GPS Solutions: Closed Forms, Critical and Special Configurations of P4P

P4P is the pseudo-ranging 4-point problem as it appears as the basic configuration of satellite positioning with pseudo-ranges as observables. In order to determine the ground receiver/satellite receiver (LEO networks) position from four positions of satellite transmitters given, a system of four nonlinear (algebraic) equations has to be solved. The solution point is the intersection of four spherical cones if the ground receiver/satellite receiver clock bias is implemented as an unknown. Here we determine the critical configuration manifold (Determinantal Loci, Inverse Function Theorem, Jacobi map) where no solution of P4P exists. Four examples demonstrate the critical linear manifold. The algorithm GS solves in a closed form P4P in a manner similar to Groebner bases: The algebraic nonlinear observational equations are reduced in the forward step to one quadratic equation in the clock bias unknown. In the backward step two solutions of the position unknowns are generated in closed form. Prior information in P4P has to be implemented in order to decide which solution is acceptable. Finally, the main target of our contribution is formulated: Can we identify a special configuration of satellite transmitters and ground receiver/satellite receiver where the two solutions are reduced to one. A special geometric analysis of the discriminant solves this problem. ? 2002 Wiley Periodicals, Inc.     

Bayesian techniques for seismic hazard assessment using imprecise data

Some Bayesian methods of dealing with inaccurate or vague data are introduced in the framework of seismic hazard assessment. Inaccurate data affected by heterogeneous errors are modeled by a probability distribution instead of the usual value plus a random error representation; these data are generically called imprecise. The earthquake size and the number of events in a certain time are modeled as imprecise data. Imprecise data allow us to introduce into the estimation procedures the uncertainty inherent in the inaccuracy and heterogeneity of the measuring systems from which the data were obtained. The problem of estimating the parameter of a Poisson process is shown to be feasible by the use of Bayesian techniques and imprecise data. This background technique can be applied to a general problem of seismic hazard estimation. Initially, data in a regional earthquake catalog are assumed imprecise both in size and location (i.e errors in the epicenter or spreading over a given source). By means of scattered attenuation laws, the regional catalog can be translated into a so-called site catalog of imprecise events. The site catalog is then used to estimate return periods or occurrence probabilities, taking into account all sources of uncertainty. Special attention is paid to priors in the Bayesian estimation. They can be used to introduce additional information as well as scattered frequency-size laws for local events. A simple example is presented to illustrate the capabilities of this methodology.     

The application of cascading consequences for emergency management operations

How societies organize themselves to respond to cascading impacts exacerbated by climate change will help define the future of disaster planning, mitigation, response, and recovery. Current emergency management risk analyses focus on identifying a broad array of threats and hazards that may affect an area. However, there is limited attention and understanding of the totality of hazard impacts, the relationship of consequences across disasters, and the dangers of not addressing critical capabilities necessary to rapidly managing consequences—including the potential to create new incidents within incidents. Through a focused review of the related literature and guiding policy documents, this study aims to provide a cascading consequence-based framework that can support emergency managers in the analysis of their jurisdictional risks, development of emergency operations plans, and decision-making. Results include the identification of an alternative framework to identify cascading networks, the creation of a supplementary model for downstream risk assessment, and refined Threat and Hazard Identification and Risk Analysis (THIRA) outputs for improved grant allocation. The proposed framework has the potential to help organizations factor both conspicuous and downstream consequences into their Emergency Operations Plans in the planning and mitigations phases. This proposed refinement, which looks deeper into the progression of a disaster, has both national and international implications.

     

The influence of foliation on the fragility of granitic rocks, image analysis and quantitative microscopy

Fabric-dependent anisotropy is important in understanding the mechanical behaviour of foliated rocks because the foliation creates mechanically weak discontinuities. Using optical microscopy, a foliation index (FIX) was calculated for a group of granitic rocks in southern Sweden that displays a range of textures from foliated to nonfoliated. Image analysis from scanning electron microscope with backscattered detector (SEM/BSE) images was used in order to measure the rock texture of these samples. The analyses were compared with the Los Angeles (LA) test, which measures resistance of rock aggregate to fragmentation. The results demonstrate that the measured grain size, shape and spatial arrangement are important parameters controlling the fragility of the rock. Both the texture and foliation must be taken into account to obtain a significant relationship with the mechanical analyses. We suggest that this alternative method could be a helpful tool for predicting a rock's suitability as an aggregate as it gives a better understanding of the material properties compared to mechanical testing.     

Elektronenmikroskopische Untersuchungen an mikritischen Kalken

Zusammenfassung Es werden die Entstehungsmöglichkeiten von mikritischen Kalken diskutiert und an Hand von elektronenmikroskopischen Aufnahmen Hinweise auf genetische Interpretationen vorgeführt.

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The origin of micritic limestones is discussed and genetic interpretation of micrites from different environments, studied by electron microscope, is given.

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Résumé L'origine des calcaires micritic est discutée et une interprétation génétique des micrites de milieux différents est donnée à l'aide de la microscopie électronique.

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Vorgetragen auf der 56. Jahresversammlung der Geologischen Vereinigung in Wien im Februar 1966.     

The spectrum of the manganese-scandium star ϕ Herculis

Among manganese stars, Herculis is of great interest because of the unusual strength of the scandium lines. We present intensity measurements for numerous lines ofCii, Mgi, Mgii, Siii, Caii, Scii, Tiii, Crii, Mni, Mnii, Fei, Feii, Coii, Srii,Yii, and Zrii.