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

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%

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

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

Determination of neomycin in the form of neomycin derivative with dabsyl chloride by thin layer chromatography and densitometry

A thin layer chromatographicñdensitometric method has been developed for identification and quantitative determination of neomycin derivative with dabsyl chloride. The analysis of antibiotic was achieved on the silica gel TLC plates with fluorescent indicator with n-butanol - 2-butanone ñ 25% ammonia - water (10 : 6 : 2 : 2, v/v/v/v) as the mobile phase. The densitometric measurements were made at 460 nm. Under these conditions good separation of chosen aminoglycoside antibiotic from reagent used to make a complex was obtained. The method is characterized by high sensitivity, LOD from 0.1953 μg per band and LOQ from 0.5918 μg per band, wide linearity range from 0.5918 to 2.1960 μg per band for neomycin. The precision of the method was good; RSD varied from 1.17 to 2.05%. Satisfactory results of validation of the method were also confirmed by determination of selected antibiotic in pharmaceutical commercial preparation. The results obtained by TLC-densitometric method were compared with those obtained by spectrophotometric method

Photodegradation assessment of ciprofloxacin, moxifloxacin, norfloxacin and ofloxacin in the presence of excipients from tablets by UPLC-MS/MS and DSC

Background: Ciprofloxacin (CIP), moxifloxacin (MOX), norfloxacin (NOR) and ofloxacin (OFL), are the antibacterial synthetic drugs, belonging to the fluoroquinolones group. Fluoroquinolones are compounds susceptible to photodegradation process, which may lead to reduction of their antibacterial activity and to induce phototoxicity as a side effect. This paper describes a simple, sensitive UPLC-MS/MS method for the determination of CIP, MOX, NOR and OFL in the presence of photodegradation products. Results: Chromatographic separations were carried out using the Acquity UPLC BEH C18 column; (2.1 × 100 mm, 1.7 μm particle size). The column was maintained at 40°C, and the following gradient was used: 0 min, 95% of eluent A and 5% of eluent B; 10 min, 0% of eluent A and 100% of eluent B, at a flow rate of 0.3 mL min-1. Eluent A: 0.1% (v/v) formic acid in water; eluent B: 0.1% (v/v) formic acid in acetonitrile. The method was validated and all the validation parameters were in the ranges acceptable by the guidelines for analytical method validation. The photodegradation of examined fluoroquinolones in solid phase in the presence of excipients followed kinetic of the first order reaction and depended upon the type of analyzed drugs and coexisting substances. Photodegradation process of analyzed drugs was confirmed by differential scanning calorimetry. In addition, the identification of degradation products was carried out by mass spectrometry. Conclusion: The developed UPLC-MS/MS method enables the determination of CIP, MOX, NOR and OFL in the presence of photodegradation products and identification of photodegradation products

Kinetic and thermodynamic studies of moxifloxacin hydrolysis in the presence and absence of metal ions in acidic solutions

Chromatographic and densitometric method for determination of moxifloxacin in the presence of products of acidic hydrolysis was developed. The established method had suitable specificity, precision, good accuracy and high sensitivity.In addition, stability of moxifloxacin in acidic solutions at temperature 90°C and 110°C in the presence and absence of metal ions, such as Cu(II), Fe(III), Zn(II), and Al(III) was studied. It was proved that decomposition of moxifloxacin proceeds according to kinetics of the first-order reaction and is dependent on temperature, incubation time and the type of the metal ion. Based on the calculated kinetic (k, t0.1 and t0.5) and thermodynamic (Ea) parameters, it was observed that among studied ions the highest effect on decomposition process of moxifloxacin had Cu(II) ions. The liquid chromatography coupled with mass spectrometry detection (LC-MS) and proton nuclear magnetic resonance (1H NMR) techniques have been used to identify degradation products of moxifloxacin

Kinetic and thermodynamic studies of moxifloxacin hydrolysis in the presence and absence of metal ions in acidic solutions

Chromatographic and densitometric method for determination of moxifloxacin in the presence of products of acidic hydrolysis was developed. The established method had suitable specificity, precision, good accuracy, and high sensitivity. In addition, stability of moxifloxacin in acidic solutions at temperature 90OC and 110OC in the presence and absence of metal ions, such as Cu(II), Fe(III), Zn(II), and Al(III) was studied. It was proved that decomposition of moxifloxacin proceeds according to kinetics of the first-order reaction and is dependent on temperature, incubation time and the type of the metal ion. Based on the calculated kinetic (k, t0.1 and t0.5) and thermodynamic (Ea) parameters, it was observed that among studied ions the highest effect on decomposition process of moxifloxacin had Cu(II) ions. The liquid chromatography coupled with mass spectrometry detection (LC-MS) and proton nuclear magnetic resonance (1H NMR) techniques have been used to identify degradation products for the compound