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A hypothetic building design problem in optimization with constraints proposed by Bhatti (2000, pp. 3-5). To save energy costs for heating and cooling, an architect wishes to ...

A curve whose name means skull-like. It is given by the polar equation r=asint+bsqrt(1-pcos^2t)+csqrt(1-qcos^2t), where a,b,c>0, a<b+c, 0<p<1, 0<q<1, and p!=q. The top of the ...

A right triangle whose legs are in the ratio 2:1 is sometimes known as a "dom," a name derived from "half a domino." The name was suggested by Andrew Clarke and preferred in ...

Efron's dice are set of four nontransitive dice such that the probabilities of A winning against B, B against C, C against D, and D against A are all the same. The images ...

Given a Poisson distribution with a rate of change lambda, the distribution function D(x) giving the waiting times until the hth Poisson event is D(x) = ...

A set of vectors in Euclidean n-space is said to satisfy the Haar condition if every set of n vectors is linearly independent (Cheney 1999). Expressed otherwise, each ...

Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...