Non-scale-invariant inverse curvature flows in Euclidean space

We consider the inverse curvature flows $\dot x=F^{-p}\nu$ of closed star-shaped hypersurfaces in Euclidean space in case $0<p\not=1$ and prove that the flow exists for all time and converges to infinity, if $0<p<1$, while in case $p>1$, the flow blows up in finite time, and where we assume the initial hypersurface to be strictly convex. In both cases the properly rescaled flows converge to the unit sphere.Comment: 21 pages, this is the published versio

Phase I clinical trial of the Src inhibitor dasatinib with dacarbazine in metastatic melanoma.

BackgroundSrc inhibitors sensitise melanoma cells to chemotherapy in preclinical models. The combination of dasatinib and dacarbazine was tested in a phase I trial in melanoma.MethodsPatients had ECOG performance status 0-2 and normal organ function. Dacarbazine was administered on day 1 and dasatinib on day 2 through 19 of each 21-day cycle. Both were escalated from 50 mg b.i.d. of dasatinib and 800 mg m(-2) of dacarbazine. Available pre-treatment biopsies were sequenced for BRAF, NRAS, and C-Kit mutations.ResultsDose-limiting toxicity was reached at dasatinib 70 mg b.i.d./dacarbazine 1000 mg m(-2), and was predominantly haematological. In 29 patients receiving dasatinib 70 mg b.i.d., the objective response rate (ORR) was 13.8%, the clinical benefit rate (ORR+SD) was 72.4%, the 6-month progression-free survival (PFS) was 20.7%, and the 12-month overall survival (OS) was 34.5%. Two out of three patients who were wild type for BRAF, NRAS, and c-KIT mutations had confirmed partial responses, and one had a minor response.ConclusionThe recommended phase II dose is dasatinib 70 mg b.i.d with dacarbazine 800 mg m(-2). PFS and OS data for dasatinib at 70 mg b.i.d. with dacarbazine compared favourably with historical controls. Preliminary data support evaluating tumour mutation status further as a biomarker of response

On the Regularity of Optimal Transportation Potentials on Round Spheres

In this paper the regularity of optimal transportation potentials defined on round spheres is investigated. Specifically, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satisfied on the round sphere, when the cost-function is the geodesic distance squared. In order to generalise Loeper's calculation to a broader class of cost-functions, the (A3) condition is reformulated via a stereographic projection that maps charts of the sphere into Euclidean space. This reformulation subsequently allows one to verify the (A3) condition for any case where the cost-fuction of the associated optimal transportation problem can be expressed as a function of the geodesic distance between points on a round sphere. With this, several examples of such cost-functions are then analysed to see whether or not they satisfy this (A3) condition.Comment: 24 pages, 4 figure

Rectifiability of Optimal Transportation Plans

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere

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

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

Simulation and analysis of grating-integrated quantum dot infrared detectors for spectral response control and performance enhancement

We propose and analyze a novel detector structure for pixel-level multispectral infrared imaging. More specifically, we investigate the device performance of a grating-integrated quantum dots-in-a-well photodetector under backside illumination. Our design uses 1-dimensional grating patterns fabricated directly on a semiconductor contact layer and, thus, adds a minimal amount of additional effort to conventional detector fabrication flows. We show that we can gain wide-range control of spectral response as well as large overall detection enhancement by adjusting grating parameters. For small grating periods, the spectral responsivity gradually changes with parameters. We explain this spectral tuning using the Fabry-Perot resonance and effective medium theory. For larger grating periods, the responsivity spectra get complicated due to increased diffraction into the active region, but we find that we can obtain large enhancement of the overall detector performance. In our design, the spectral tuning range can be larger than 1 mu m, and, compared to the unpatterned detector, the detection enhancement can be greater than 92% and 148% for parallel and perpendicular polarizations. Our work can pave the way for practical, easy-to-fabricate detectors, which are highly useful for many infrared imaging applications. (C) 2014 AIP Publishing LLCopen1

Commercial Hybrid SNCR/SCR Demonstration

The U.S. Department of Energy (DOE), Electric Power Research Institute (EPRI), Pennsylvania Electric Energy Research Council, (PEERC), New York State Electric and Gas and GPU Generation, Inc. are jointly funding a demonstration to determine the capabilities of a Hybrid SNCR/SCR (Selective Non-Catalytic Reduction/Selective Catalytic Reduction). The demonstration site is at GPU Generation`s Seward Unit 5 (147 MW) located in Seward Pennsylvania. The demonstration will begin in late October of 1997 and will continue for a period of one year. The DOE funding is being provided through Grant No. DE-FG22-96PC96256 with T.J. Feeley as the Project Manager. The project will demonstrate the operation of a Hybrid SNCR/SCR NO{sub x} control process on a full scale coal fired utility boiler. The hybrid technology is expected to provide a cost effective method of reducing NO{sub x} while balancing capital and operating costs. The process also provides a method for staging the NO{sub x} reduction performance and costs to suit the needs of the utility. An urea based SNCR system is currently in operation on Seward Unit 5 and the ammonia slip from the SNCR will be used as the reducing agent for the hybrid catalyst. The project goals are: demonstrate that hybrid technology is capable of achieving greater than 55% reduction from baseline NO{sub x} emissions while maintaining less than 2 ppm ammonia slip at the inlet to the air heaters; maintain fly ash marketability; verify the performance capabilities of two different types of catalysts (plate and monolith); determine the cost benefit and applicability of hybrid post combustion technology; and reduce forced outages due to ABS fouling of the air heaters. Since the demonstration will begin in October of 1997 and continue for a period of one year operating data is not available. Therefore this paper will describe the methodology of the system design and construction

Thiosemicarbazones and 2-Thio-4-(phthalimidoalkylidene) thiazolid-5-ones of N-Phthaloyl Amino Aldehydes. Preparation and Antibacterial Activity

Thiosemicarbazones of the formula I and 2-thio-4-(phthalimidoalkylidene) thiazolid-5-ones of the formula II derived from glycine, L-alanine; B-alanine, DL-leucine, DL-valine, L-tyrosine, DL-serine and a-amino-n-butyric acid were prepared and tested against Staphylococcus aureus, B. pyocyaneus, E. coli and Enterococcus