Affine Lie Algebraic Origin of Constrained KP Hierarchies

We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and we show that these approaches are equivalent. The model is recognized to be the generalized non-linear Schr\"{o}dinger (\GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-B\"{a}cklund transformations and interpolate between \GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers origin of the Toda lattice structure behind the latter hierarchy.Comment: 25 pgs, LaTeX, IFT-P/029/94 and UICHEP-TH/93-1

Riemann Hypothesis and Random Walks: the Zeta case

In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line $\Re (s) > \tfrac{1}{2}$, and the Riemann Hypothesis for this class of $L$-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet $L$-functions. We apply these results to the study of the argument of the zeta function. In another application, we define and study a 1-point correlation function of the Riemann zeros, which leads to the construction of a probabilistic model for them. Based on these results we describe a new algorithm for computing very high Riemann zeros, and we calculate the googol-th zero, namely $10^{100}$-th zero to over 100 digits, far beyond what is currently known.Comment: version 2: A significantly better estimate of the error incurred in computing zeros from the primes has been include. version 3: Re-written in a more informal style; change of notation to avoid confusion with S(t

High energy-efficiency buildings

In cold, central European climates, hyper-insulated, heat-conserving buildings have proven a very effective way to reduce current energy consumption to 1/10 th of a traditional house. Using dry, stratified building techniques (Str/En) allows to obtain quite easily the required thermal and acoustical performances, also enhancing the construction process and allowing for the final recycling of the components. In a warmer climate – such as the Italian one – a heat-conserving strategy has to be balanced against the potential overheating problems. Among the possible solutions, the use of building-integrated Phase Change Materials, which could create a " light thermal inertia " (that is, without heavy mass), was also investigated

Testing for (in)finite moments

This paper proposes a test to verify whether the k-th moment of a random variable is Önite. We use the fact that, under general assumptions, sample moments either converge to a Önite number or diverge to inÖnity according as the corresponding population moment is Önite or not. Building on this, we propose a test for the null that the k-th moment does not exist. Since, by construction, our test statistic diverges under the null and converges under the alternative, we propose a randomised testing procedure to discern between the two cases. We study the application of the test to raw data, and to regression residuals. Monte Carlo evidence shows that the test has the correct size and good power; the results are further illustrated through an application to Önancial data

Status of the Construction of the First 15 m Long Superconducting Dipole Prototype for the LHC

CERN and INFN are jointly building the first full-size superconducting dipole prototype for the LHC. This magnet, whose construction was launched in spring 1995, is completely manufactured in industry . Its fabrication required the upgrade of the tooling which was used to build three 10-m long prototypes under a previous CERN-INFN Collaboration. The construction is being completed and the cryostate d magnet is expected to be at CERN for testing by the end of 1997. In this paper we discuss the results of the measurements carried out at 4.2 K and 2 K to determine the conductor properties (Ic of wi res and cables, magnetization), as well as the short sample limit. The main features of the coil construction are presented, together with the results of the main fabrication phases. In particular, th e validity of the fabrication techniques is assessed based on the obtained results

Characterization of the earth-based construction techniques used in the 18th and 19th centuries in the historical centre of São Luís (MA, Brazil)

The architectural heritage of the historical city centre of Sao Luis of Maranhao, located in the northeast region of Brazil, has approximately 5,600 registered buildings, out of which 1,400 were included in the UNESCO World-Heritage List in December 1997. The architectural heritage of 18(th) and 19(th) centuries is made up of sobrados (ground storey for commercial and upper storeys for residential use), solares (constructions with distinguished finishing, exclusively for residential use by privileged families) and single-storey constructions where poorer families used to live. Different construction systems can be found in the same building of the historical city centre. It is common to have structural walls made of stone masonry with lime mortar (in rare cases made of adobe) and interior partition walls made of pau-a-pique (also called taipa de mao), cruz de Santo Andre (resembling the gaiola pombalina style) and tabique. Therefore, in the majority of the internal partition walls earth-based masonry is found, which, in many interventions, was replaced by contemporary techniques. This article discusses the earth based masonry typologies found in the buildings from the 18(th) and 19(th) centuries in the historical centre of Sao Luis belonging to the registered areas at federal and state level. It characterizes the different typologies of the earth-based masonries, analysing the historical, cultural and socio-economic period when they were used in the region. It is designed to contribute to the scientific and technological knowledge of the earth-based masonry systems used in Sao Luis in the 18(th) and 19(th) centuries and thus to the preservation and rehabilitation of its heritage

Proposal for the nomination of Lower Globigerina Limestone of the Maltese Islands as a "Global Heritage Stone Resource"

The Lower Globigerina Limestone of the Maltese Islands is here being proposed for nomination as a “Global Heritage Stone Resource”. This stone, continuously used for building and sculpture for 6000 years, is well suited to fit this global designation as it is not only of great local cultural, historic and economic importance, but it is also the building stone used in construction of the UNESCO, and hence internationally recognized, World Heritage city of Valletta, as well as the UNESCO-listed Prehistoric Megalithic Temples of the Maltese Islands. The stone was also exported to several European and North African countries especially in the early 20 th century. The entire range of archaeological remains and historic architecture which cover the Maltese Islands have been built in this stone, and encompass innumerable palaces and churches, including the fortified cities of Valletta, Mdina (the old capital of Malta), the Three Cities on the Grand Harbour and the Citadel of Gozo, as well as the vernacular architecture ubiquitous within the village cores all over the Islands. The soft limestone has also been widely used over the millennia for elaborate and extensive sculptural motifs. Practically the only natural resource of the Islands, it continues to be quarried today, and is used not only for new construction, but also for the regular restoration of Malta’s great and imposing architectural heritage, remaining thus an important pillar of the Maltese economy.peer-reviewe