Combinatorial Properties of Finite Models

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite presentation). Extending classical work of Rado (for the random graph), we find a finite presentation for each of the following classes: homogeneous undirected graphs, homogeneous tournaments and homogeneous partially ordered sets. We also give a finite presentation of the rational Urysohn metric space and some homogeneous directed graphs. We survey well known structures that are finitely presented. We focus on structures endowed with natural partial orders and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism orders for various combinatorial objects. We give a new combinatorial proof of the existence of embedding-universal objects for homomorphism-defined classes of structures. This relates countable embedding-universal structures to homomorphism dualities (finite homomorphism-universal structures) and Urysohn metric spaces. Our explicit construction also allows us to show several properties of these structures.Comment: PhD thesis, unofficial version (missing apple font

Relations Between Graphs

Given two graphs G and H, we ask under which conditions there is a relation R that generates the edges of H given the structure of graph G. This construction can be seen as a form of multihomomorphism. It generalizes surjective homomorphisms of graphs and naturally leads to notions of R-retractions, R-cores, and R-cocores of graphs. Both R-cores and R-cocores of graphs are unique up to isomorphism and can be computed in polynomial time.Comment: accepted by Ars Mathematica Contemporane

Determination of retinyl palmitate in ointment by HPLC with diode array detection

A simple and rapid HPLC with diode array detection method was developed for the determination of retinyl palmitate present together with other active substances in an ointment. Chromatographic separation was performed on 100 RP-18 Lichrospher column of particle size 5 μm. The mobile phase was methanol:water (98:2, v/v) and flow rate was 2.0 mL/min in isocratic mode. Samples were analyzed for 30 min. Spectophotometric detection was conducted at 325 nm. Under these conditions, the method featured high sensitivity, good precision and comparability of results as proven by the method validation and statistical analysis of the results. The limits of detection and determination were 0.4317 mg/100 mL and 1.3081 mg/100 mL, respectively, recovery values were measured at three levels 80%, 100% and 120% and yielded 101.05%, 101.34% and 100.43%, respectively. The linearity range was checked from 2 mg/100 mL to 10 mg/100 mL. The precision and inter-day precision of the method was expressed by relative standard deviation value and did not exceed 1.68%

Quantification of active pharmaceutical ingredients in commercially available poly pharmaceutical tablets by means of DSC

Differential scanning calorimetry is the first line technique indispensable for industrial quality controllaboratories and, next to many routine applications, could be used in quantitative assays. For this purpose, a relationship between the signal value of analyte (enthalpy change ΔH) and its concentration in the matrix isused. However, there are several limitations of its application, concerning solid state interactions between APIs, other APIs and/or coexisting excipients. With respect to their physical properties, it is known that amorphization state and/or permanent particle deformation can produce relatively large areas of interparticle contact and thus high particle-particle bonding forces. Finally, it may affect the DSC quantitative measurements. The problem was shown using commercially available, different poly component tablets containing ibuprofen in the presence of pseudoephedrine hydrochloride or paracetamol and coexisting excipients