A critical condition for the cost density in the circular city model

In regard to the problem of determining minimal-cost routes in a region with variable cost density, it has been shown elsewhere that, for a radially symmetric cost density which is inversely proportional to the distance from a central point O, the minimal cost between two pointsP ₁ andP ₂ which are equidistant from O is attained along a circular arc. This is not true in general for an arbitrary, radially symmetric cost density. In the present paper, critical conditions for determining when a circular arc will be a relative minimal-cost path are derived. These criteria are then employed to examine a class of special cases in which the cost density is constant outside the city limits.The author would like to express his appreciation to Professor J. B. Keller for calling his attention to the work of R. K. Luneberg and to Professor K. A. Brakke for some helpful advice.     

Further optimal cost routes in the circular city model

The following results are announced here. Two generalizations for the location of the endpoints of a road are studied in a circular city model treated previously by one of the authors. The existence of optimal cost routes has been proven. The forms of these routes are presented, along with the critical values of the parameters where the nature of the optimal routes changes discontinuously.     

Optimum preventive maintenance policies maximizing the mean time to the first system failure for a two-unit standby redundant system

A two-unit standby redundant system with repair and preventive maintenance is considered under the following assumptions: (I) the inspection of an operative unit is made only if the other unit is in standby; and (II) an operative unit, which forfeited inspection due to assumption (I), undergoes inspection just upon repair completion of the failed unit (or inspection completion). We derive the Laplace-Stieltjes transform of the cumulative distribution function of the time to the first system failure and the mean time to the first system failure. Further, we obtain the necessary and sufficient conditions for an optimum preventive maintenance policy to exist with respect to the mean time to the first system failure. More importantly, under certain conditions, we find the analytical form of an optimum inspection time maximizing the mean time to the first system failure. A numerical example is presented.The work reported in this article was supported by the National Institutes of Health under Grant No. GM-16197-05. The authors would like to express their appreciation to Professor D. L. Jaquette and Professor R. Vasudevan, University of Southern California, for their advice and encouragement.     

The discovery of the Mach reflection effect and its demonstration in an auditorium

This paper examines the historical background leading to the discovery of the Mach reflection effect and applies original documents from Mach's residue which are kept in the archives of the Ernst-Mach-Institut in Freiburg. Two experimental setups for the generation and demonstration of the Mach reflection effect, incorporating an overhead projector, are described: (a) Mach's historic mechanical shock wave reflection and interaction experiments with soot covered glass plates, performed in 1875. The Mach triple points sharply erase the soot which results in a residual picture of funnel-shaped V-formations. The head-on collision of two shock waves is marked as a narrow line of piled-up soot. (b) CalTech's hydraulic jump reflection experiments in a shallow ripple tank, performed during World War II. Regular reflection and its transition into a Mach reflection wave. Using a slightly inclined tank and providing a shoreline in the middle of the tank, Mach stem propagation slows down to zero when hitting the shore line and, therefore, can be observed live without the use of a slow motion technique.Visiting graduate student on an IAESTE grantThe International Mach Reflection Symposia have been held in Victoria, BC, Canada (1981); Sydney, Australia (1982); Freiburg, FRG and Melbourne, Australia (1983); Tokyo and Sendai, Japan (1984); Menlo Park, CA, USA (1985); Beer Sheva, Israel (1986); Albuquerque, USA (1987) and Toronto, Canada (1988)This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Development of a shear char strength sensing technique to study thermoplastic polyurethane elastomer nanocomposites

Ablative materials, such as thermoplastic elastomer nanocomposites (TPUNs) are used as internal insulation materials for solid rocket motors. These TPUNs are thermoplastic elastomer reinforced by montmorillonite nanoclays, carbon nanofibers, and multi‐walled carbon nanotubes. When these TPUN materials are exposed to an extreme heat flux, a char layer forms along the surface as it ablates. This research aims to use the newly developed shear strength sensor to evaluate the shear strength of this char layer, a characteristic that is important to evaluate ablative materials. This device consists of a method to apply a transverse loading on a test specimen, while measuring the reaction force and the induced strain. This device was used on several types of TPUN test specimens to demonstrate its effectiveness. As a means to determine which ablative exhibited the best performance, the energy of destruction or the energy of dissipation was developed. The maximum force was also accounted for as a secondary quantity for determining the char shear strength. This new shear char strength sensor is fully automated to ensure that each test is repeatable. This guaranteed reliability when collecting the data and eliminated the potential for human error. Copyright © 2017 John Wiley & Sons, Ltd.     

减速运动活塞表面空化的可视化研究

通过实验研究了液体中作减速运动活塞表面的游移空化现象以及不同液体和不同导管长度对空化的影响,基于数字图象处理方法,对空化随时间发展进行了描述并对活塞表面空化原因及有关现象进行了分析。     

Fast Liquid Chromatography for High‐Throughput Screening of Polymers

Liquid chromatography of polymers is traditionally a slow technique with analysis times of typically 30 min per sample. For the application of liquid chromatographic techniques to combinatorial materials research the analysis time per sample must be reduced considerably. Analysis time in SEC can be reduced to about 2 min per sample when high‐throughput columns are used. For HPLC small columns with improved separation efficiencies can be used. As compared to conventional technology, time savings of more than 80% are achieved.

Chromatogram from conventional SEC column compared to high‐speed SEC column tested on an identical instrument with polystyrene standards in THF.     

Metals in Medicine

Not only the 24 or so essential elements , but also nonessential and even radioactive elements have enormous potential for applications in medicine. In the fight against cancer cisplatin, one of the world's best selling anticancer drugs, is being joined by other platinum, titanium, and ruthenium complexes. Gadolinium(III ) complexes can be safely injected as magnetic resonance imaging contrast agents, and ligand design allows targeting of paramagnetic ions as well as radiodiagnostic (e.g. ^99mTc) and radiotherapeutic isotopes (e.g. ¹⁸⁶Re). Manganese superoxide dismutase mimics, vanadium insulin mimics, ruthenium nitric oxide scavengers, lanthanide-based photosensitizers, and metal-targeted organic agents show exciting clinical potential.