Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations one needs an algorithm which for any given $N$ and a given compact four-dimensional manifold $M$ constructs all possible triangulations of $M$ with $\leq N$ simplices. Our first result is that such algorithm does not exist. Then we discuss recursion-theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four-dimensional manifold.Comment: 8 Pages, LaTex, PUPT-132

System of key performance indicators as a method for executive decision-making

Key performance indicators, KPI are a proven cutting-edge tool for process productivity and staff performance monitoring. Therefore, today it is possible to find the use of this tool in the most varied spheres and industries. However, the system implementation is a long and painstaking process, which requires financial, labor and time expenditures. But in case of its successful implementation, KPI technology will provide the balance of advantage for the company management and contribute to its growth. The article presents the selection mechanism of KPI system development and implementation methods. Using key performance indicators, the organization is able to manage the process and modify it, as well as define objectives for employees and motivate them to achieve their objectives. KPIs are based on measuring quantitative benefits. Control shall be based on comprehensive and reliable information about the company’s process productivity. This is the only way to take quick management decisions, make adjustments to the operation of processes that will contribute to the achievement of strategic objectives as a whole

Spin design of iron complexes on Fe-ZSM-5 zeolites

The spin state of iron ions in Fe-ZSM-5 zeolites can be purposefully varied by adsorption of gaseous probe molecules. The resulting Fe complexes with half-integer spin (, and ) can be reliably identified by electron paramagnetic resonance (EPR). A good correlation has been found between the concentration of surface sites active in low-temperature nitrous oxide decomposition and the concentration of low-spin () nitrosyl complexes of Fe formed after adsorption of NO molecules. Based on the analysis of the formation of such complexes under varying conditions, we conclude that these active sites contain a binuclear iron complex with S = 0 and three adsorbed NO molecules. An approach to investigate various Fe-containing sites in oxidation catalysts is discussed

Spin design of iron complexes on Fe-ZSM-5 zeolites

The spin state of iron ions in Fe-ZSM-5 zeolites can be purposefully varied by adsorption of gaseous probe molecules. The resulting Fe complexes with half-integer spin (, and ) can be reliably identified by electron paramagnetic resonance (EPR). A good correlation has been found between the concentration of surface sites active in low-temperature nitrous oxide decomposition and the concentration of low-spin () nitrosyl complexes of Fe formed after adsorption of NO molecules. Based on the analysis of the formation of such complexes under varying conditions, we conclude that these active sites contain a binuclear iron complex with S = 0 and three adsorbed NO molecules. An approach to investigate various Fe-containing sites in oxidation catalysts is discussed

Aerobic Co or Cu/NHPI-catalyzed oxidation of hydride siloxanes: Synthesis of siloxanols

A highly efficient preparative method for the synthesis of siloxanols based on aerobic Co(OAc)2 or Cu(OAc)2/NHPI-catalyzed oxidation of hydride siloxanes using "green", commercially available, simple inexpensive reagents and mild reaction conditions has been proposed. This is a general reaction for the synthesis of mono-, oligo- and polymeric siloxanols with various structures (linear, branched and cyclic). © 2018 The Royal Society of Chemistry