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- Adam Doliwa
- 1999

It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour-type reduction of the fundamental transformation of quadrilateral lattices is found as well, and superposition of the Ribaucour transformations is presented in the vectorial… (More)

- Adam Doliwa
- 1997

The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the discrete version of the generalized Toda equation.

- Adam Doliwa, Paolo Santini, Manuel Mañas
- 1997

Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x : Z −→ R , N ≤ M , whose elementary quadrilaterals are planar. Our investigation is based on the discrete analogue of the theory of the… (More)

- Adam Doliwa
- 2008

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformation of the Koenigs lattice and we show permutability of superpositions of such transformations, thus proving integrability… (More)

- Adam Doliwa, Susana Santoyo, Pilar Ygartua
- Skin pharmacology and applied skin physiology
- 2001

The interactions between piroxicam (Px) and hydroxypropyl-beta-cyclodextrin (HPbetaCD) were thoroughly investigated both in solution and the solid state. The solubility studies have demonstrated the formation of a Px:HPbetaCD inclusion complex with 1:1 stoichiometry. The addition of propylene glycol to the medium produced less stable complexes, revealing… (More)

- Adam Doliwa, Susana Santoyo, Miguel Ángel Campanero, Pilar Ygartua
- Journal of pharmaceutical and biomedical analysis
- 2001

A direct, very sensitive, simple and rapid high-performance liquid chromatographic (HPLC) method for the determination of piroxicam, with tenoxicam as internal standard, has been developed and validated. Samples were chromatographed on a 5 microm Scharlau C(18) column. The mobile phase was a mixture of acetonitrile-acetic acid 4% (pH 2.8) (45:55, v/v).… (More)

- Adam Doliwa
- 2006

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa’s discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projectivegeometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corresponding theta functions. We also present… (More)

- Adam Doliwa
- 2008

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plücker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Moutard transformation, it is constructed… (More)

- Adam Doliwa, P . Grinevich, Maciej Nieszporski, Paolo Santini
- 2008

We introduce the sub-lattice approach, a procedure to generate, from a given integrable lattice, a sub-lattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sub-lattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in… (More)

Abstract. We review recent results on asymptotic lattices and their integrable reductions. We present the theory of general asymptotic lattices in R together with the corresponding theory of their Darboux-type transformations. Then we study the discrete analogues of the Bianchi surfaces and their transformations. Finally, we present the corresponding theory… (More)