X-Ray spectra of superheavy and quasi-superheavy elements

We discuss the possibility of identifying superheavy elements from the observation of their M-shell x-ray spectra, which might occur during the collision of a superheavy element with a heavy target. The same question is discussed for the possible observation of the x-rays from the quasimolecule (quasi-superheavy element) which is formed during such a heavy-ion collision. It is shown that it is very difficult, if not impossible, to determine any information about the interesting quantum electrodynamical effects from the M-shell x-ray spectra of these quasimolecules.

Evidence for an additional coupling of the innermost shells in very heavy quasi-molecular ion-atom collisions

Due to the tremendous spin-orbit splitting of quasi-molecular levels in superheavy collision systems (Z = Z_1 + Z_2 {\ge\approx} 137) bombarding energy 0.5-6 MeV N{^-1}, unusual couplings may occur around Z \simeq 165. Experimental evidence for such a theoretically predicted coupling is discussed.

Theoretical evidence for quasi-molecular structure at small internuclear distances in elastic ion-atom scattering

The potential energy curve of the system Ne-Ne is calculated for small internuclear distances from 0.005 to 3.0 au using a newly developed relativistic molecular Dirac-Fock-Slater code. A significant structure in the potential energy curve is found which leads to a nearly complete agreement with experimental differential elastic scattering cross sections. This demonstrates the presence of quasi-molecular effects in elastic ion-atom collisions at keV energies.

Das Einzugsgebiet der Fulda - Untersuchung der Methoden der Hochwasserstatistik im Zeichen des Klimawandels

Numerous studies have proven an effect of a probable climate change on the hydrosphere’s different subsystems. In the 21st century global and regional redistribution of water has to be expected and it is very likely that extreme weather phenomenon will occur more frequently. From a global view the flood situation will exacerbate. In contrast to these discoveries the classical approach of flood frequency analysis provides terms like “mean flood recurrence interval”. But for this analysis to be valid there is a need for the precondition of stationary distribution parameters which implies that the flood frequencies are constant in time. Newer approaches take into account extreme value distributions with time-dependent parameters. But the latter implies a discard of the mentioned old terminology that has been used up-to-date in engineering hydrology. On the regional scale climate change affects the hydrosphere in various ways. So, the question appears to be whether in central Europe the classical approach of flood frequency analysis is not usable anymore and whether the traditional terminology should be renewed. In the present case study hydro-meteorological time series of the Fulda catchment area (6930 km²), upstream of the gauging station Bonaforth, are analyzed for the time period 1960 to 2100. At first a distributed catchment area model (SWAT2005) is build up, calibrated and finally validated. The Edertal reservoir is regulated as well by a feedback control of the catchments output in case of low water. Due to this intricacy a special modeling strategy has been necessary: The study area is divided into three SWAT basin models and an additional physically-based reservoir model is developed. To further improve the streamflow predictions of the SWAT model, a correction by an artificial neural network (ANN) has been tested successfully which opens a new way to improve hydrological models. With this extension the calibration and validation of the SWAT model for the Fulda catchment area is improved significantly. After calibration of the model for the past 20th century observed streamflow, the SWAT model is driven by high resolution climate data of the regional model REMO using the IPCC scenarios A1B, A2, and B1, to generate future runoff time series for the 21th century for the various sub-basins in the study area. In a second step flood time series HQ(a) are derived from the 21st century runoff time series (scenarios A1B, A2, and B1). Then these flood projections are extensively tested with regard to stationarity, homogeneity and statistical independence. All these tests indicate that the SWAT-predicted 21st-century trends in the flood regime are not significant. Within the projected time the members of the flood time series are proven to be stationary and independent events. Hence, the classical stationary approach of flood frequency analysis can still be used within the Fulda catchment area, notwithstanding the fact that some regional climate change has been predicted using the IPCC scenarios. It should be noted, however, that the present results are not transferable to other catchment areas. Finally a new method is presented that enables the calculation of extreme flood statistics, even if the flood time series is non-stationary and also if the latter exhibits short- and longterm persistence. This method, which is called Flood Series Maximum Analysis here, enables the calculation of maximum design floods for a given risk- or safety level and time period.

Online Learning of Non-stationary Sequences

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. The performance of each expert may change over time in a manner unknown to the learner. We formulate a class of universal learning algorithms for this problem by expressing them as simple Bayesian algorithms operating on models analogous to Hidden Markov Models (HMMs). We derive a new performance bound for such algorithms which is considerably simpler than existing bounds. The bound provides the basis for learning the rate at which the identity of the optimal expert switches over time. We find an analytic expression for the a priori resolution at which we need to learn the rate parameter. We extend our scalar switching-rate result to models of the switching-rate that are governed by a matrix of parameters, i.e. arbitrary homogeneous HMMs. We apply and examine our algorithm in the context of the problem of energy management in wireless networks. We analyze the new results in the framework of Information Theory.

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period.

Distributions on the simplex

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Randomization tests for ABAB designs : Comparing-data-divisionspecific and common distributions. 'Pruebas de aleatorizaci??n para dise??os ABAB : comparaci??n entre distribuciones espec??ficas y comunes'

Resumen tomado de la publicaci??n. Resumen tambi??n en ingl??s

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA167exam01pdf

Exam questions and solutions in PDF

MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files