Contents
Contents
Convergence and stability constant of the theta-method
The Euler methods are the most popular, simplest and widely used methods for the solution of the Cauchy problem for the first order ODE. The simplest and usual generalization of these methods are the so called theta-methods (notated also as -methods), which are, in fact, the convex linear combination of the two basic variants of the Euler methods, namely of the explicit Euler method (EEM) and of the implicit Euler method (IEM). This family of the methods is well-known and it is introduced almost...
Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability
In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problem are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.
Counting triangles that share their vertices with the unit -cube
This paper is about -triangles, which are the simplest nontrivial examples of -polytopes: convex hulls of a subset of vertices of the unit -cube . We consider the subclasses of right -triangles, and acute -triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of .
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¿Cuál es el papel del Álgebra en la Matemática Aplicada?.
Detection codes in railway interlocking systems
This paper describes a model of influence of random errors on the safety of the communication. The role of the communication in railway safety is specified. To ensure a safe communication, using of safety code is important. The most important parameter of the safety code is the maximal value of the probability of undetected error. Problems related with computing of this value are outlined in the article. As a model for the information transmission the binary symmetrical channel is introduced. ...
Differential algebraic equations of Filippov type
We will study discontinuous dynamical systems of Filippov-type. Mathematically, Filippov-type systems are defined as a set of first-order differential equations with discontinuous right-hand side. These systems arise in various applications, e.g. in control theory (so called relay feedback systems), in chemical engineering (an ideal gas--liquid system), or in biology (predator-prey models). We will show the way how to extend these models by a set of algebraic equations and then study the resulting...
Dimension reduction for incompressible pipe and open channel flow including friction
We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompressible Navier-Stokes equations under shallow water assumptions with prescribed "well-suited" boundary conditions.
Diskuse o užitečnosti matematiky
Dynamic contact problems in bone neoplasm analyses and the primal-dual active set (PDAS) method
In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful methods and efficient algorithms for their solutions. Because the geometry of the system of loaded and possible fractured bones with enlarged neoplasms changes in time, the corresponding mathematical models of tumor's and cyst's evolutions lead to the coupled free boundary problems and the dynamic...
Enumeration in musical theory.
Escher ako matematik. Rozhovor s N. G. de Bruijnom a Hendrikom Lenstrom
Factorization makes fast Walsh, PONS and other Hadamard-like transforms easy
A simple device, based on the factorization of invertible matrix polynomials, enabling to identify the possibility of fast implementation of linear transforms is presented. Its applicability is demonstrated in the case of Hadamard matrices and their generalization, Hadamard matrix polynomials.
Fast optical tracking of diffusion in time-dependent environment of brain extracellular space
An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability that occur,...
Finite element analysis for a regularized variational inequality of the second kind
In this paper, we investigate the a priori and the a posteriori error analysis for the finite element approximation to a regularization version of the variational inequality of the second kind. We prove the abstract optimal error estimates in the - and -norms, respectively, and also derive the optimal order error estimate in the -norm under the strongly regular triangulation condition. Moreover, some residual–based a posteriori error estimators are established, which can provide the global upper...
Finite element modelling of flow and temperature regime in shallow lakes
A two-dimensional depth-averaged flow and temperature model was applied to study the circulation patterns in the Oder (Szczecin) Lagoon located on the border between Germany and Poland. The system of shallow water and temperature evolution equations is discretized with the modified Utnes scheme [4], which is characterized by a semi-decoupling algorithm. The continuity equation is rearranged to Helmholtz equation form. The upwinding Tabata method [3] is used to approximate convective terms. Averaged...