Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold （hot） dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Maximal androgen blockade versus castration alone in patients with metastatic prostate cancer

Maximum androgen blockade （MAB）, consisting of an antiandrogen plus either a luteinizing hormone- releasing hormone agonist （LHRHA） or orchiectomy, is a standard care for patients with prostate cancer. Although, clinical trial results have been equivocal, none has shown a significant advantage in favor of MAB over castration alone in metastatic prostate cancer and MAB has been the subject of considerable controversy. The aim of this study was to compare MAB （orchiectomy or LHRHA＂Goserelin＂） and anti-androgen ＂Bicalutamide＂ with castration alone （orchiectomy or LHRHA） in previ- ously untreated metastatic prostate cancer patients. Methods： Hundred eligible patients with adequate performance status and adequate hematologic, hepatic and renal functions were included. MAB arm, fifty patients underwent castration either surgically by orchiectomy or medically by receiving Goserelin （3.6 rag） depot, which was injected subcutaneously every 28 days plus bicalutamide 50 mg once daily. Castration alone arm, fifty patients underwent castration alone either surgically by orchiectomy or medically by receiving Goserelin （3.6 mg） depot. Results： During the period from January 2011 to January 2013, with a median follow up of 18 months （range 6 to 24 months）, there were eight deaths （16%）, in MAB arm and ten deaths （20%） in castration alone arm. At three months, there were 35 patients （70%） with prostate specific antigen （PSA） normalization （-〈 4 mg/dL） in MAB arm versus 17 patients （34%） with PSA normalization in castration alone arm （P = 0.001）. The median progression free survival （PFS） times were 22.18 months （95% CI, 19.7 to 24.2 months） for MAB arm versus 22 months in castration alone arm （95% CI, 18 to 25.9 months; P = 0.045）. The survival rates for MAB arm were 82% at 18 months and 70.6% at 24 months versus 78.7% at 18 months and 75.1% at 24 months in castration alone arm （P 〉 0.05）. The median overall survival （OS） was not reached in either arm. Both hematological and non-hematological toxicities were com- parable in both arms. Conclusion： MAB significantly improves the PSA normalization rate at 12 weeks and PFS compared to castration alone with no significant difference in overall survival and with comparable acceptable toxicities. However further studies are needed to document such findings.

Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation

The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.