We survey mathematical models of the fluid flow in porous media based on quasilinear parabolic partial differential equations. We focus on singular and/or degenerate parabolic equations, which are suitable for modeling of turbulent filtration such as groundwater flow trough gravel and/o...

Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool to an efficient implementation is a local evaluation of the approximated gradients together with sparsity of the resulting Hessian matrix....

We deal with efficient techniques for numerical simulation of the incompressible fluid flow based on the Navier–Stokes equations discretized using the isogeometric analysis approach. Typically, the most time-consuming part of the simulation is solving the large saddle-point type linear systems ar...

For a class of objects with a well-defined isomorphism relation the isomorphism problem asks to determine the algorithmic complexity of the decision whether two given objects are, or are not, isomorphic. Theorems by Steinitz (1916), Whitney (1933) and Mani (1971) show that the isom...

Possibilities of distance teaching of geometry at different types of schools and levels of education. Experience with the creation of materials and the method of passing information in the field of geometry in order to develop discussion and exchange of experience in this field.

The study of technical practice areas is part of the teaching at various technical faculties. The aim of this article is to present and offer materials created in the Geogebra program, which were created as part of lectures to support full-time teaching, but especially for...

This paper is devoted to the problem of solving the steady incompressible Navier–Stokes equations discretized by the Galerkin method on the spaces generated by the B-spline/NURBS basis functions, which is called isogeometric analysis. Two pressure-correction methods are presented for the sol...

We construct a polynomial-time algorithm that, for a graph X with 4p We construct a polynomial-time algorithm that for a graph X with 4p vertices (p is prime), finds (if any) a Cayley representation of X over the group C2 × C2 × Cp. This result, together with&#x...

The nonlinear second order ordinary differential equation u''(x) + m^2 u(x) + g(x, u(x)) = f(x) , x in [0, p] , u(0) = u(p) = 0 is investigated in this article. We suppose that the nonlinearity g is unbounded and satisfies an ALP type condition. We prove...

The purpose of our work is to develop an automatic shape optimization tool for runner wheel blades in reaction water turbines, especially in Kaplan turbines. The fluid flow is simulated using an in-house incompressible turbulent flow solver based on recently introduced isogeometric anal...

There are many methods and approaches to solving convection– diffusion problems. For those who want to solve such problems the situation is very confusing and it is very difficult to choose the right method. The aim of this short overview is to provide basic guidelines an...

This paper is focused on multivariate estimation of density and distribution function by nonparametric kernel approach. The main goal is to describe univariate and multivariate nonparametric kernel estimation using selected kernel functions and smoothing parameters including a real application. The&#x...

Outliers can significantly impact data summarization results and data analysis across all types of data analysis. Identifying outliers in multidimensional data is, therefore, one of the key approaches in data preprocessing. across all types of data analysis. In this article, we present ...

This paper describes various representations of the space of planes. The main focus is on the plane space representation in the symmetry plane detection in E3 where many candidate planes for many pairs of points of the given object are created and then the most often ...

The paper deals with whether the Money Flow Index (MFI) can still be used successfully for trading, and whether the parameters recommended in the literature are the best that an investor can use. Simulations in randomized time interval for the largest companies in the S&P&...

This paper deals with the Relative Strength Index (RSI), a popular oscillator. It answers the question whether – almost 40 years after its publication – the RSI can be still useful in trading. To answer this question, we compare four strategies: RSI with recommended parameters...

The paper presents one of the possible methodologies for comparing two time series by estimating the probability that both series will increase or decrease (in probability) synchronously. This procedure is analogous to the specific measures of dependence (concordance) between random variables...