Two problems related to prescribed curvature measures

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo

Fundamental limits of super-resolution microscopy by dielectric microspheres and microfibers

In recent years, optical super-resolution by microspheres and microfibers emerged as a new paradigm in nanoscale label-free and fluorescence imaging. However, the mechanisms of such imaging are still not completely understood and the resolution values are debated. In this work, the fundamental limits of super-resolution imaging by high-index barium-titanate microspheres and silica microfibers are studied using nanoplasmonic arrays made from Au and Al. A rigorous resolution analysis is developed based on the object's convolution with the point-spread function that has width well below the conventional (∼λ/2) diffraction limit, where λ is the illumination wavelength. A resolution of ∼λ/6-λ/7 is demonstrated for imaging nanoplasmonic arrays by microspheres. Similar resolution was demonstrated for microfibers in the direction perpendicular to the fiber axis with hundreds of times larger field-of-view in comparison to microspheres. Using numerical solution of Maxwell's equations, it is shown that extraordinary close point objects can be resolved in the far field, if they oscillate out of phase. Possible super-resolution using resonant excitation of whispering gallery modes is also studied. Keywords: Optical super-resolution; near-field microscopy; confocal microscop

Self-Assembly of Supramolecular Triblock Copolymer Complexes

Four different poly(tert-butoxystyrene)-b-polystyrene-b-poly(4-vinylpyridine) (PtBOS-b-PS-b-P4VP) linear triblock copolymers, with the P4VP weight fraction varying from 0.08 to 0.39, were synthesized via sequential anionic polymerization. The values of the unknown interaction parameters between styrene and tert-butoxystyrene and between tert-butoxystyrene and 4-vinylpyridine were determined from random copolymer blend miscibility studies and found to satisfy 0.031<χS,tBOS<0.034 and 0.39<χ4VP,tBOS<0.43, the latter being slightly larger than the known 0.30<χS,4VP≤0.35 value range. All triblock copolymers synthesized adopted a P4VP/PS core/shell cylindrical self-assembled morphology. From these four triblock copolymers supramolecular complexes were prepared by hydrogen bonding a stoichiometric amount of pentadecylphenol (PDP) to the P4VP blocks. Three of these complexes formed a triple lamellar ordered state with additional short length scale ordering inside the P4VP(PDP) layers. The self-assembled state of the supramolecular complex based on the triblock copolymer with the largest fraction of P4VP consisted of alternating layers of PtBOS and P4VP(PDP) layers with PS cylinders inside the latter layers. The difference in morphology between the triblock copolymers and the supramolecular complexes is due to two effects: (i) a change in effective composition and, (ii) a reduction in interfacial tension between the PS and P4VP containing domains. The small angle X-ray scattering patterns of the supramolecules systems are very temperature sensitive. A striking feature is the disappearance of the first order scattering peak of the triple lamellar state in certain temperature intervals, while the higher order peaks (including the third order) remain. This is argued to be due to the thermal sensitivity of the hydrogen bonding and thus directly related to the very nature of these systems.

Pharmacokinetic/pharmacodynamic analysis of adjuvant pegylated interferon α-2b in patients with resected high-risk melanoma

PurposeHigh-dose pegylated interferon α-2b (peginterferon α-2b) significantly decreased disease recurrence in patients with resected stage III melanoma in a clinical study. We investigated the pharmacokinetics (PK) and safety of high-dose peginterferon α-2b in patients with high-risk melanoma.MethodsFor PK analysis, 32 patients received peginterferon α-2b 6 μg/(kg week) subcutaneously for 8 weeks (induction) then 3 μg/(kg week) for 4 weeks (maintenance). PK profiles were determined at weeks 1, 8, and 12. Exposure-response relationships between peginterferon α-2b and absolute neutrophil count (ANC) and alanine aminotransferase (ALT) level were also studied.ResultsPeginterferon α-2b was well-absorbed following SC administration, with a median T (max) of 24 h. Mean half-life estimates ranged from 43 to 51 h. The accumulation factor was 1.69 after induction therapy. PK parameters showed moderate interpatient variability. PK profiles were described by a one-compartmental model with first-order absorption and first-order elimination. Toxicity was profiled and was acceptable; observed side effects were similar to those previously described. Dose reduction produced proportional decreases in exposure and predictable effects on ANC in an Imax model; however, a PK/pharmacodynamic (PK/PD) relationship between peginterferon α-2b and ALT could not be established with high precision.ConclusionsPeginterferon α-2b was well-absorbed and sustained exposure to peginterferon α-2b was achieved with the doses tested. These data confirm and extend previous PK observations of peginterferon α-2b in melanoma and solid tumors. Our PK/PD model of exposure and ANC effect provides useful information for prediction of peginterferon α-2b-related hematologic toxicity

Phase II trial of sagopilone, a novel epothilone analog in metastatic melanoma

BackgroundSagopilone is a novel fully synthetic epothilone with promising preclinical activity and a favourable toxicity profile in phase I testing.MethodsA phase II pharmacokinetic and efficacy trial was conducted in patients with metastatic melanoma. Patients had measurable disease, Eastern Cooperative Oncology Group performance status 0-2, adequate haematological, and organ function, with up to 2 previous chemotherapy and any previous immunotherapy regimens. Sagopilone, 16 mg m⁻², was administered intravenously over 3 h every 21 days until progression or unacceptable toxicity.ResultsThirty-five patients were treated. Sagopilone showed multi-exponential kinetics with a mean terminal half-life of 64 h and a volume of distribution of 4361 l m⁻² indicating extensive tissue/tubulin binding. Only grade 2 or lower toxicity was observed: these included sensory neuropathy (66%), leukopenia (46%), fatigue (34%), and neutropenia (31%). The objective response rate was 11.4% (one confirmed complete response, two confirmed partial responses, and one unconfirmed partial response). Stable disease for at least 12 weeks was seen in an additional eight patients (clinical benefit rate 36.4%).ConclusionSagopilone was well tolerated with mild haematological toxicity and sensory neuropathy. Unlike other epothilones, it shows activity against melanoma even in pretreated patients. Further clinical testing is warranted