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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)
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)
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)
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)
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)
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)
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)