Finite element methods for the incompressible Stokes equations with variable viscosity

Finite element error estimates are derived for the incompressible Stokes equations with variable viscosity. The ratio of the supremum and the infimum of the viscosity appears in the error bounds. Numerical studies show that this ratio can be observed sometimes. However, often the numerical results show a weaker dependency on the viscosity

Persistent Digermenes with Acyl and α-Chlorosilyl Functionalities

We report the preparation of α-chlorosilyl- and acyl-substituted digermenes. Unlike the corresponding transient disilenes, these species with a Ge=Ge double bond show an unexpectedly low tendency for cyclization, but in turn are prone to thermal Ge=Ge bond cleavage. Triphenylsilyldigermene has been isolated as a crystalline model compound, and is the first fully characterized example of a neutral digermene with an A2 GeGeAB substitution pattern. Spectroscopic and computational evidence prove the constitution of 1-adamantoyldigermene as a first persistent species with a heavy double bond conjugated with a carbonyl moiety

Luminescent Symmetrically and Unsymmetrically Substituted Diboranes(4)

A series of 4‐(dimethylamino)phenyl and pentafluorophenyl‐substituted 1,2‐bis(dimethylamino)diboranes(4) of type A, benzo‐fused cyclic 1,4‐diaza‐2,3‐diborinanes of type B, and 1,2‐diduryldiboranes(4) of type C were synthesized and structurally characterized. Spectroscopic studies revealed that the substitution pattern is a decisive factor for the observation of fluorescence in most of the derivatives A to C. For diboranes(4) of type A, unsymmetrical substitution with electron‐donating and ‐withdrawing groups at the boron centers is crucial to invoke fluorescence, albeit weak. Substitution at the boron atoms of 1,4‐diaza‐2,3‐diborinane species B leads to a modified skeletal structure. Finally, the grafting of 4‐(dimethylamino)phenyl groups to diboranes(4) of type C results in extraordinary Stokes shifts in nonpolar solvents

Prospective Multicenter Randomized Phase III Study of Weekly versus Standard Docetaxel plus Doxorubicin (D4) for First-Line Treatment of Metastatic Breast Cancer

Purpose: Previous phase II studies have indicated a greatly reduced hematotoxicity of docetaxel-based regimens administered on weekly schedules. The present trial was initiated to compare the toxicity and efficacy of weekly docetaxel versus its standard 3-weekly application in combination with doxorubicin. Methods: Patients previously untreated with chemotherapy for metastatic disease were recruited. Inclusion criteria were age = grade 3 was observed in the standard arm of the D4 study compared to the weekly schedule (per-patient analysis: 61.9% q3w vs. 65.1% q1w; p > 0.05). Grade 3 and grade 4 fever, diarrhea, and infections occurred more frequently in the standard arm, whereas neurotoxicity and skin/nail disorders were observed more frequently in the weekly arm. Except for fever, none of these differences reached a level of significance. Dose delays, dose reductions, and the rate of omitted doses were increased in the weekly arm. The overall response rate was 44.2% in the weekly arm compared to 52.4% in the standard arm (p = 0.52). Time to progression was 6.2 (q1w) versus 10.3 (q3w) months (p = 0.36), and overall survival was 20.5 (q1w) versus 28.7 (q3w) months (p = 0.98). Conclusion: The present data support the feasibility of both weekly and 3-weekly application of docetaxel in combination with doxorubicin. Nevertheless, given that leukopenia was similar in both arms and the efficacy parameters were at least numerically inferior with the weekly schedule, standard 3-weekly application seems to be preferable for patients requiring combination chemotherapy. Copyright (C) 2011 S. Karger AG, Base

Prospective Multicenter Randomized Phase III Study of Weekly versus Standard Docetaxel (D2) for First-Line Treatment of Metastatic Breast Cancer

