This essay describes the development of groups used for the specification of symmetries from ordinary and magnetic point groups to Fedorov and magnetic space groups, as well as other varieties of groups useful in the study of symmetric objects. In particular, we consider the problem of some incorrectness in Vol. A of the International Tables for Crystallography. Some results of tensor calculus ...

We define a set of orthogonal functions on the complex projective space CPN−1, and compute their Clebsch-Gordan coefficients as well as a large class of 6–j symbols. We also provide all the needed formulae for the generation of high-temperature expansions for U(N)-invariant spin models defined on CPN−1.

In this paper twelve different empirical resistance coefficients expressed in terms of Manning's roughness are used apiece in seventeen known compositing methods. The data obtained from ten different cross-sections of the Sefidrood River, Iran, are used for the evaluation of the empiricalformulas. The present case-study is selected from a reach with gravel bed topology. Then no remarkable bed f...

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, give...

Heat and vapour convective surface coefficients are required in practically all heat and vapour transport calculations. In building envelope research, such coefficients are often assumed constants for a set of conditions. Heat transfer surface coefficients are often determined using empirical correlations based on measurements of different geometry and flows. Vapour transfer surface coefficient...

Polydimethylsiloxane (PDMS) is commonly used as the coated polymer in the solid phase microextraction (SPME) technique. In this study, the partition coefficients of organic compounds between SPME/PDMS and the aqueous solution were compiled from the literature sources. The correlation analysis for partition coefficients was conducted to interpret the effect of their physicochemical properties an...