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This work aims to construct a new regularisation version for the perturbed two-body problem using bipolar coordinates. We mainly use two transformation techniques to deal with this problem when the distance between two bodies tends to be zero. The system exhibits a well-stabilised periodic orbit over a long time span through numerical simulations. With the increase in the oblate parameter value of the body, the periodic orbit will gradually evolve into a quasi-periodic form.

In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.

May Gaber, Hanan Selim, Tamer El-NahasDepartment of Clinical Oncology, Cairo University, Cairo, EgyptPurpose: In view of the documented toxicity of continuous daily radiosensitizer doses of temozolomide concomitant with radiation in the treatment of glioblastoma multiforme, we aimed to compare it with a different schedule of abbreviated radiosensitizer dosing.Patients and methods: This was a randomized prospective study comparing toxicity and survival in 60 Egyptian patients with glioblastoma multiforme. Patients in arm I received temozolomide at a dose of 75 mg/m2 daily with radiotherapy for 42 days, starting 4 weeks after surgery and reaching to a total radiation dose of 60 Gy/30 Fractions/6 weeks, while patients in arm II received temozolomide at a dose of 75 mg/m2 concomitantly with the same radiotherapy schedule daily in the first and last weeks of the same radiotherapy program.Results: Common grade 1–2 adverse events were malaise in 28 patients (46.7%), followed by alopecia (40%) and nausea (26.7%). Grade 3–4 convulsion and decreased level of consciousness was seen in only four patients who were all from arm I. The median progression-free survival (PFS) for the entire study population was 10.6 months (95% confidence interval [CI] 7.3–14), and PFS at 12 months was 32%. The median PFS in arm I was 8.8 months (95% CI 5.9–11.7) and in arm II 11.5 months (95% CI 8.9–14.2), and PFS at 12 months for both arms was 32% and 30% respectively (P=0.571). The median overall survival (OS) of the whole group of patients was 14.2 months (95% CI 13–15.5), and OS was 70% at 12 months and 25% at 18 months. The median OS for patients in arm I was 12.3 months (95% CI 7.7–16.9), whereas in arm II it was 14.3 months (95% CI 14–14.7) (P=0.83).Conclusion: Reduced radiosensitizer dosing of temozolomide concomitant with radiotherapy in glioblastoma multiforme exhibited comparable efficacy with a classic continuous daily schedule, though with better tolerability.Keywords: glioblastoma multiforme, temozolomide, radiosensitizer, high-grade glioma