Absolute Configuration of β-Hydroxy-β-phenylpropionic acid*

(+)-Methyl β-methoxy-β-phenylpropionate (VIII) was prepared from (+)-mandelic acid and from (+)-β-hydroxy-β-phenylpropionic acid (I). In this way the configuration of I was correlated with that of mandelic acid

Absolute Configuration of β-Hydroxy-β-phenylpropionic acid*

(+)-Methyl β-methoxy-β-phenylpropionate (VIII) was prepared from (+)-mandelic acid and from (+)-β-hydroxy-β-phenylpropionic acid (I). In this way the configuration of I was correlated with that of mandelic acid

Photonic band structure of highly deformable, self-assembling systems

We calculate the photonic band structure at normal incidence of highly deformable, self-assembling systems - cholesteric elastomers subjected to external stress. Cholesterics display brilliant reflection and lasing owing to gaps in their photonic band structure. The band structure of cholesteric elastomers varies sensitively with strain, showing new gaps opening up and shifting in frequency. A novel prediction of a total band gap is made, and is expected to occur in the vicinity of the previously observed de Vries bandgap, which is only for one polarisation

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

Isolated singularities for some types of curvature equations

AbstractWe consider the removability of isolated singularities for the curvature equations of the form Hk[u]=0, which is determined by the kth elementary symmetric function, in an n-dimensional domain. We prove that, for 1⩽k⩽n−1, isolated singularities of any viscosity solutions to the curvature equations are always removable, provided the solution can be extended continuously at the singularities. We also consider the class of “generalized solutions” and prove the removability of isolated singularities

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.

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

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