analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...

• We often approximate a large number of periods, even if the horizon is known and finite, by assuming an infinite number of periods, and hope that this assumption will simplify the solution. Indeed, even if the general theory becomes more involved, the solution obtained often is simpler and has important computational and conceptual advantages: in particular, the optimal policy is often statio...

If one player guesses randomly and the others pass, the probabi l i ty of a win is 1/2. But Ebert 's th ree-p layer solution is better: pass if the two visible hats are different colors, and guess the missing color if they are the same. This strategy yields a win, on average, 3/4 of the time: of the eight poss ib le hat assignments, it fails only on the two in which all three hats are the same ...