Seminars
Köbe-poliéderek "centrálása” 2
On the Package ReactionKinetics.wl
When investigating the deterministic and/or stochastic models of chemical reactions a large amount of calculations have to be carried out. The preliminary steps are creating and studying different graphs describing reactions. This involves the use of combinatorics and linear algebra. One is also interested if mass is conserved in a model or not. This can be decided using the methods of linear programming. Stationary points and stationary distributions are to be determined which means the solution of large polynomial equations. One has to solve (quite often: stiff) ordinary differential equations, simulate Markovian jump processes. Parameters of these processes are to be estimated based on measurements even in cases when not all the concentration time curves are known. This problem is implicit and highly nonlinear. Our package gives help to all these tasks arising in chemistry (atmospheric chemistry), biochemistry (modeling metabolism), chemical engineering (combustion), but the models of chemical reaction kinetics are used outside chemistry, as well. We show the problems and solution methods from the point of programming and also a series of applications. A comparison with other programs will also be presented. A detailed description and instructions for use will be found in our book: J. Tóth, A. L. Nagy, D. Papp: Reaction Kinetics: Exercises, Programs and Theorems. (Mathematica for deterministic and stochastic kinetics), Springer, 2018 (to appear). (Joint talk with A. L. Nagy and D. Papp.)
Cikloisok izoptikus görbéi
Recurrence of the vertex-reinforced jump process in two dimensions
Köbe-poliéderek "centrálása”
Conditional measure on the Brownian path and other random sets II.
Establishing and maintaining datbases of self-affine tiles
Conditional measure on the Brownian path and other random sets I.
Step-size coefficients for boundedness of linear multistep methods
Monotonicity or boundedness properties (e.g. strong-stability-preserving, total-variation-diminishing or total-variation-boundedness properties) for linear multistep methods (LMMs) can be guaranteed by imposing step-size restrictions on the methods. To describe these restrictions, one introduces the concept of step-size coefficient for monotonicity (SCM, also referred to as the strong-stability-preserving (SSP) coefficient) and its generalization, the step-size coefficient for boundedness (SCB coefficient). A LMM with larger SCM or SCB is more efficient. The computation of the maximum SCM for a particular LMM is straightforward, however, it is more challenging to decide whether a SCB exists, or determine if a given number is a SCB. Based on some recent theorems in the literature we present methods to find the exact optimal SCB for a LMM. As an illustration, we consider SCBs in the BDF, extrapolated BDF, and Adams--Bashforth families.