A generalized skew information and uncertainty relation

A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and Z.Zhang. Finally we point out that Theorem 1 in {\it S.Luo and Q.Zhang, IEEE Trans.IT, Vol.50, pp.1778-1782 (2004)} is incorrect in general, by giving a simple counter-example.Comment: to appear in IEEE TI

Novel orthogonalization and biorthogonalization algorithms - Towards multistate multiconfiguration perturbation theory

Orthogonalization with the prerequisite of keeping several vectors fixed is examined. Explicit formulae are derived both for orthogonal and biorthogonal vector sets. Calculation of the inverse or square root of the entire overlap matrix is eliminated, allowing computational time reduction. In this special situation it is found sufficient to evaluate functions of matrices of the dimension matching the number of fixed vectors. The (bi)orthogonal sets find direct application in extending multiconfigurational perturbation theory to deal with multiple reference vectors

Development of e-Learning Modules for Teaching Energy for Sustainable World

Within the project ”Teaching Energy for Sustainable World” (SustEner) financed by the European Union nine practically oriented modules with remote experiments or interactive animation materials will be offered in a web based learning portal. Here the development and the operation of two modules titled ”Solar Powered Electric Vehicles” and ”Luminous Efficacy of Modern Light Sources” are described in some detail

Reduced-scaling correlation methods for the excited states of large molecules: implementation and benchmarks for the second-order algebraic-diagrammatic construction approach

A framework for the reduced-scaling implementation of excited-state correlation methods is presented. An algorithm is introduced to construct excitation-specific local domains, which include all the important molecular orbitals for the excitation as well as for the electron correlation. The orbital space dimensions of the resulting compact domains are further decreased utilizing our reduced-cost techniques developed previously [J. Chem. Phys. 148, 094111 (2018)] based on the natural auxiliary function and local natural orbital approaches. Additional methodological improvements for the evaluation of density matrices are also discussed. Benchmark calculations are presented at the second-order algebraic-diagrammatic construction level. Compared to our reduced-cost algorithm significant, up to 3-9-fold speedups are achieved even for systems of smaller than 100 atoms. At the same time the additional errors introduced by the domain approximations are highly acceptable being about 2-4 meV on the average. The presented reduced-scaling algorithm allows us to carry out correlated excited-state calculations using triple-zeta basis sets with diffuse functions for systems of up to 400 atoms or 13000 atomic orbitals in a matter of days using an 8-core processor