On the effect of d orbitals on relativistic bond-length contractions

5d AOs are found to diminish the usual relativistic bond-length contraction in some hydrides. This is shown to be a first-order effect, unrelated to the relativistic expansion of 5d AOs, by both the perturbative Dirac-Fock one-center expansion and Hartree-Fock-Slater methods. The latter method is used to investigate the chemical similarity of Zr and Hf.     

Evaluation of Cost Efficiency in Finnish Electricity Distribution

This paper describes the process of developing an approach to evaluating the cost-efficiency of Finnish electricity distribution companies based on Data Envelopment Analysis (DEA). The process consisted of three main stages (1) describing of the problem and exploring the key factors, (2) finding measurable quantities for the most essential factors, and (3) selecting the final model to be used in the regulation. Especially the selection of environmental variables, which allow the comparison of distribution companies operating in different environments, played a key role in the process. The selected model is used as a part of the regulation of distribution pricing.     

Dirichlet Forms,Poincaré Inequalities,and the Sobolev Spaces of Korevaar and Schoen

We answer a question of Jost on the validity of Poincaré inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.     

Comments on calculations of nuclear spin-spin coupling constants using the blinder operator

It is pointed out that the finite second-order hyperfine self-coupling energies, obtained by the Blinder operator, are unphysical and 10² times too large. The additional terms in the first-order matrix element are also unphysical. Therefore the Blinder operator gives no improvement over the simple delta function. The consequences on the recent calculations by Paviot and Hoarau and by Sänger and Voitländer are discussed.     

The standard model of quantum measurement theory: History and applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable to be measured is multiplied by some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their principal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.     

Remarks on separability of compound quantum systems and time reversal

A separability test for density matrices of compound quantum systems proposed recently by Peres is formulated in a manifestly basis independent way using antiunitary operators. We prove that the test amounts to a criterion for pure states, while it is known to fail to do so in the case of mixed states. An interesting connection with the operation of time reversal is thus exhibited.     

Measurement and probability in quantum mechanics

Measurement-theoretical foundations of quantum probabilities are investigated in the form of measurement statistics and a statistical ensemble interpretation of quantum mechanics.     

Solving some optimal control problems using the barrier penalty function method

In this paper we present a new approach to solve a two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary-value problems. The problem considered is to find a minimum of a functional with respect to the control variablesu. The minimized functional depends on control variables and state variablesx. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend onu.Our main idea is to replace this QP problem by its dual and then apply the barrier penalty method to this dual QP problem or to the primal one if it is in an appropriate form. As a result we obtain a problem approximating the original one. Its good property is the differentiable dependence of state variables with respect to the control variables. Furthermore, we propose a method for finding an approximate solution of a penalized lower-level problem if the optimal solution of the original QP problem is known. We apply the result obtained to some optimal shape design problems governed by the Dirichlet-Signorini boundary-value problem.This research was supported by the Academy of Finland and the Systems Research Institute of the Polish Academy of Sciences.     

On the quantum theory of sequential measurements

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations, repeatability, and ideality. The problem of the operational definition of continuous observables is briefly revisited, with a special emphasis on the localization observable. Finally, a brief overview is given of possible applications of the theory to various fields and problems in quantum physics.     

On compactness of the difference of composition operators

Let φ and ψ be analytic self-maps of the unit disc, and denote by C_φ and C_ψ the induced composition operators. The compactness and weak compactness of the difference T=C_φ−C_ψ are studied on H^p spaces of the unit disc and L^p spaces of the unit circle. It is shown that the compactness of T on H^p is independent of p∈[1,∞). The compactness of T on L¹ and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H¹ but non-compact on L¹. Other given results deal with L^∞, weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro.