The notion of [Formula: see text]-ideal was introduced in [G. Q. Abbasi, S. Ahmad, I. Anwar and W. A. Baig, [Formula: see text]-Ideals of degree 2, Algebra Colloq. 19(1) (2012) 921–926] in 2012 and has been studied in many papers after that. In this paper, we have studied those graphs whose Stanley–Reisner ideals turn out to be [Formula: see text]-ideals. We give a characterization and construction of these graphs and show that, unlike [Formula: see text]-graphs, these graphs are always connected. We have also discussed when these graphs are complete bipartite graphs. Moreover, we classify those graphs for which both the facet ideal (the edge ideal) and the Stanley–Resiner ideal, are [Formula: see text]-ideals.

The notion of f -graphs and f -ideals are relatively new and have been studied in many papers. In this paper, we have generalized the idea of f -graphs and f -ideals to quasi f -graphs and quasi f -ideals, respectively. We have characterized all quasi f -graphs and quasi f -ideals of degree 2 and determined all the minimal primes ideals of these ideals. Furthermore, construction of quasi f -ideals of degree 2 has been described; the formula for computing Hilbert function and Hilbert series of the polynomial ring modulo the edge ideal of the quasi f -graph has been provided.

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BackgroundBecause of the anatomical properties of the inferior calyx, lower pole stones are difficult to remove through the ureter, even if the stones are fragmented. Retrograde intra-renal surgery (RIRS) is typically employed to treat the smaller lower pole stones (1.0-2.0 cm) while percutaneous nephrolithotomy (PCNL) is primarily used to treat the larger diameter stones or when RIRS has failed to clear the stones. This study was conducted to compare mini-PCNL and RIRS for the management of lower pole kidney stones in terms of stone clearance.

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Aim: To determine the frequency of prolongation of QT interval as a result of combination therapy of oral Artemether-Lumefantrine Study design: A cross-sectional study Place and Duration: This study was conducted at Karachi Institute of Heart Diseases Karachi Pakistan from June 2020 to June 2021. Methodology: The study included a total of 120 participants. Participants were selected by a consecutive sampling method. All the patients were adults and had been diagnosed with malaria by positive blood smear for plasmodium falciparum. The patients had not taken any antimalarial therapy for the last seven days of reporting to the hospital. The treatment was given in six doses of AL combination therapy. The strength of one dose was 80 mg Artemether and 480 mg of Lumefantrine. The QT interval was calculated before and after the therapy administration. Bazett’s formula (Qtc (s) = QT interval / √ RR interval) was used for the calculation of the corrected QT interval (Qtc) Results: The mean age of the patients was 30 ± 2.96 years. A total of 85 (70.83%) were male and 35 (29.17%) were female. According to the age distribution, 31 (25.83%) patients were between the age of 20 years and 30 years. A total of 42 (35%) patients were between the age of 31 and 40 years. 36 (30%) were in the age range of 41 and 50 years. A total of 11 (9.17%) were above the age of 50 years All the patients were analyzed for QT interval prolongation and the QT interval was not prolonged in any of the participants. Conclusion: As QT interval prolongation was not observed in any of the patients, oral AL can be considered a safe combination therapy for the treatment of malaria caused by plasmodium falciparum. Keywords: Artemether, Lumefantrine, QT prolongation, Malaria, Plasmodium Falciparum