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- Marko Petkovsek
- J. Symb. Comput.
- 1992

Let K be a field of characteristic zero . We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations . Let KN denote the ring of all sequences over K, with addition and multiplication defined term-wise . Following Stanley (1980) we identify two sequences if… (More)

- Sergei A. Abramov, Marko Petkovsek
- J. Symb. Comput.
- 2002

We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. On the basis of this form we propose an algorithm which, given a rational function R, extracts a rational part F from the product of consecutive values of R: ∏n−1 k=n0 R(k) = F (n) ∏n−1 k=n0 V (k) where the… (More)

- Manuel Bronstein, Marko Petkovsek
- Theor. Comput. Sci.
- 1996

Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling… (More)

- Mireille Bousquet-Mélou, Marko Petkovsek
- Discrete Mathematics
- 2000

While in the univariate case solutions of linear recurrences with constant coe cients have rational generating functions we show that the multivariate case is much richer even though initial conditions have rational generating functions the corresponding solutions can have generating functions which are algebraic but not rational D nite but not algebraic… (More)

- Sergei A. Abramov, Manuel Bronstein, Marko Petkovsek
- ISSAC
- 1995

Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantages, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to… (More)

- Sergei A. Abramov, Marko Petkovsek
- ISSAC
- 2001

We present an algorithm which, given a hypergeometric term <i>T</i>(<i>n</i>), constructs hypergeometric terms <i>T</i><subscrpt>1</subscrpt>(<i>n</i>) and <i>T</i><subscrpt>2</subscrpt>(<i>n</i>) such that <i>T</i>(<i>n</i>) = <i>T</i><subscrpt>1</subscrpt>(<i>n</i> + 1) -<i>T</i><subscrpt>1</subscrpt>(<i>n</i>) + <i>T</i><subscrpt>2</subscrpt>(<i>n</i>),… (More)

- Damijan Miklavcic, Gorazd Pucihar, +8 authors Gregor Sersa
- Bioelectrochemistry
- 2005

Muscle contractions present the main source of unpleasant sensations for patients undergoing electrochemotherapy. The contractions are a consequence of high voltage pulse delivery. Relatively low repetition frequency of these pulses (1 Hz) results in separate muscle contractions associated with each single pulse that is delivered. It would be possible to… (More)

- Marko Puc, Selma Corovic, Karel Flisar, Marko Petkovsek, Janez Nastran, Damijan Miklavcic
- Bioelectrochemistry
- 2004

Electropermeabilization is a phenomenon that transiently increases permeability of the cell plasma membrane. In the state of high permeability, the plasma membrane allows ions, small and large molecules to be introduced into the cytoplasm, although the cell plasma membrane represents a considerable barrier for them in its normal state. Besides introduction… (More)

- Sergei A. Abramov, Marko Petkovsek
- ISSAC
- 1994

D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals (resp. sums) of hyperexponential functions. They are a subclass of Liouvillian solutions, and can be constructed by recursively finding hyperexponential solutions and reducing the order. Knowing d'Alembertian solutions of <italic>Ly =… (More)

- Mireille Bousquet-Mélou, Marko Petkovsek
- Theor. Comput. Sci.
- 2003

We consider planar lattice walks that start from a prescribed position, take their steps in a given finite subset of Z, and always stay in the quadrant x ≥ 0, y ≥ 0. We first give a criterion which guarantees that the length generating function of these walks is D-finite, that is, satisfies a linear differential equation with polynomial coefficients. This… (More)