44 research outputs found
On a generalisation of the Banach indicatrix theorem
We prove that for any regulated function
and the infimum of the
total variations of functions approximating with accuracy is equal
where is the number of
times that crosses the interval $[y,y+c].
Spectral parameter power series method for discontinuous coefficients
Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We
show that a general solution (in the weak sense) of the equation (pu')'+qu =
zru on (a,b) can be constructed in terms of power series of the spectral
parameter z. The series converge uniformly on [a,b] and the corresponding
coefficients are constructed by means of a simple recursive procedure. We use
this representation to solve different types of eigenvalue problems. Several
numerical tests are discussed
The probability of non-confluent systems
We show how to provide a structure of probability space to the set of
execution traces on a non-confluent abstract rewrite system, by defining a
variant of a Lebesgue measure on the space of traces. Then, we show how to use
this probability space to transform a non-deterministic calculus into a
probabilistic one. We use as example Lambda+, a recently introduced calculus
defined through type isomorphisms.Comment: In Proceedings DCM 2013, arXiv:1403.768