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Journals and Conferences
There were two reasons why this work was conducted. The first was to help determine the time of death of suicide and homicide victims inside vehicles. The second was to investigate the serious threat to life of children or pets left in stationary vehicles on a hot summers day. This paper demonstrates that when a vehicle is parked in the sun, temperature… (More)
The torsion function of a plane domain is a function which is zero on the boundary of the domain and whose Laplacian is minus one at every point in the interior of the domain. We survey qualitative properties of the torsion function, and bounds on it and its derivatives, available when the plane domain is convex.
A porous rectangular dam is above a horizontal impermeable base. There is a steady ow in which water seeps through the dam from one reservoir (on the left) to a lower reservoir (on the right). Because of gravity the water does not ow through the entire dam and the dam is dry near its upper right corner. The interface separating the dry and wet regions of… (More)
A graph is (m, k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on the set of all vertices receiving the same colour is at most k. The k-defective chromatic number χ k (G) is the least positive integer m for which graph G is (m, k)-colourable. Let f (m, k; planar) be the smallest order of a… (More)
Consider convex plane domains D(t) = (1 − t)D 0 + tD 1 , 0 ≤ t ≤ 1. We first prove that the 1/4-power of the polar moment of inertia about the centroid of D(t) is concave in t. From this we deduce some isoperimetric inequalities.
Consider positive solutions of the one-dimensional heat equation. The space variable x lies in (?a; a): the time variable t in (0; 1). When the solution u satisses (i) u(a; t) = 0, and (ii) u(:; 0) is logconcave, we give a new proof based on the Maximum Principle, that, for any xed t > 0, u(:; t) remains logconcave. The same proof techniques are used to… (More)
SUMMARY Flow resistance laws, as used for example in water-supply pipe networks, are formulae relating the volume ow rate q along a pipe to the pressure-head diierence t between its ends, q = (t). is monotonic. The simple Hazen-Williams power \law" is often used: it has been claimed that the more complicated Colebrook-White law (CW) better represents… (More)
The (generalised) torsion function u of a domain Ω ⊂ IR n is a function which is zero on the boundary of the domain and whose Laplacian is minus one at every point in the interior of the domain. Denote by |Ω| the measure of Ω, x c its centroid. We establish, for convex Ω, 3 2(n + 1) 2 ≤ 1 (n + 1) 2 |Ω| Ω u max Ω u ≤ |Ω|u(x c) Ω u ≤ |Ω| Ω u max Ω u ≤ 1 2 (n… (More)
Suppose two bounded subsets of IR n are given. Parametrise the Minkowski combination of these sets by t. The Classical Brunn-Minkowski Theorem asserts that the 1/n-th power of the volume of the convex combination is a concave function of t. A Brunn-Minkowski-style theorem is established for another geometric domain functional.