Estimation of the mean of a univariate normal distribution when the variance is not known

We consider the problem of estimating the first k coefficients in a regression equation with k+1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We generalize this estimator to the case where the unknown variance is estimated by least squares and find that main properties of the Laplace estimator only change marginally. Therefore we recommend the neutral Laplace estimator to be used in practice

Некоторые эквивалентности в линейном оценивании

Under normality, the Bayesian estimation problem, the best linear unbiased estimation problem, and the restricted least-squares problem\u3cbr/\u3eare all equivalent. As a result we need not compute pseudo-inverses and\u3cbr/\u3eother complicated functions, which will be impossible for large sparse systems. Instead, by reorganizing the inputs, we can rewrite the system as a new\u3cbr/\u3ebut equivalent system which can be solved by ordinary least-squares methods

Асимптотическая сложность оценки по столкновениям для решения линейных систем

An analysis of the complexity of the collisions estimator is carried out in the Neumann–Ulam adjoint scheme for solving sets of linear algebraic equations. It is shown that the stochastic method considered has not only a better asymptotic order of complexity than iterative methods, but, in some cases, is asymptotically optimal. For example, the indicated optimality property appears in sets of grid\u3cbr/\u3eequations for certain boundary value problems of mathematical physics

Battery Modeling: A Versatile Tool to Design Advanced Battery Management Systems

Fundamental physical and (electro) chemical principles of rechargeable battery operation form the basis of the electronic network models developed for Nickel-based aqueous battery systems, including Nickel Metal Hydride (NiMH), and non-aqueous battery systems, such as the well-known Li-ion. Refined equivalent network circuits for both systems represent the main contribution of this paper. These electronic network models describe the behavior of batteries during normal operation and during over (dis) charging in the case of the aqueous battery systems. This makes it possible to visualize the various reaction pathways, including convention and pulse (dis) charge behavior and for example, the self-discharge performance

Adaptive thermal modeling of rechargeable batteries for advanced automotive battery management systems

Proper functioning of secondary (rechargeable) batteries is of primary importance for any electrical vehicle, especially for Full Electrical Vehicles (FEV). One of the challenging problems arising when large battery packs are used in modern FEV and Hybrid Vehicles (HEV) is the thermal management. The Battery Management System (BMS) should be able to predict changes in the temperature of the battery and intervene if necessary. Simple and exact model describing the thermal behaviour of the battery pack is therefore required. However, the performance of the batteries deteriorates during the cycle life, in particular the capacity fades and impedance grows, leading to changes in thermal behaviour. The ageing of batteries is a complex process depending on calendar time, intensity of usage, operation regime and temperature. Forecasting the ageing is complicated and unreliable procedure. Advanced BMS must, therefore, adapt to the ageing of the battery. Algorithms providing adaptive determination of capacity fade and impedance increase have been previously developed by members of Energy Materials and Devices (EMD) group. Combination of these algorithms with classical models of thermal behaviour of the battery lead to concept of adaptive thermal modelling of the battery (packs). BMS equipped with adaptive thermal model is able to predict battery temperature evolution and apply preventive cooling when necessary, thus reducing wear of the battery. Application of such BMS can significantly improve durability and performance of FEV and HEV facilitating their mass production

Tolerance of Cheating: An Analysis Across Countries

Cheating is a serious problem in many countries. The cheater gets higher marks than deserved, thus reducing the efficiency of a country's educational system. In this study, the authors did not ask if and how often the student had cheated, but rather what the student's opinion was about a cheating situation. They investigated whether attitudes differ among students in Russia, the Netherlands, Israel, and the United States and conclude that attitudes toward cheating differ considerably between these countries. They offer various explanations of this phenomenon. In addition, they find that the student's attitude toward cheating depends on the student's educational level (high school, undergraduate, postgraduate). Finally, they show that the data from the sample can be aggregated in a natural and elegant way, and they suggest a tolerance-of-cheating index for each country

Modeling all-solid-state Li-ion batteries

A mathematical model for all-solid-state Li-ion batteries is presented. The model includes the charge transfer kinetics at the electrode/electrolyte interface, diffusion of lithium in the intercalation electrode, and diffusion and migration of ions in the electrolyte. The model has been applied to the experimental data taken from a 10 µAh planar thin-film all-solid-state Li-ion battery, produced by radio frequency magnetron sputtering. This battery consists of a 320 nm thick polycrystalline LiCoO2 cathode and a metallic Li anode separated by 1.5 µm Li3PO4 solid-state electrolyte. Such thin-film batteries are nowadays often employed as power sources for various types of autonomous devices, including wireless sensor nodes and medical implants. Mathematical modeling is an important tool to describe the performance of these batteries in these applications. The model predictions agree well with the galvanostatically measured voltage profiles. The simulations show that the transport limitations in the solid-state electrolyte are considerable and amounts to at least half of the total overpotential. This contribution becomes even larger when the current density reaches 0.5 mA cm-2 or higher. It is concluded from the simulations that significant concentration gradients develop in both the positive electrode and the solid-state electrolyte during a high current (dis)charge

Sodium-ion battery materials and electrochemical properties reviewed

The demand for electrochemical energy storage technologies is rapidly increasing due to the proliferation of renewable energy sources and the emerging markets of grid- scale battery applications. The properties of batteries and electrochemical energy storage (EES) technologies ideal for most of these applications, yet, faced with resource constraints, the ability of current lithium-ion batteries (LIB) to match this overwhelming demand is uncertain. Sodium-ion batteries (SIB) are a novel class of batteries with similar performance characteristics to LIB. Since they are composed of earth abundant elements, cheaper and utility scale battery modules can be assembled. As a result of the learning curve in LIB technology, a phenomenal progression in material development has been realised in the SIB concept. In this SIB review, various innovative strategies used in material development, as well as the electrochemical properties of possible anode, cathode and electrolyte combinations are unravelled. Attractive performance characteristics are herein evidenced, based on comparative gravimetric and volumetric energy densities to state-of-the-art LIB. Furthermore, opportunities and challenges towards commercialization are herein discussed. Combined with more industrial adaptations, the commercial prospects of SIB look promising and this challenging new technology is set to play a major role in grid-scale EES applications