Nitro- and fluoropolyformals. III. Copolyformals from mixtures of fluoro- and nitro-α,ω-diols

Polyformals of fluoro-, nitramine-, and C-nitrodiols show widely differing properties with respect to glass transition temperature, melting transition, and solubility. Polymers with desirable combinations of these properties, e.g., low T_g, high nitro content, and good solubility in polar solvents, were expected to result from acid-promoted copolycondensation of appropriate mixtures of diols with formaldehyde. A series of such condensations were carried out and the polymers obtained from binary mixtures of fluoro- and nitrodiols, different nitrodiols, and fluoro- or nitrodiols and carboranediols, were characterized by GPC, ¹H-NMR, and DSC analysis.     

The ambient gamma dose-rate and the inventory of fission products estimations with the soil samples collected at Canadian embassy in Tokyo during Fukushima nuclear accident

In this study, soil samples were collected at Canadian embassy in Tokyo (about 300 km from Fukushima) on 23 March and 23 May of 2011 for purposes of estimating concentrations of radionuclides in fallout, the total fallout inventory, the depth distribution of radionuclide of interest and the elevated ambient gamma dose-rate at this limited location. Some fission products and actinides were analyzed using gamma-ray spectrometry, alpha spectrometry and liquid scintillation counting. The elevated activity concentration levels of ¹³¹I, ¹³²I, ¹³⁴Cs, ¹³⁷Cs, ¹³⁶Cs, ¹³²Te, ¹²⁹mTe, ¹²⁹Te, ¹⁴⁰Ba and ¹⁴⁰La were measured by the gamma-ray spectrometer in the first sample collected on 23 March. Two months after the accident, the ¹³⁴Cs and ¹³⁷Cs became only detectable nuclides. A mass relaxation depth of 3.0 g/cm² was determined by the activities on the depth distribution of ¹³⁷Cs in a soil core. The total fallout inventory was thus calculated as 225 kBq/m² on March sampling date and 25 kBq/m² on May sampling date. The ambient gamma dose-rates in the sampling area estimated by the fallout fission products inventory and ¹³⁷Cs depth distribution ranged from 184 to 38 nGy/h. There was no detectable americium or plutonium in the soil samples by alpha spectrometry. Although ⁹⁰Sr or ⁸⁹Sr were detected supposedly as a result of this accident, it was less than the detection limit, which was about 0.4 Bq/kg in the soil samples.     

Around random algebra

It is shown that there is a subalgebra of the measure algebra forcing dominating reals. Also results are given about iterated forcing connected with random reals.The first author would like to thank NSF for its partial support under Grant DMS-8701828The second author would like to thank U.S.-Israel BSF for partial supportNote. In the first version of this paper we proved only a weak form of the main result of Sect. 2 (see 2.2). Also, the first version contained a third section, but the main result of that version is a weak form of 2.5     

Oriented matroids

In this paper, the basic properties of oriented matroids are examined. A topological representation theorem for oriented matroids is proven, utilizing the notion of an “arrangement of pseudo-hemispheres”. The duality theorem of linear programming is extended to oriented matroids.     

A Laboratory,Computer and Calculus Based Course in Mathematics

The paper describes the designing and testing of a laboratory, computer and calculus based course in mathematics. The laboratory is central to the course and stimulates in the student the need and desire to know more about mathematics. Further, it enables mathematics to be taught in a real world context. Computers are used to take the drudgery out of the mathematics and make it possible to attack real scientific and technical problems. This new approach to calculus is less formal and depends to a smaller extent upon prior mathematical training so that it appeals to a much wider audience. The proposed course, with its emphasis on laboratory measurements, is ideally suited to the exploration of numerical methods and their application to the calculation of derivatives, definite integrals and the solution of differential equations.