Analysis of the fractional relativistic polytropic gas sphere.

Many stellar configurations, including white dwarfs, neutron stars, black holes, supermassive stars, and star clusters, rely on relativistic effects. The Tolman-Oppenheimer-Volkoff (TOV) equation of the polytropic gas sphere is ultimately a hydrostatic equilibrium equation developed from the general relativity framework. In the modified Riemann Liouville (mRL) frame, we formulate the fractional TOV (FTOV) equations and introduce an analytical solution. Using power series expansions in solving FTOV equations yields a limited physical range to the convergent power series solution. Therefore, combining the two techniques of Euler-Abel transformation and Padé approximation has been applied to improve the convergence of the obtained series solutions. For all possible values of the relativistic parameters ([Formula: see text]), we calculated twenty fractional gas models for the polytropic indexes n = 0, 0.5, 1, 1.5, 2. Investigating the impacts of fractional and relativistic parameters on the models revealed fascinating phenomena; the two effects for n = 0.5 are that the sphere's volume and mass decrease with increasing [Formula: see text] and the fractional parameter ([Formula: see text]). For n = 1, the volume decreases when [Formula: see text] = 0.1 and then increases when [Formula: see text] = 0.2 and 0.3. The volume of the sphere reduces as both [Formula: see text] and [Formula: see text] increase for n = 1.5 and n = 2. We calculated the maximum mass and the corresponding minimum radius of the white dwarfs modeled with polytropic index n = 3 and several fractional and relativistic parameter values. We obtained a mass limit for the white dwarfs somewhat near the Chandrasekhar limit for the integer models with small relativistic parameters ([Formula: see text], [Formula: see text]). The situation is altered by lowering the fractional parameter; the mass limit increases to Mlimit = 1.63348 M⊙ at [Formula: see text] and [Formula: see text].

Phase II trial of metronomic chemotherapy as salvage therapy for patients with metastatic breast cancer.

AIM OF WORK: To evaluate the efficacy and tolerability of metronomic chemotherapy (which is the continuous administration of chemotherapy at relatively low minimally toxic doses on a frequent schedule of administration at close regular intervals with no prolonged drug-free breaks) in metastatic breast cancer patients as salvage therapy. PATIENTS AND METHODS: In this phase II study we evaluated the clinical efficacy and tolerability of low dose, oral Methotrexate (MTX) and Cyclophosphamide (CTX) in patients with metastatic breast cancer. Between January 2004 and December 2005, 42 patients received MTX 2.5mg bid on day 1 and 2 each week and CTX 50mg/day administered continuously. RESULTS: Forty two patients were evaluable. The overall clinical benefit was 31% complete response, partial response and stable disease (CR+PR+SD >or=24 weeks), while the overall response rate was 16.7% (none of the patients attained CR). Toxicity was generally mild. The most common non hematological toxicity was elevation in transaminases level, it was reported in 40.4% of patients and was reversible, while mild grade 1 or 2 neutropenia was the most common hematological toxicity, (28.5% of patients). Median time to response was 3+/-0.18 while progression free survival (PFS) among patients with clinical benefit was 10 months (95% CI 6.65-13.44). CONCLUSIONS: This phase II study shows that, the combination of continuously low dose MTX and CTX is an active minimally toxic and significantly cost effective regimen for the treatment of metastatic breast cancer patients.