On the Convergence of Lacunary Walsh-Fourier Series

We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.e. Integral condition is only slightly larger than what the sharp integrability condition would be, by a result of Konyagin. The condition is: f is in L loglog L (logloglog L). The method of proof uses four ingredients, (1) analysis on the Walsh Phase Plane, (2) the new multi-frequency Calderon-Zygmund Decomposition of Nazarov-Oberlin-Thiele, (3) a classical inequality of Zygmund, giving an improvement in the Hausdorff-Young inequality for lacunary subsequences of integers, and (4) the extrapolation method of Carro-Martin, which generalizes the work of Antonov and Arias-de-Reyna.Comment: 18 pages. v2: Several typos corrected. Final version of the paper, accepted to LM

A scaling proof for Walsh's Brownian motion extended arc-sine law

We present a new proof of the extended arc-sine law related to Walsh's Brownian motion, known also as Brownian spider. The main argument mimics the scaling property used previously, in particular by D. Williams in the 1-dimensional Brownian case, which can be generalized to the multivariate case. A discussion concerning the time spent positive by a skew Bessel process is also presented

No Child Left Behind: The Adam Walsh Act and Pennsylvania Juvenile Sex Offenders

At a White House ceremony on July 27, 2006, President Bush signed into law the Adam Walsh Child Protection and Safety Act of 2006. At the ceremony, the President hailed the Walsh Act as being comprehensive and an important part of the “solemn responsibility” of lawmakers to protect children. Indeed, the Walsh Act is the latest in a series of federal legislation, dating back to the 1980s, which aims to protect the public, and children in particular, from becoming victims of sexual crimes. The public’s fear of the rapist and the child molester led to a great increase in the criminal penalties for sexual crimes throughout the 1980s and 1990s, as well as the imposition of federal laws focusing on these crimes. And at a time when television shows such as “To Catch a Predator” receive millions of viewers, it is clear that the nation’s fear of those who would commit sexual crimes against children, and the desire that they be brought to justice, remains at a fever pitch. By passing the Walsh Act, Congress and the President responded to a national outcry that children were not safe from sex offenders

Independent Counsel and Vigorous Investigation and Prosecution

Two completed investigations into allegations of presidential wrongdoing, Watergate and Iran-Contra, are examined and the offices of Independent Counselor and Special Prosecutor are discussed

In loco parentis and the professional responsibilities of teachers.

This paper examines the concept of in loco parentis in the light of its legal origins and considers its relevance to contemporary schooling, particularly the professional responsibilities of teachers. It is argued that from a legal perspective, in loco parentis is now largely an anachronism in New Zealand education, although it appears to have some limited application in non-compulsory and out-of-school-hours educational activities. From an ethical point of view, the concept remains useful because it stresses the duty of care that professional teachers have towards their students. However, teachers need to be clear about its extremely limited legal relevance as either a source of teacher authority or a legal basis for teachers to attend to the health and well-being of their students. In the main, its old functions have been superseded by much more specific legislatio

Time Inconsistency: An Updated Survey of the Literature

We provide an updated survey of the literature on time inconsistency, focusing on the key contributions that followed the seminal papers of Kydland and Prescott (1977) and Barro and Gordon (1983a). Starting from the traditional models addressing the time inconsistency problem of monetary policy, we then proceed to analyse the more recent contributions accounting for the important monetary and fiscal policy interactions. We conclude by sketching an encompassing open-economy model summarising the most recent positions concerning the optimal management of fiscal policies.Time Inconsistency, Monetary Policy, Central Banking, EMU, Policy Co-ordination

Discrepancy bounds for low-dimensional point sets

The class of $(t,m,s)$-nets and $(t,s)$-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of $(t,m,s)$-nets and $(t,s)$-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, as they are interesting mathematical objects from a theoretical point of view, and simultaneously serve as examples that make it easier to understand the structural properties of $(t,m,s)$-nets and $(t,s)$-sequences in arbitrary dimension. For these reasons, a considerable number of papers have been written on the properties of low-dimensional nets and sequences