Strutture numeriche, autoorganizzazione e senso del bello
Superconvergence for convection-diffusion problems with low regularity
Symetrie: Ano či ne?
Symmetry: Art and Science - 2004 Sixth Interdisciplinary Symmetry Congress and Exhibition of ISIS-Symmetry
Symmetry in Architecture
Systems of Proportion in Design and Architecture and their Relationship to Dynamical Systems Theory
The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation
Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.
The Geometry of History; 032147658
The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics
Tonality / Atonality, Order / Disorder or Order / New Order
Uniform error bounds for semi-discrete finite element solutions of evolutionary integral equations
In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem where A is an elliptic partial-differential operator and is positive, nonincreasing and log-convex on with . Error estimates are derived in the norm of , and some estimates for the first order time derivatives of the errors are also given.
Use of a differential evolution algorithm for the optimization of the heat radiation intensity
This article focuses on the heat radiation intensity optimization on the surface of an aluminium shell mould. The outer mould surface is heated by infrared heaters located above the mould and the inner mould surface is sprinkled with a special PVC powder. This is an economic way of producing artificial leathers in the automotive industry (e.g. the artificial leather on car dashboards). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity...
Věda o významných formách
Viscosity solutions to a new phase-field model for martensitic phase transformations
We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.
Visual Mathematics: A missing link in a Split Culture
Vzbuzení zájmu o aplikace matematiky
What is industrial mathematics?
Why quintic polynomial equations are not solvable in radicals
We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations , and . Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.
Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations
A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a comprehensive...