Purpose: Previous phase II studies have indicated a greatly reduced hematotoxicity of docetaxel-based regimens administered on weekly schedules. The present trial was initiated to randomly compare the toxicity and efficacy of weekly docetaxel versus its standard 3-weekly application. Methods: Patients previously untreated with chemotherapy for metastatic disease were recruited. Patients aged >60 years or with a Karnofsky Perfomance Status (KPS) of 60-80% were eligible for the D2 study. Patients were randomized to receive docetaxel either on a 3-weekly {[}75 mg/m(2) every 3 weeks (q3w)] or on a weekly (30 mg/m(2) on days 1, 8, and 15; q4w) schedule. Treatment was continued until a maximum of 8 cycles, unacceptable toxicity, or disease progression. All patients received standard corticosteroid prophylaxis. Results: Since statistical significance for the primary endpoint (toxicity) was achieved in the interim analysis, the study was closed according to the study protocol (102 of 162 patients). Compared to the standard arm, leukopenia >= grade 3 was a rare event in the weekly arm of the D2 study (per-patient analysis: 4.2% q1w vs. 51.9% q3w; p < 0.0001). No difference was observed between the 2 schedules regarding the occurrence of anemia or thrombocytopenia. With regard to non-hematological toxicity, there was a higher incidence of skin/nail and hepatological toxicity with the weekly schedule, whereas neurotoxicity was observed more often in the standard arm. The rate of omitted doses was significantly increased in the weekly arm (8.6% q1w vs. 0% q3w). The overall response rate was 22.9% in the weekly arm compared to 42.6% in the standard arm (p = 0.039). Time to progression was 5.4 (q1w) versus 6.3 (q3w) months (p = 0.91), and overall survival was 22.7 (q1w) versus 15.8 (q3w) months (p = 0.24). Conclusion: The present data support the feasibility of both weekly and 3-weekly application of docetaxel. As expected, severe leukopenia seems avoidable in weekly scheduled single-agent docetaxel and may serve as an important treatment option, particularly in elderly patients and patients with a reduced performance status. Copyright (C) 2011 S. Karger AG, Base

Gemcitabine and carboplatin in intensively pretreated patients with metastatic breast cancer

Background: Patients with metastatic breast cancer (MBC) are increasingly exposed to anthracyclines and taxanes either during treatment of primary breast cancer or during initial therapy of metastatic disease. The combination of gemcitabine and carboplatin was therefore investigated as an anthracycline- and taxane-free treatment option. Patients and Methods: MBC patients previously treated with chemotherapy were enrolled in a multicenter phase II study. Treatment consisted of gemcitabine (1,000 mg/m(2) i.v. on days 1 and 8) and carboplatin (AUC 4 i.v. on day 1) applied every 3 weeks. Results: Thirty-nine patients were recruited, and a total of 207 treatment cycles were applied with a median of 5 cycles per patient. One complete response and 11 partial responses were observed for an overall response rate of 31% (95% CI: 17-48%). Twelve patients (31%) had stable disease. Median time to progression was 5.3 months (95% CI: 2.6-6.7 months) and median overall survival from start of treatment was 13.2 months (95% CI: 8.7-16.7 months). Grade 3/4 hematological toxicity included leukopenia (59%/5%), thrombo-cytopenia (26%/23%) and anemia (10%/0%). Nonhematological toxicity was rarely severe. Conclusion: Combination chemotherapy with gemcitabine and carboplatin is an effective and generally well-tolerated treatment option for intensively pretreated patients with MBC. Due to a considerable incidence of severe thrombocytopenia it would be reasonable to consider starting gemcitabine at the lower dose level of 800 mg/m(2). Copyright (c) 2008 S. Karger AG, Basel

Classification of image distortions in terms of Petrov types

An observer surrounded by sufficiently small spherical light sources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light bundles. In lowest non-trivial order with respect to the distance, this pattern is completely determined by the conformal curvature tensor (Weyl tensor) at the observation event. In this paper we derive formulas that allow to calculate these distortion patterns in terms of the Newman-Penrose formalism. Then we represent the distortion patterns graphically for all Petrov types, and we discuss their dependence on the velocity of the observer.Comment: 22 pages, 8 eps-figures; revised version, parts of Introduction and Conclusions rewritte