An addendum to the AAPM's TG-51 protocol for the determination of absorbed dose to water in megavoltage photon beams is presented. This addendum continues the procedure laid out in TG-51 but new kQ data for photon beams, based on Monte Carlo simulations, are presented and recommendations are given to improve the accuracy and consistency of the protocol's implementation. The components of the un...

Comparison between the results from the design procedure based upon the value of D2L (volume of iron) and IEC standard used by manufacturers indicates that the basic design equation of electrical machines must be modified by a proper modification factor. This modification factor is evaluated for single- and three-phase induction motors and its variation with motor rating and poles number is obt...

Any finite distributive lattice has a unique Heyting structure. Every finite Heyting semilattice has, of course, a unique lattice structure and it is necessarily distributive. ∗ This ms was born in 2002. The first appendix was added in 2005, the first footnote in 2013, the subscorings in 2015 and the addendum in 2017. 1 [ ] See 2nd appendix for subscorings. First x and y meet x↔ y in the same w...

The purpose of this document is to clarify the inductive step described in the proof of Theorem 3.2 in [2]. In the second last sentence of the proof, it says, ‘it follows from the inductive proof that Rn is of index two.’ The question of how this assertion is verified was first raised by Dror Bar Natan and his student Ofer Ron [1]. To avoid any confusions that may arise in the future, the autho...

We provide a multiperiod model of political competition in which voters imperfectly observe the electoral promises made to other voters. Imperfect observability generates an incentive for candidates to offer excessive transfers even if voters are homogeneous and taxation is distortionary. Government spending is larger than in a world of perfect observability. Transfers are partly financed throu...

1.1 Small and semismall maps Let f : X → Y be a proper surjective map of varieties with X nonsingular. We say that a decomposition of Y = ⊔ k Sk into finitely many non-singular locally closed subvarieties Sk is a stratification relative to f if each restriction f : f(Sk)→ Sk is a topological locally trivial fibration. Proposition 1.1. The following conditions are equivalent. (a) Rf∗CX [dimX] is...

where x ∈ R, {Ap, p ∈ P} is a compact set of n × n matrices, P is an index set, and σ : [0,∞) → P is a piecewise constant switching signal. The main result of [1] (Theorem 2) states that the system (1) is globally exponentially stable, uniformly over all switching signals, if all the matrices Ap, p ∈ P are Hurwitz and the Lie algebra generated by these matrices is solvable. (Hurwitzness of the ...