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

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

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

Solid Freeform Fabrication of Transparent Fused Quartz using a Filament Fed Process

Glass is a critical material for many scientific and engineering applications including optics, communications, electronics, and hermetic seals. Despite this technological relevance, there has been minimal research toward Additive Manufacturing (AM) of glass, particularly optically transparent glass. Additive Manufacturing of transparent glass offers potential advantages for lower processing costs for small production volumes, increased design freedom, and the ability to locally vary the optical properties of the part. Compared to common soda lime glass, fused quartz is better for AM since it has lower thermal expansion and higher index homogeneity. This paper presents a study of additive manufacturing of transparent fused quartz by a filament fed process. A CW CO2 laser (10.6 µm) is used to melt glass filaments layer by layer. The laser couples to phononic modes in the glass and is well absorbed. The beam and melt pool are stationary while the work piece is scanned using a standard lab motion system. Representative parts are built to explore the effects of variable laser power on the properties of printed fused quartz. During printing the incandescent emission from the melt pool is measured using a spectrometer. This permits process monitoring and identifies potential chemical changes in the glass during printing. After deposition, the printed parts are polished and the transmission measured to calculate the absorption/scattering coefficient. Finally, a low-order thermal analysis is presented and correlated to experimental results, including an energy balance and finite volume analysis using Fluent. These results suggest that optical quality fused quartz parts with low absorption and high index of refraction uniformity may be printed using the filament-fed process

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

Investigating diagrammatic reasoning with deep neural networks

Diagrams in mechanised reasoning systems are typically en- coded into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. We present a new method of using Deep artificial Neu- ral Networks (DNN) to learn continuous, vector-form representations of diagrams without any human input, and entirely from datasets of dia- grammatic reasoning problems. Based on this DNN, we developed a novel reasoning system, Euler-Net, to solve syllogisms with Euler diagrams. Euler-Net takes two Euler diagrams representing the premises in a syl- logism as input, and outputs either a categorical (subset, intersection or disjoint) or diagrammatic conclusion (generating an Euler diagram rep- resenting the conclusion) to the syllogism. Euler-Net can achieve 99.5% accuracy for generating syllogism conclusion. We analyse the learned representations of the diagrams, and show that meaningful information can be extracted from such neural representations. We propose that our framework can be applied to other types of diagrams, especially the ones we don’t know how to formalise symbolically. Furthermore, we propose to investigate the relation between our artificial DNN and human neural circuitry when performing diagrammatic reasoning

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