Some twenty-five years ago Balitsky, Fadin, Kuraev and Lipatov (BFKL) set out to determine the high-energy behaviour of the scattering of hadronic objects within perturbative QCD. They found terms going as (αs ln s) n, where s is the squared centre-of-mass energy. Since ln s is large it can compensate the smallness of ᾱs and thus it was necessary to sum this whole series of leading logarithmic ...

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

English We show that the ring Z p 14; 1=2] is Euclidean and that this ring admits a totally multiplicative Euclidean function. This example is interesting because it is related to the ring Z p 14] which is conjectured to be Euclidean but for which a proof is lacking. French Nous montrons que l'anneau Z p 14; 1=2] est euclidien et que cet an-neau admet une fonction euclidienne totalement multipl...

• DECIMAL or NUMERIC is the type of numbers represented as strings of decimal digits. This will have some upper bound on the length of representations that the system is willing to tolerate. Although internally DECIMALs are stored just like strings, they are interpreted as numbers. Therefore any leading zeros are removed. On the other hand, trailing zeros are preserved because they could indica...

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials P (αn,βn) n is studied, assuming that lim n→∞ αn n = A , lim n→∞ βn n = B , with A and B satisfying A > −1, B > −1, A + B < −1. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a...

We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s totient function and σ is the sum-of-divisors function. This proves a 50-year old conjecture of Erdős. Moreover, we show that there are infinitely many integers n such that φ(a) = n and σ(b) = n each have more than n solutions, for some c > 0. The proofs rely on the recent work of the first two authors and K...

The elevated aerodynamic performance of insects has been attributed in part to the generation and maintenance of a stable region of vorticity known as the leading edge vortex (LEV). One explanation for the stability of the LEV is that spiraling axial flow within the vortex core drains energy into the tip vortex, forming a leading-edge spiral vortex analogous to the flow structure generated by d...

Anti-slug control applied to two-phase flow provides a very challenging and important application for feedback control. It is important because it allows for operation that would otherwise be impossible, and challenging because of the presence of both RHP-poles and RHP-zeros. To conduct experiments on pipeline-riser anti-slug control, a small-scale slug-loop has been build. The loop has been mo...

Instituto Interuniversitario de Desarrollo Social y Paz (WHO Collaborating Centre on Social Inclusion and Health), Universidad de Alicante, Alicante, España Departamento de Enfermería Comunitaria, Medicina Preventiva y Salud Pública, e Historia de la Ciencia, Universidad de Alicante, Alicante, España CIBER de Epidemiología y Salud Pública (CIBERESP), España UNGA, Asociación Gitana de Asturias, ...