Dixmier traces and some applications to noncommutative geometry

This is a survey of some recent advances in the theory of singular traces in which the authors have played some part and which were inspired by questions raised by the book of Alain Connes (Noncommutative Geometry, Academic Press 1994). There are some original proofs and ideas but most of the results have appeared elsewhere. Detailed information on the contents is contained in the Introduction.Comment: To appear in Russian Mathematical Surveys (in Russian). New version corrects Latex problems, minor errors and reference

The caloron correspondence and higher string classes for loop groups

We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $\Omega G$-bundles on $M$, where $\Omega G$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $\Omega G$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.Comment: 21 pages. Author addresses adde

System Energy Assessment (SEA), Defining a Standard Measure of EROI for Energy Businesses as Whole Systems

A more objective method for measuring the energy needs of businesses, System Energy Assessment (SEA), identifies the natural boundaries of businesses as self-managing net-energy systems, of controlled and self-managing parts. The method is demonstrated using a model Wind Farm case study, and applied to defining a true physical measure of its energy productivity for society (EROI-S), the global ratio of energy produced to energy cost. The traceable needs of business technology are combined with assignable energy needs for all other operating services. That serves to correct a large natural gap in energy use information. Current methods count traceable energy receipts for technology use. Self-managing services employed by businesses outsource their own energy needs to operate, and leave no records to trace. Those uncounted energy demands are often 80% of the total embodied energy of business end products. The scale of this "dark energy" was discovered from differing global accounts, and corrected so the average energy cost per dollar for businesses would equal the world average energy use per dollar of GDP. Presently the energy needs of paid services that outsource their own energy needs are counted for lack of information to be "0". Our default assumption is to treat them as "average". The result is to assign total energy use and impacts to the demand for energy services, for a "Scope 4" GHG assessment level. Counting only the energy uses of technology understates the energy needs of business services, as if services were more energy efficient than technology. The result confirms a similar finding by Hall et. al. in 1981 [9]. We use exhaustive search for what a business needs to operate as a whole, locating a natural physical boundary for its working parts, to define businesses as physical rather than statistical subjects of science. :measurement, natural systemsComment: 33 pages, 15 figures, accepted as part of pending special issue on EROI organized by Charlie Hall for Sustainability (MDPI

Credit risk rating at large U.S. banks

Large banks use internally developed credit rating systems to differentiate the riskiness of their commercial loans. Internal ratings are an essential ingredient of effective credit risk management for such banks, whose commercial borrowers may number in the tens of thousands. This article describes these rating systems, how their design varies across institutions, and how they are used in risk management. The article also outlines conceptual and practical difficulties currently faced by banks in achieving accurate and consistent ratings and describes ways in which some institutions have attempted to deal with these difficulties. This article is based on a detailed review of policy documents and internal management reports from the fifty largest U.S. bank holding companies and interviews by the authors at a selection of these institutions.Credit ratings ; Risk

Amino acids and amino sugars in calcified tissues of portunid crabs

Amino acid and amino sugar in calcified tissues of portunid crab