The theorem on existence of singular solutions to nonlinear equations

The aim of this paper is to present some applications of pregularity theory to investigations of nonlinear multivalued mappings. The main result addresses to the problem of existence of solutions to nonlinear equations in the degenerate case when the linear part is singular at the considered initial point. We formulate conditions for existence of solutions of equation F(x) = 0 when first p - 1 derivatives of F are singular

New properties of scalar field dynamics in brane isotropic cosmological models

Several aspects of scalar field dynamics on a brane which differs from corresponding regimes in the standard cosmology are investigated. We consider asymptotic solution near a singularity, condition for inflation and bounces and some detail of chaotic behavior in the brane model. Each results are compared with those known in the standard cosmology.Comment: 13 pages with 2 eps figures, submitted to Astronomy Letter

igh-order extremal principles and P-factor penalty function method for solving irregular optimization problems

There is given a description of the solution set to p-regular equality - constrained optimization problems. Based on the apparatus of factor-operators P-order conditions for optimality are presented. The method for solving irregular optimization problems is proposed

Seafloor massive sulfides from mid-ocean ridges: Exploring the causes of their geochemical variability with multivariate analysis

The neovolcanic zones of mid-ocean ridges are host to seawater-derived hydrothermal systems forming seafloor massive sulfide (SMS) deposits. These deposits have high concentrations of base metals and potentially economic enrichment of a wide range of trace elements. The factors controlling this enrichment are currently poorly understood. We have investigated the main factors controlling SMS compositional variability through robust principal component analysis and robust factor analysis of published and newly obtained bulk geochemical data for samples collected from SMS deposits worldwide. We found that a large part of the observed variability is produced by a combination of three independent factors, which are interpreted to reflect (in order of importance): (1) the temperature of deposition, (2) the ridge spreading rate, and (3) zone refining. The first and the third factors are mostly related to processes operating near the seafloor, such as conductive cooling, mixing of the hydrothermal fluids with seawater and metal remobilization, and determine the relative proportions of the main minerals and, thus, of Cu and Zn (Co, Se, Sb, Pb). The ridge spreading rate influences the structure of the oceanic lithosphere, which exerts a major control on the length and depth of the hydrothermal convection cell and on the rock-to-water ratios in the reaction zone, which in turn control the behavior of the precious metals Au and Ag and elements including Ni (Mo, Se). Despite the obvious role of substrate rocks as metal sources, their composition (specifically mafic vs. ultramafic) does not emerge as a statistically significant independent factor

Potential Routes for Thermochemical Biorefineries

This critical review focuses on potential routes for the multi-production of chemicals and fuels in the framework of thermochemical biorefineries. The up-to-date research and development in this field has been limited to BTL/G (biomass-to-liquids/gases) studies, where biomass-derived synthesis gas (syngas) is converted into a single product with/without the co-production of electricity and heat. Simultaneously, the interest on biorefineries is growing but mostly refers to the biochemical processing of biomass. However, thermochemical biorefineries (multi-product plants using thermo-chemical processing of biomass) are still the subject of few studies. This scarcity of studies could be attributed to the limitations of current designs of BTL/G for multi-production and the limited number of considered routes for syngas conversion. The use of a platform chemical (an intermediate) brings new opportunities to the design of process concepts, since unlike BTL/G processes they are not restricted to the conversion of syngas in a single-reaction system. Most of the routes presented here are based on old-fashioned and new routes for the processing of coal- and natural-gas-derived syngas, but they have been re-thought for the use of biomass and the multi-production plants (thermochemical biorefinery). The considered platform chemicals are methanol, DME, and ethanol, which are the common products from syngas in BTL/G studies. Important keys are given for the integration of reviewed routes into the design of thermochemical biorefineries, in particular for the selection of the mix of co-products, as well as for the sustainability (co-feeding, CO2 capture, and negative emissions).Ministerio de Educación FPU Program (AP2010-0119)Ministerio de Economía y Competitividad ENE2012-3159