Abstract:
Using the recently proposed ALPHA algorithm (and the resulting code) I compute the rate (at tree level) for the process $\gamma\gamma\rightarrow\bar\nu_e e^- u \bar d$. The bulk of the contribution is due to W pair production and decay. However a non negligible ($\sim10 \%$) contribution comes from other channels, mainly the production and decay of a W and a collinear charged fermion. Requiring that the reconstructed invariant $u \bar d$ mass lies in the intervals $M_W\pm 5 $ GeV and $M_W\pm 20 $ GeV one obtains a rate which is lower, by 25 \% and 4 \% respectively, than the rate obtained in the $narrow$ $width$ approximation, thus demonstrating the relevance of the finite W width.

Abstract:
The ALPHA algorithm to evaluate the exact, tree-level matrix elements is reviewed in the context of multi-parton processes in QCD. The algorithm is suited for the authomatic calculation of tree-level scattering amplitudes and allows for straightforward inclusion of mass effects. It's CPU cost grows like K^n (K constant, n number of external particles) as opposed to the factorial growth of Feynman graphs. I also discuss the summation over colour configurations which is designed to allow the construction of parton-level event generators suitable to interfacing with a parton-shower evolution including the effects of colour-coherence. Explicit results for the total rates and differential distributions of processes with 8 final-state partons are given.

Abstract:
Before establishing a communication link in a cellular network, the user terminal must activate a synchronization procedure called initial cell search in order to acquire specific information about the serving base station. To accomplish this task, the primary synchronization signal (PSS) and secondary synchronization signal (SSS) are periodically transmitted in the downlink of a Long Term Evolution (LTE) network. Since SSS detection can be performed only after successful identification of the primary signal, in this work we present a robust scheme for joint PSS detection, sector index identification and integer frequency offset (IFO) recovery in an LTE system. The proposed algorithm relies on the maximum likelihood (ML) estimation criterion and exploits a suitable reduced-rank representation of the channel frequency response to take multipath distortions into account. We show that some PSS detection methods that were originally introduced through heuristic reasoning can be derived from our ML framework by selecting an appropriate model for the channel gains over the PSS subcarriers. Numerical simulations indicate that the proposed scheme can be effectively applied in the presence of severe multipath propagation, where existing alternatives provide unsatisfactory performance.

Abstract:
the purpose of the present study is to raise questions regarding the divergences among evaluators in respect to the grades attributed in mathematics exams. these interrogations are relevant since, in the university entrance exams, many important brazilian institutions adopt essay questions. when the exam is based on multiple choice, the correction is automatized and the error, if it occurs, can be easily spotted. also, there is an exact comprehension of the manner in which it affects all those who are taking the exam. this is not the case in essay question exams, in which the correction is not automatized and suffers significant influence of those who correct them. this study will show that certain elements present in the students' answers in the exam can bring about strong divergence among the evaluators. these divergences are an alert to the entrance exam committees, who must pursue some form of grade standardization for these exams.

Abstract:
in the 3rd century b.c., the sign rule for multiplication was presented by diophantus of alexandria without any demonstration. only in 1867 was the rule demonstrated by hankel as being the only one with the advantage of satisfying both left and right distributivity. thus, hankel solves the problem from the mathematical point of view when he uses the extension principle to apply the distributivity property, which has been used for many years with positive numbers, to negative numbers. this paper shows that this approach is still present in mathematics teaching today. the paper also presents studies from a teaching perspective of this rule based on the idea of semantic congruence and the extension principle in mathematics.

Abstract:
We apply the iterative numerical algorithm ALPHA, which automatically generates the N-point Green functions (as recently suggested \cite{alpha}) to the computation of the production rate of four fermions and four fermions plus photon in electron-positron annihilation. The discussion of the physical results is preceded by an introduction on the algorithm.

Abstract:
In this paper we suggest an {\it iterative} algorithm to compute automatically the scattering matrix elements of any given effective lagrangian, $\Gamma$. By exploiting the relation between $\Gamma$ and the connected Green function generator, $Z$, we provide a formula which does not require the use of the Feynman graphs and it is suitable to implement a numerical routine. By means of this algorithm we have built a relatively simple and fast fortran code which we have used to calculate, at the tree level, the rate of four fermion production at LEP I\negthinspace{I} (finding a very good agreement with previous calculation) with and without the emission of one observable photon.

Abstract:
We study the structure of soft breaking terms in the context of a gaugino condensation scenario. Assuming that the Supergravity Lagrangian is the correct quantum field theory limit, at some momentum scale $\mu_{UV}$, of a more fundamental one, we demonstrate that the correct result is obtained simply by substituting, in the tree level Supergravity Lagrangian, $\lambda \lambda$ (the gaugino condensate) by its vacuum expectation value $\Lambda^3$. In string inspired scenarios this implies, in particular, that the scalar masses are vanishing at the string tree-level and receive a contribution, at the one loop level, which is proportional to the Green Schwarz coefficient $\delta_{GS}$. Our results do not agree with the ones obtained in the effective Lagrangian approach. We study in detail the origin of this discrepancy, and we argue that the use of the supertrace anomaly to determine the effective theory for the condensate does not fix its gravitational interactions, leaving the soft breaking terms and the vacua of the theory unspecified.

Abstract:
We discuss the role of dislocation assemblies such as grain boundaries in the dynamic response of a driven vortex lattice. We simulate the depinning of a field-cooled vortex polycrystal and observe a general enhancement of the critical current as well as a distinct crossover in the characterisitic of this quantity as a function of pinning density. The results agree with analytical predictions for grain boundary depinning. The dynamics of grain boundaries thus proves an essential mechanism underlying the flow response of defected vortex lattices and the corresponding transport properties of the superconducting material. We emphasize the connection between the topological rearrangements of the lattice and its threshold dynamics. Our theory encompasses a variety of experimental observations in vortex matter as well as in colloidal crystals.