This paper uses Monte Carlo simulations to calculate the Spencer-Attix water/medium stopping-power ratios (sw, med) for the dosimetry of scanned proton pencil beams. It includes proton energies from 30 to 350 MeV and typical detection materials such as air (ionization chambers), radiochromic film, gadolinium oxysulfide (scintillating screens), silicon and lithium fluoride. Track-ends and partic...

We propose a new point of view of the Spencer cohomology appearing in the formal theory of differential equations based on a dual approach via comodules. It allows us to relate the Spencer cohomology with standard constructions in homological algebra and, in particular, to express it as a Cotor. We discuss concrete methods for its construction based on homological perturbation theory. Appears i...

6. Lewis DW, Ismail AI. Preventive Dental Care (Chapter 36). Canadian Task Force on the Periodic Health Examination. Ottawa: Canada Communication Group, 1994. 7. US Preventive Services Task Force cited in Canadian Task Force on the Periodic Health Examination. Canadian guide to clinical preventive health care. Ottawa: Canada Communication Group, 1994: 408-431. 8. Allister J, Stewart J, Spencer ...

It is conjectured by Erdős, Graham and Spencer that if 1 ≤ a1 ≤ a2 ≤ · · · ≤ as are integers with ∑s i=1 1/ai < n − 1/30, then this sum can be decomposed into n parts so that all partial sums are ≤ 1. This is not true for ∑s i=1 1/ai = n − 1/30 as shown by a1 = · · · = an−2 = 1, an−1 = 2, an = an+1 = 3, an+2 = · · · = an+5 = 5. In 1997 Sandor proved that Erdős–Graham–Spencer conjecture is true ...