Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Cutting Arcs For Torus Links And Trees

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings.

Trace element concentrations and Li isotope composition in DSDP and ODP sediments from island arcs

We have studied the sedimentary and basaltic inputs of lithium to subduction zones. Various sediments from DSDP and ODP drill cores in front of the Mariana, South Sandwich, Banda, East Sunda and Lesser Antilles island arcs have been analysed and show highly variable Li contents and d7Li values. The sediment piles in front of the Mariana and South Sandwich arcs largely consist of pelagic sediments (clays and oozes). The pelagic clays have high Li contents (up to 57.3 ppm) and Li isotope compositions ranging from +1.3? to +4.1?. The oozes have lower Li contents (7.3-16 ppm) with d7Li values of the diatom oozes from the South Sandwich lower (+2.8? to +3.2?) than those of the radiolarian oozes from the Mariana arc (+8.1? to +14.5?). Mariana sediment also contains a significant portion of volcanogenic material, which is characterised by a moderate Li content (14 ppm) and a relatively heavy isotope composition (+6.4?). Sediments from the Banda and Lesser Antilles contain considerable amounts of continental detritus, and have high Li contents (up to 74.3 ppm) and low d7Li values (around 0?), caused by weathering of continental bedrock. East Sunda sediments largely consist of calcareous oozes. These carbonate sediments display intermediate to high Li contents (2.4-41.9 ppm) and highly variable d7Li values (-1.6? to +12.8?). Basaltic oceanic crust samples from worldwide DSDP and ODP drill cores are characterised by enrichment of Li compared to fresh MORB (6.6-33.1 vs. 3.6-7.5 ppm, respectively), and show a large range in Li isotope compositions (+1.7? to +11.8?). The elemental and isotopic enrichment of Li in altered basalts is due to the uptake of isotopically heavy seawater Li during weathering. However, old oceanic crust samples from Sites 417/418 exhibit lighter Li isotope compositions compared to young basaltic crust samples from Sites 332B and 504B. This lighter Li isotope signature in old crust is unexpected and further research is needed to explore this issue.

Composition of Fe-Mn minerals from island arcs of the West Pacific

This paper presents materials on the chemical and mineralogical composition of Fe-Mn mineralization in island arcs (Kuril, Nampo, Mariana, New Britain, New Hebrides, and Kermadec) in the western part of the Pacific Ocean. The mineralization was proved to be of hydrothermal and/or hydrogenic genesis. The former is produced by hydrothermal Fe and Mn oxi-hydroxides that cement volcanic-terrigenous material in sediments. Some Fe oxyhydroxides can be derived via the halmyrolysis of volcaniclastic material. Crusts of this stage are characterized by fairly low concentrations of trace and rare elements, and their REE composition is inherited from the volcanic-terrigenous material. The minerals of the Mn oxyhydroxides are todorokite and "Ca-birnessite". The Mn/Fe ratio increases away from the discharge sites of the hydrothermal solutions. The hydrogenic Fe-Mn crusts are characterized by high concentrations of trace and minor elements of both the Mn group (Co, Ni, Tl, and Mo) and the Fe group (REE, Y, and Th). The hydrogenic crusts consist of Fe-vernadite and Mn-feroxyhyte. Some of the hydrothermal crusts originally had a hydrothermal genesis. The first data were obtained on crust B30-72-10 from the Macauley Seamount in the Kermadec island arc, which contained anomalously high concentrations of Co (2587 ppm) and other Mn-related trace elements in the absence of hydrogeneous Fe oxyhydroxides.

Efficient algorithms for dynamic probabilistic safety assessment. An application to convex damage domain.

