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Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs (USGV), an alternative characterisation of the well-known rectilinear graphs. We extend known combinatorial results for USGV and we show that, in the weak case (i.e., visibilities do not necessarily translate into edges of the represented combinatorial graph), the area minimisation variant of their recognition problem is N P -hard. We also provide combinatorial insights with respect to USV, and as our main result, we prove their recognition problem to be N P -hard, which settles an open question., (© The Author(s) 2023.)

A simple, precise, and rapid method to simultaneously determine the levels of oseltamivir (OS) and oseltamivir carboxylate (OSC) in human plasma was developed. Additionally, the stability of both substances in plasma was investigated under different conditions. The method involved protein precipitation (0.01 % HCl in acetonitrile), and then the supernatant was injected into the high-performance liquid chromatography (HPLC)-MS/MS. The chromatographic separation was achieved on a YMC-Triart C18 (100 × 2.0 mm, 5 μm) column using acetonitrile/water (30:70, v/v) containing 0.1 % formic acid as the mobile phase. Sample volume was 5 μl. The linearity of the method was established in the concentration range of 0.5-100 ng/mL for OS and 1.0-1000 ng/mL for OSC. The intra-day precision and accuracy for oseltamivir were 1.5-8.9 and 94.4-101.0 %, respectively. For oseltamivir carboxylate, the intra-day precision and accuracy were 3.2-12.7 and 92.8-108.8 %, respectively, whereas the inter-day precision and accuracy were 5.5-11.5 and 94.6-104.0 % for oseltamivir and 4.7-11.5 and 99.9-103.9 % for oseltamivir carboxylate, respectively. The application of this method was demonstrated by a bioequivalence study in 28 healthy humans with 75 mg oseltamivir phosphate capsules (Tamiflu®). Sodium fluoride (2.4 mg/mL) with potassium oxalate (3 mg/mL) was used as anticoagulant within sampling of trial. The assay reproducibility was established by reanalysis of 80 incurred samples.

A reliable and high throughput high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) method was developed and validated for determining levels of the antitubercular drug-D -cycloserine in human plasma. Plasma samples analyte with an internal standard (IS) (niacin) were prepared by solid-phase extraction using Waters Oasis MCX cartridges. The chromatographic separation was performed using the HILIC mode on a YMC-Pack SIL-06 column (150 × 4.6 mm; 3 μm) under isocratic conditions. The run time of analysis was 5 min. The mobile phase consisted of methanol, propanol-2 and 0.075 % trifluoroacetic acid (66.5:28.5:5, v/v/v). Protonated ions formed by turbo ion spray in positive mode were used to detect the analyte and the IS. MS/MS detection was used to monitor the fragmentation of 103-75 m/z for cycloserine and 124 to 80 m/z for niacin (IS) on an API 4000 (AB Sciex) triple quadrupole mass spectrometer. A linear dynamic range of 0.3-30 μg/mL was established for cycloserine using 0.2 mL human plasma and a 1 μL injection volume. The mean relative recovery of cycloserine and niacin were 77.2 and 82.4 %, respectively. The procedure of sample preparation was consistent and reproducible (precision, 0.8-3.4 %; accuracy, 93.8-104.9 %). The method was validated in accordance with requirements of the European Medicines Agency and successfully applied to a bioequivalence study of 250 mg tablet formulations in 23 healthy human subjects.