Scalar differential invariants of symplectic Monge–Ampère equations

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère PDEs with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. A series of invariant differential forms and vector fields are also introduced: they allow one to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution to the symplectic equivalence problem for Monge-Ampère equations

Phase transitions related to the pigeonhole principle

Since Paris introduced them in the late seventies (Paris1978), densities turned out to be useful for studying independence results. Motivated by their simplicity and surprising strength we investigate the combinatorial complexity of two such densities which are strongly related to the pigeonhole principle. The aim is to miniaturise Ramsey's Theorem for $1$-tuples. The first principle uses an unlimited amount of colours, whereas the second has a fixed number of two colours. We show that these principles give rise to Ackermannian growth. After parameterising these statements with respect to a function f:N->N, we investigate for which functions f Ackermannian growth is still preserved

Growth of the Brownian forest

Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton--Watson forests with i.i.d. exponential branch lengths. We give elementary proofs of this composition rule and explain how it is intimately linked with Williams' decomposition for Brownian motion with drift.Comment: Published at http://dx.doi.org/10.1214/009117905000000422 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries

A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper solutions of the quantum master equations in the osp(1,2)-covariant formalism are realized in that superspace as invariance under translations combined with mass-dependent special conformal transformations. The Sp(2) symmetry - in particular the ghost number conservation - and the "new ghost number" conservation are realized as invariance under symplectic rotations and dilatations, respectively. The transformations of the gauge fields - and of the full set of necessarily required (anti)ghost and auxiliary fields - under the superalgebra sl(1,2) are determined both for irreducible and first-stage reducible theories with closed gauge algebra.Comment: 35 pages, AMSTEX, precision of reference

Transmittivity measurements by means of squeezed vacuum light

A method for measuring the transmittivity of optical samples by using squeezed--vacuum radiation is illustrated. A squeezed vacuum field generated by a below--threshold optical parametric oscillator is propagated through a nondispersive medium and detected by a homodyne apparatus. The variance of the detected quadrature is used for measuring the transmittivity. With this method it is drastically reduced the number of photons passing through the sample during the measurement interval. The results of some tests are reported.Comment: 14 pages, 8 figure

Creating figures: why re-imagining urban structure supports a regenerative urban model

Some authors describe the contemporary metropolis like the field where co-exist simultaneous strategies of exploitation of fragmentary opportunities provided by the specific conditions of places (Florida, Bagnasco, Solá-Morales): physical (geography, infrastructures, etc.), social (people, culture and local values, etc.) and economic conditions. In their opinion, the causes of the ‘lateral’ development of the city could be (i) the relationships between the different elements of the land mosaic (Forman) and (ii) the fragmentary logics of the current urban realities. This important process of transformation would integrate the classic ‘lineal’ growth, more related to the urban rising along infrastructures. The result of these interactions is the change of scales in the performing of contemporary urban phenomena. Several authors have been interested in studying this new reality, called ‘exopolis’ (Soja), city-region (De las Rivas, Portas & al.) or metropolizated territory (Indovina, Monclús). Those not-conventional approaches are necessary to understand the contemporary urban condition and its complex, unstable, transient dynamics. Nowadays, several traditional concepts and ideas have become less useful and too rigid to achieve this target. This lack of effectiveness regards the discipline as a whole, divided between sectorial analysis and fragmentary solutions. In our opinion, using figures as ‘images with the potential to represent new territorial realities’ is one of the most important steps to produce an innovative and non-conventional understanding of post-metropolitan (Soja) urban space. This paper is aimed at explaining why figures are more useful than images to understand the complex urban pattern of current territory, as well as demonstrating this idea with the case studies of Valladolid and its emerging urban area. The result is a way to show the structure of this territory, which is more coherent with a contemporary narrative of space, and closer to its spatial and temporal dimensions. This is something not completely original but in this paper we present our views on it

Proposal of semi-nested polimerase chain reaction (PCR) for diagnosing and differentiating BK and JC virus

Objetivos: Implantar e otimizar a reação em cadeia da polimerase (PCR) semi-nested para pesquisa e diferenciação dos vírus BK e JC a partir de amostras clínicas armazenadas. Métodos: Foram testadas 9 amostras clínicas (urina e líquor). As amostras foram submetidas à PCR semi-nested, e foram testadas também com diferentes condições, visando a otimização da reação. Resultados: Primeiramente os controles positivos foram testados quanto à especificidade através de uma PCR direta, e os resultados obtidos confirmaram a especificidade. Quando testadas por PCR semi-nested, as amostras apresentaram os seguintes resultados: 100% (nove amostras) positivas para o vírus BK e 66,6% (seis amostras) positivas para o vírus JC. Conclusões: Otimizou-se a reação de PCR seminested, específica para a identificação dos poliomavírus, para assim atuar como uma ferramenta diagnóstica para melhor acompanhamento de pacientes imunocomprometidos.Aims: To implant and optimize the semi-nested polimerase chain reaction (PCR) to identify and differentiate BK and JC virus. Methods: Nine clinical (urine and liquor) samples have been tested with semi-nested PCR. In order to optimize this reaction, different conditions have been tested. Results: Specificity has been confirmed by using JC and BK positive controls. When tested with semi-nested PCR, the clinical samples showed the following results: 100% (nine samples) positive from BK virus, and 66.6% (six samples) positive from JC virus. Conclusions: The semi-nested PCR reaction, specific for identification of polyomavirus, was optimized for acting as a tool for better follow-up of immunocompromised patients

The Counterpart Principle of Analogical Support by Structural Similarity

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures

A two-step optimized measurement for the phase-shift

A two-step detection strategy is suggested for the precise measurement of the optical phase-shift. In the first step an unsharp, however, unbiased joint measurement of the phase and photon number is performed by heterodyning the signal field. Information coming from this step is then used for suitable squeezing of the probe mode to obtain a sharp phase distribution. Application to squeezed states leads to a phase sensitivity scaling as $\Delta\phi\simeq N^{-1}$ relative to the total number of photons impinged into the apparatus. Numerical simulations of the whole detection strategy are also also presented

A study on PDC drill bits quality

The quality of innovating PDC (Polycrystalline Diamond Compact) bits materials needs to be determined with accuracy by measuring cutting efficiency and wear rate, both related to the overall mechanical properties. An original approach is developed to encompass cutting efficiency and wear contribution to the overall sample quality. Therefore, a lathe-type test device was used to abrade specific samples from various manufacturers. Post-experiment analyzes are based on models establishing coupled relationships between cutting and friction stresses related to the drag bits excavation mechanism. These models are implemented in order to evaluate cutting efficiency and to estimate wear of the diamond insert. Phase analysis by XRD and finite element simulations were performed to explain the role of physicochemical parameters on the calculated quality factor values. Four main properties of PDC material were studied to explain quality results obtained in this study: cobalt content in samples that characterizes hardness/fracture toughness compromise, undesired phase as tungsten carbide weakening diamond structure, diamond grains sizes and residual stresses distribution affecting abrasion resistance