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Algorithms for Solving Darcian Flow in Structured Porous Media
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
This paper presents several algorithms that were implemented in DRUtES [1], a new open source project. DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual ...
Non-Hermitian Star-shaped Quantum Graphs
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowedwith certain specific, manifestly ...
Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and ...
Inherited Properties of Effect Algebras Preserved by Isomorphisms
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other ...
Spectral Singularities do not Correspond to Bound States in the Continuum
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We show that, contrary to a claim made in arXiv:1011.0645, the von Neumann-Winger bound states that lie in the continuum of the scattering states are fundamentally different from Naimark’s spectral singularities.
Emmy Noether and Linear Evolution Equations
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have ...
On an Algorithm for Multiperiodic Words
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We consider an algorithm by Tijdeman and Zamboni constructing a word of length k thathas periods p1, . . . , pr, and the richest possible alphabet. We show that this algorithm can be easilystated and its correctness briefly ...
LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference ...
ITINERARIES INDUCED BY EXCHANGE OF TWO INTERVALS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We focus on the exchange T of two intervals with an irrational slope α. For a general subinterval I of the domain of T, the first return time to I takes three values. We describe the structure of the set of return itineraries ...
MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
We show that in any generalized effect algebra (G;⊕, 0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;⊕, 0), called a summability block. If G is lattice ordered, then every summability ...