Cores with distinct parts and bigraded Fibonacci numbers

The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$. Recent research shows that $(a,a+1)$ cores with distinct parts are enumerated by another important sequence- Fibonacci numbers $F_a$. In this paper, we consider the abacus description of $(a,b)$-cores to introduce the natural grading and generalize this result to $(a,as+1)$-cores. We also use the bijection with Dyck paths to count the number of $(2k-1,2k+1)$-cores with distinct parts. We give a second grading to Fibonacci numbers, induced by bigraded Catalan sequence $C_{a,b} (q,t)$

Long-range Energy Transfer and Ionization in Extended Quantum Systems Driven by Ultrashort Spatially Shaped Laser Pulses

The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schr\"odinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has been explored within a linear three-dimensional model, including two z coordinates of the electrons and the internuclear distance R. An efficient energy transfer from the laser-excited H atom (atom A) to the other H atom (atom B) and the ionization of the latter have been found. It has been shown that the physical mechanisms of the energy transfer as well as of the ionization of atom B are the Coulomb attraction of the laser driven electron of atom A by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions strongly overlap in the domain of atom B.Comment: 11 pages, 7 figure

Fundamental characteristics of transverse deflecting field

The Panofsky-Wenzel theorem connects the transverse deflecting force in an rf structure with the existence of a longitudinal electric field component. In this paper it is shown that a transverse deflecting force is always accompanied by an additional longitudinal magnetic field component which leads to an emittance growth in the direction perpendicular to the transverse force. Transverse deflecting waves can thus not be described by pure TM or TE modes, but require a linear combination of basis modes for their representation. The mode description is preferably performed in the HM--HE basis to avoid converge problems, which are fundamental for the TM--TE basis.Comment: The sign in Eq.8 is corrected in May 201

First principles studies of a Si tip on Si(100) 2x1 reconstructed surface

We present a systematic study of the interaction between a silicon tip and a reconstructed Si(100)2×1 surface by means of total energy calculations using Density Functional Theory. We perform geometry optimisation to obtain the reconstructed Si surface using the Local Density Approximation and the Generalized Gradient Approximation methods and compare our results with those obtained experimentally. We then study the effects of the tip of a scanning probe of an Atomic Force Microscope (AFM) on the behaviour of atoms on the reconstructed surface when the tip translates at distances close to it. Our results show that at certain positions of the tip relative to the surface and depending on the direction of the scan, the Si dimer on the surface flips, resulting to a local reconstruction of the surface into p(2×2) or c(4×2) configurations. These configurations exhibit energy lower by 0.05 eV/dimer compared to the Si(100)2×1 structure

W/Z + jets and W/Z + heavy flavor production at the LHC

The ATLAS and CMS experiments at the LHC conduct an extensive program to study production of events with a W or Z boson and particle jets. Dedicated studies focus on final states with the jets containing decays of heavy-flavor hadrons (b-tagged jets). The results are obtained using data from proton-proton collisions at sqrt{s}=7 TeV from the LHC at CERN. The set of measurements constitute a stringent test of the perturbative QCD calculations.Comment: 4 pages, proceedings of the 47th Rencontres de Moriond on QCD and High Energy Interactions, La Thuile, Italy, 10-17 Mar 201

Sketched Answer Set Programming

Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models is not trivial. We propose a novel method, called Sketched Answer Set Programming (SkASP), aiming at supporting the user in resolving this issue. The user writes an ASP program while marking uncertain parts open with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. The sketched model is rewritten into another ASP program, which is solved by traditional methods. As a result, the user obtains a functional and reusable ASP program modelling her problem. We evaluate our approach on 21 well known puzzles and combinatorial problems inspired by Karp's 21 NP-complete problems and demonstrate a use-case for a database application based on ASP.Comment: 15 pages, 11 figures; to appear in ICTAI 201