Discriminants in characteristic two

The Kronecker-Weierstrass theory of pencils is extended to give a necessary and sufficient condition that two 2×m×n tensors are equivalent. The connection between equivalence class representatives and the triple transitivity of PGL(2,F) is discussed. One consequence of the discussion is that the number of inequivalent 2×3×n tensors is finite. An efficient algorithm is given for testing the condition which ultimately depends on a fast pattern matching algorithm.     

Ultrashort pulse compression and delivery in a hollow-core photonic crystal fiber at 540 nm wavelength

We have fabricated a bandgap-guiding hollow-core photonic crystal fiber (PCF) capable of transmitting and compressing ultrashort pulses in the green spectral region around 532 nm. When propagating subpicosecond pulses through 1 m of this fiber, we have observed soliton-effect temporal compression by up to a factor of 3 to around 100 fs. This reduces the wavelength at which soliton effects have been observed in hollow-core PCF by over 200 nm. We have used the pulses delivered at the output of the fiber to machine micrometer-scale features in copper.     

Thermogravimetric analysis of polyester/cotton blends treated with Thpc-urea-poly(vinyl bromide)

Polyester/cotton fabric swith blend ratios of 0/100, 11/89, 20/80, 30/70, 50/50, and 65/35 were investigated via thermogravimetric analysis in both nitrogen and air atmospheres. The samples were heated from ambient to 750°C at a heating rate of 5°C min^?1. The same fabrics were analyzed after treatment with tetrakis (hydroxymethyl) phosphonium chloride-urea-poly(vinyl bromide) (Thpc-urea-PVBr) flame retardant.Weight losses observed during pyrolysis were assigned to the cotton and polyester portions of the blends. Both cotton and polyester thermally decompose to yield gases and solid char byproducts. In nitrogen the 100% cotton fabric undergoes one major weight loss between 270 and 370°C, with the maximum rate of weight loss, 0.15 mg/min-mg occurring at 346°C. Thermal decomposition of the 100% polyester occurs over a range of 335–470°C, with the peak rate of weight loss, 0.11 mg/min-mg, measured at 416°C. In an air atmosphere, both volatile gases and solid char by- products of pyrolysis undergo combustion. The combustion reactions are associated with measured weight losses. The maximum rate of weight loss for the cotton portion increases to 0.25 mg/min-mg and occurs at 317°C. The maximum rate of polyester decomposition remains the same in both air and nitrogen, but the temperature decreases to 405°C.