influence of a polyclonal antibody preparation against lactate-producing and proteolytic bacteria in cows fed different energy sources

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sieved para-orthogonal polynomials on the unit circle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Pathotypes and probiotics: response to a commentary on the detection of a Shiga toxin producing Escherichia coli in a Crohn’s disease patient

A recent report on the detection in a Crohn's disease (CD) patient of an adherent and invasive Shiga toxin producing Escherichia coli (STEC) (Gut pathogens 2015, 7:2) prompted a commentary expressing some skepticism on the significance of the paper findings (Gut pathogens 2015, 7:15). Besides focusing on recurrent issues concerning the difficulties in defining a pathogen, the opinion considers recent data demonstrating the presence of virulence factors in a commercial probiotic. In response to the commentary's observations, additional information on the described STEC strain, as well as a short discussion on CD associated E. coli are presented here.

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the zeros of a class of generalized hypergeometric polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)