Inversion of analytically perturbed linear operators that are singular at the origin

Let H and K be Hilbert spaces and for each z∈C let A(z)∈L(H,K) be a bounded but not necessarily compact linear map with A(z) analytic on a region |z|<a. If A(0) is singular we find conditions under which A⁻¹(z) is well defined on some region 0<|z|<b by a convergent Laurent series with a finite order pole at the origin. We show that by changing to a standard Sobolev topology the method extends to closed unbounded linear operators and also that it can be used in Banach spaces where complementation of certain closed subspaces is possible. Our method is illustrated with several key examples.²     

On Nonlinear Operator Approximation with Preassigned Accuracy

In this paper, we provide a state-of-the-art survey of some recent methods in nonlinear operator approximation theory and its applications. We give existence theorems for approximating operators. and discuss corresponding numerical schemes. The new results are natural but very specific extensions of known techniques to the so-called realistic operator approximation.     

Copulas with maximum entropy

We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration. Finally, we discuss the numerical calculations for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall.     

Textilindustrie

Ohne Zusammenfassung     

Optimal Recursive Estimation of Raw Data

We present a new approach to the optimal estimation of random vectors. The approach is based on a combination of a specific iterative procedure and the solution of a best approximation problem with a polynomial approximant. We show that the combination of these new techniques allow us to build a computationally effective and flexible estimator. The strict justification of the proposed technique is provided. This work was supported by the Australian Research Council under the ARC Large Grant Scheme.     

Optimising organic ionic plastic crystal electrolyte for all solid-state and higher than ambient temperature lithium batteries

Organic ionic plastic crystal (OIPC) electrolytes are among the key enabling materials for solid-state and higher than ambient temperature lithium batteries. This work overviews some of the parameter studies on the Li|OIPC interface using lithium symmetrical cells as well as the optimisation and performance of Li|OIPC|LiFePO₄ cells. The effects of temperature and electrolyte thickness on the cycle performance of the lithium symmetrical cell, particularly with respect to the interfacial and bulk resistances, are demonstrated. Whilst temperature change substantially alters both the interfacial and bulk resistance, changing the electrolyte thickness predominantly changes the bulk resistance only. In addition, an upper limit of the current density is demonstrated, above which irreversible processes related to electrolyte decomposition take place. Here, we demonstrate an excellent discharge capacity attained on LiFePO₄|10 mol% LiNTf₂-doped [C₂mpyr][NTf₂]|Li cell, reaching 126 mAh g^-1 at 50 °C (when the electrolyte is in its solid form) and 153 mAh g^-1 at 80 °C (when the electrolyte is in its liquid form). Most remarkably, at high temperature operation, the capacity retention at long cycles and high current is excellent with only a slight (3%) drop in discharge capacity upon increasing the current from 0.2 C to 0.5 C. These results highlight the real prospects for developing a lithium battery with high temperature performance that easily surpasses that achievable with even the best contemporary lithium-ion technology.