From resolvents to generalized equations and quasi-variational inequalities: existence and differentiability

We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of both mappings. We demonstrate that the directional differentiability of the solution map can be verified by using the directional differentiability of the single-valued operator and of the resolvent of the set-valued mapping. The result is applied to quasi-generalized equations in which we have an additional dependence of the solution within the set-valued part of the equation.

Application of generalized equations of finite difference method to computation of bent isotropic stretched and/or compressed plates of variable stiffness under elastic foundation

The computation of bent isotropic plates, stretched and/or compressed, is a topic widely explored in the literature from both experimental and numerical point of view. We expose in this work an application of the generalized equations of Finite difference method to that topic. The strength of the proposed method is the ability to reconstruct the approximate solution with respect of eventual discontinuities involved in the investigated function as well as its first and second derivatives, including the right-hand side of the equilibrium equation. It is worth mentioning that by opposition to finite element methods our method needs neither fictitious points nor a special condensation of grid. Well-known benchmarks are used in this work to illustrate the efficiency of our numerical and the high accuracy of calculation as well. A comparison of our results with those available in the literature also shows good agreement.

OPTICAL-ELECTRONIC INSTRUMENT FOR MEASURING THE RADIATION COEFFICIENT AND TEMPERATURE OF THE CONTROLLED OBJECT

The operating principle of optoelectronic instruments for measuring the temperature of the heated products based on the measurement of the radiation flux from the heated product, which depends on the temperature and emissivity of the surface material. The main error of such optocal-electronic devices is the methodological component, which is due to the variability of the radiation coefficient of the surface of the product material. The radiation coefficient of an object depends on the material, the surface state of the material, and the temperature. In the measurement process, it is difficult to take this dependence into account, since there are no exact analytical expressions of these dependencies. In practice, the radiation coefficient of the surface of material the product is determined approximately using reference books. For a more accurate determination of the radiation coefficient, a preliminary study is necessary, which requires more complex equipment than a device for measuring the radiation flux from a heated body. To solve this problem, there are empirical generalized equations of the functional dependences of the radiation coefficient. The article analyzes the errors in determining the radiation coefficient using generalized equations in comparison with experimental data. The analysis indicates that the error in determining the radiation coefficient can reach large values that may not meet the requirements of consumers. To improve the accuracy of measuring the temperature of the object, a device has been developed that implements the method of sample signals. The developed device predetermines the radiation coefficient of the measured product at a certain temperature and introduces a correction when measuring the temperature.

TOWARDS QUANTITATIVE FORECASTING OF SPECIES YIELDS WITH INCOMPLETE INFORMATION ON MODEL PARAMETERS

Predicting both the absolute and the relative abundance of species in a spatial patch is of paramount interest in areas like, agriculture, ecology and environmental science. The linear Lotka-Volterra generalized equations (LLVGE) serve for describing the dynamics of communities of species connected by negative as well as positive interspecific interactions. Here we particularize these LLVGE to the case of single trophic ecological communities, like mixtures of plants, with S >2 species. Thus, by estimating the LLVGE parameters from the yields in monoculture and biculture experiments, the LLVGE are able to produce decently accurate predictions for species yields. However, a common situation we face is that we don't know all the parameters appearing in the LLVGE. Indeed, for large values of S, only a fraction of the experiments necessary for estimating the model parameters is commonly carried out. We then analyze which quantitative predictions are possible with an incomplete knowledge of the parameters.

New non-perturbative de Sitter vacua in α′-complete cosmology

The α′-complete cosmology developed by Hohm and Zwiebach classifies the O(d, d; ℝ) invariant theories involving metric, b-field and dilaton that only depend on time, to all orders in α′. Some of these theories feature non-perturbative isotropic de Sitter vacua in the string frame, generated by the infinite number of higher-derivatives of O(d, d; ℝ) multiplets. Extending the isotropic ansatz, we construct stable and unstable non-perturbative de Sitter solutions in the string and Einstein frames. The generalized equations of motion admit new solutions, including anisotropic d + 1-dimensional metrics and non-vanishing b-field. In particular, we find dSn+1× Td−n geometries with constant dilaton, and also metrics with bounded scale factors in the spatial dimensions with non-trivial b-field. We discuss the stability and non-perturbative character of the solutions, as well as possible applications.