The design of nuclear power plant has to follow a number of regulations aimed at limiting the risks inherent in this type of installation. The goal is to prevent and to limit the consequences of any possible incident that might threaten the public or the environment. To verify that the safety requirements are met a safety assessment process is followed. Safety analysis is as key component of a safety assessment, which incorporates both probabilistic and deterministic approaches. The deterministic approach attempts to ensure that the various situations, and in particular accidents, that are considered to be plausible, have been taken into account, and that the monitoring systems and engineered safety and safeguard systems will be capable of ensuring the safety goals. On the other hand, probabilistic safety analysis tries to demonstrate that the safety requirements are met for potential accidents both within and beyond the design basis, thus identifying vulnerabilities not necessarily accessible through deterministic safety analysis alone. Probabilistic safety assessment (PSA) methodology is widely used in the nuclear industry and is especially effective in comprehensive assessment of the measures needed to prevent accidents with small probability but severe consequences. Still, the trend towards a risk informed regulation (RIR) demanded a more extended use of risk assessment techniques with a significant need to further extend PSA’s scope and quality. Here is where the theory of stimulated dynamics (TSD) intervenes, as it is the mathematical foundation of the integrated safety assessment (ISA) methodology developed by the CSN(Consejo de Seguridad Nuclear) branch of Modelling and Simulation (MOSI). Such methodology attempts to extend classical PSA including accident dynamic analysis, an assessment of the damage associated to the transients and a computation of the damage frequency. The application of this ISA methodology requires a computational framework called SCAIS (Simulation Code System for Integrated Safety Assessment). SCAIS provides accident dynamic analysis support through simulation of nuclear accident sequences and operating procedures. Furthermore, it includes probabilistic quantification of fault trees and sequences; and integration and statistic treatment of risk metrics. SCAIS comprehensively implies an intensive use of code coupling techniques to join typical thermal hydraulic analysis, severe accident and probability calculation codes. The integration of accident simulation in the risk assessment process and thus requiring the use of complex nuclear plant models is what makes it so powerful, yet at the cost of an enormous increase in complexity. As the complexity of the process is primarily focused on such accident simulation codes, the question of whether it is possible to reduce the number of required simulation arises, which will be the focus of the present work. This document presents the work done on the investigation of more efficient techniques applied to the process of risk assessment inside the mentioned ISA methodology. Therefore such techniques will have the primary goal of decreasing the number of simulation needed for an adequate estimation of the damage probability. As the methodology and tools are relatively recent, there is not much work done inside this line of investigation, making it a quite difficult but necessary task, and because of time limitations the scope of the work had to be reduced. Therefore, some assumptions were made to work in simplified scenarios best suited for an initial approximation to the problem. The following section tries to explain in detail the process followed to design and test the developed techniques. Then, the next section introduces the general concepts and formulae of the TSD theory which are at the core of the risk assessment process. Afterwards a description of the simulation framework requirements and design is given. Followed by an introduction to the developed techniques, giving full detail of its mathematical background and its procedures. Later, the test case used is described and result from the application of the techniques is shown. Finally the conclusions are presented and future lines of work are exposed.

Planar point sets with large minimum convex decompositions

We show the existence of sets with n points (n ? 4) for which every convex decomposition contains more than (35/32)n?(3/2) polygons,which refutes the conjecture that for every set of n points there is a convex decomposition with at most n+C polygons. For sets having exactly three extreme pointswe show that more than n+sqr(2(n ? 3))?4 polygons may be necessary to form a convex decomposition.

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

Sento el Formal, y Tito Bufalampolla van à correr la bolta de la procesó, y fan una descripció de tot quant ya en ella, tant de altars y arcs, com dels demes adornos de la carrera [Texto impreso]

Hay un ejemplar encuadernado con: Individual noticia de todos los altares, arcos pinturas, adornos y lo mas exquisito y notable que havia en la carrera de la procession, y de las iluminaciones en general ... : (XVIII/1705).

Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Hybrid convex combinations for IIR system identification.

The low complexity of IIR adaptive filters (AFs) is specially appealing to realtime applications but some drawbacks have been preventing their widespread use so far. For gradient based IIR AFs, adverse operational conditions cause convergence problems in system identification scenarios: underdamped and clustered poles, undermodelling or non-white input signals lead to error surfaces where the adaptation nearly stops on large plateaus or get stuck at sub-optimal local minima that can not be identified as such a priori. Furthermore, the non-stationarity in the input regressor brought by the filter recursivity and the approximations made by the update rules of the stochastic gradient algorithms constrain the learning step size to small values, causing slow convergence. In this work, we propose IIR performance enhancement strategies based on hybrid combinations of AFs that achieve higher convergence rates than ordinary IIR AFs while keeping the stability.