We propose a new approach to the model reduction of biochemical reaction networks governed by various types of enzyme kinetics rate laws with non-autocatalytic reactions, each of which can be reversible or irreversible. This method extends the approach for model reduction previously proposed by Rao et al. which proceeds by the step-wise reduction in the number of complexes by Kron reduction of the weighted Laplacian corresponding to the complex graph of the network. The main idea in the current manuscript is based on rewriting the mathematical model of a reaction network as a model of a network consisting of linkage classes that contain more than one reaction. It is done by joining certain distinct linkage classes into a single linkage class by using the conservation laws of the network. We show that this adjustment improves the extent of applicability of the method proposed by Rao et al. We automate the entire reduction procedure using Matlab. We test our automated model reduction to two real-life reaction networks, namely, a model of neural stem cell regulation and a model of hedgehog signaling pathway. We apply our reduction approach to meaningfully reduce the number of complexes in the complex graph corresponding to these networks. When the number of species’ concentrations in the model of neural stem cell regulation is reduced by 33.33%, the difference between the dynamics of the original model and the reduced model, quantified by an error integral, is only 4.85%. Likewise, when the number of species’ concentrations is reduced by 33.33% in the model of hedgehog signaling pathway, the difference between the dynamics of the original model and the reduced model is only 6.59%.

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Results of corrosion resistance tests of different types of refractory materials (fusion cast baddeleyite-corundum, high-zirconium, corundum, and chromium-containing materials) in melts of borosilicate and phosphate glass used for vitrification of radioactive wastes are presented. It is shown that the fusion cast high-chromium refractory materials KhPL-85 and KhMG-5, both of which contain more than 80.0% Cr 2 O 3 , possess more than twice the corrosion resistance of the chromium-aluminum-zirconium refractory KhATs-30 (an analog of the refractory material ER 2161) and more than triple that of the baddeleyite-corundum refractories ER 1681 and ER 1711. High-chromium refractory materials may be considered promising candidates for use as the material of melters in plants for vitrification of radioactive wastes.Vitrification of radioactive wastes is a new and promising trend that supports the reprocessing and conversion of hot liquid radioactive wastes into a vitreious state safe for long-term storage. The industrial technology of vitrification of radioactive wastes is based on a process of electrofounding of glass from solutions of wastes, fluxing additions to directly fired glass-making electric kilns (ceramic melter) at temperatures up to 1150°C, and pouring of the vitreous product into thick-walled tanks made of corrosion-proof steel for immobilization and subsequent burial.The German plant Pamela was the first plant provided with a ceramic melter at which highly active wastes were subjected to vitrification [1]. Industrial plants that subject radioactive wastes to vitrification on the basis of a ceramic melter are now functioning in Russia, the United States, and Japan.The first domestic technology of vitrification of highly active liquid radioactive wastes on an industrial scale was implemented in 1987 at FGUP PO Mayak [2]. Three EP-500 furnaces were in operation at this enterprise from 1987 to 2006. A fourth furnace (EP-500/4 type) with a three-year service life has been in operation since 2007; construction of another two furances that would be capable of vitrification and reduction to safe state of around 60 million C of radioactive wastes is planned to be completed by 2012. Obviously, the demand for vitrification furnaces can be expected to increase in the furture with the development of the atomic energy complex in Russia and the growth in the volume of radioactive wastes.A new generation of furnaces of enhanced reliability that satisfy the requirements of ecological safety and possess a service life of up to ten years are now under development. In view of the rather high cost of such furnaces (the EP-500/3 furnace cost more than US$17,000,000 in 2001) and the requirements of maximal reliability and safety, the refractory materials used in the lining of the furnace must exhibit maximal corrosion resistance to the action of molten glass [3].In the EP-500 the refractory brickwork of the furnace that comes into contact with the glass melt is produced from Bk-33 baddeleyite-corundum refractory at OAO Shcherbinsk...