The Erdős–Faber–Lovász conjecture for the class of δEFL graphs

In this paper, we present the class of [Formula: see text] graphs and then prove a generalized statement of the Erdős–Faber–Lovász conjecture for this graph class. Then, the Erdős–Faber–Lovász conjecture follows for every graph in this class.

Numerical Investigation of Nonlinear Filtration Problems of High-Viscosity Fluids in Porous Media

We consider a steady process of filtration of the incompressible high-viscosity fluid, following non-linear filtration law. Generalized statement of this problem is formulated in the form of operator equation with monotone operator in Banach space. To solve the operator equation, we suggest iterative method that does not require the inversion of the original operator. Each step of the iterative process can essentially be reduced to the solution of the boundary-value problem for the Laplace operator. This method was realized numerically. The numerical experiments made for the model problems confirmed the efficiency of the iterative method.

Estimation of peak discharges of historical floods

There is no doubt that the hazard assessment of future floods, especially under consideration of recent environmental change, can be significantly improved by the consideration of historic flood events. While flood frequency inventories on local, regional and even European scale have already been developed and published, the estimation of their magnitudes indicated by discharges is still challenging. Such data are required due to significant human impacts on river channels and floodplains, though historic flood levels cannot be related to recent ones or recent discharges. Based on experiences from single local key studies, we present the general outline of an approach to estimate the discharge of the previous flood based on handed-down flood level and topographic data. The model for one-dimensional steady flow is based on the empirical Manning equation for the mean flow velocity. Background and potential sources of information, acceptable simplifications and data transformation for each element of the model equation are explained and discussed. Preliminary experiences regarding the accuracy of ±10% are documented, and potential approaches for the validation of individual estimations are given. A brief discussion of benefits and limitations, including a generalized statement on alternative approaches, concludes the review of the approach.

Numerical Method for Solving Variation Problems in Mathematical Physics

We consider one axisymmetric problem of the equilibrium position of a soft rotation shell. Generalized statement of this problem is formulated in the form of variational inequality with a pseudo-monotone operator in Banach space. To solve this variational inequality, we suggest the iterative method. This method was realized numerically. The numerical experiments made for the model problems confirmed the efficiency of the iterative method.

Estimation of peak discharges of historical floods

There is no doubt, that the hazard assessment of future floods especially under consideration of the recent environmental change can be significantly improved by the consideration of historic flood events. While flood frequency inventories on local, regional and even European scale are already developed and published, the estimation of their magnitudes indicated by discharges is still challenging. Such data are required due to significant human impact on river channels and floodplains though historic flood levels cannot be related to recent ones or recent discharges. Based on own experiences from single local key studies the general outline of an approach to estimate the discharge of the previous flood based on handed down flood level and topographic data is presented. The model for one-dimensional steady flow is based on the empirical Manning equation for the mean flow velocity. Background and potential sources of information, acceptable simplifications and data transformation for each element of the model-equation are explained and discussed. Preliminary experiences on the accuracy of ±10% are documented and potential approaches for the validation of individual estimations given. A brief discussion on benefits and limitations including a generalized statement on alternative approaches closes the review presentation of the approach.

On the Equilibrium Problem of a Soft Network Shell in the Presence of Several Point Loads

We consider a spatial equilibrium problem of a soft network shell in the presence of several external point loads concentrated at some pairwise distinct points. A generalized statement of the problem is formulated in the form of integral identity. Then we introduce an auxiliary problem with the right-hand side given by the delta function. For the auxiliary problem we are able to find the solution in an explicit form. Due to this, the generalized statement of the problem under consideration is reduced to finding the solution of the operator equation. We establish the properties of the operator of this equation (boundedness, continuity, monotonicity, and coercitivity), which makes it possible to apply known general results from the theory of monotone operatorsfor the proof of the existence theorem. It is proved that the set of solutions of the generalized problem is non-empty, convex, and closed.