A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written terms bubble-volume variation is solved through linear iterative procedure. The model validated, and its accuracy fast convergence are shown analysis several examples different physical meanings. simplicity usefulness presented method here relation to direct resolution whole system, wh...

In this paper, an iterative algorithm to solve a special class of Hamilton-JacobiBellman-Isaacs (HJBI) equations is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local converge...

We describe a procedure which finds a hierarchical clustering by hillclimbing. The cost function we use is a hierarchical extension of the k-means cost; our local moves are tree restructurings and node reorderings. We show these can be accomplished efficiently, by exploiting special properties of squared Euclidean distances and by using techniques from scheduling and VLSI algorithms.

s A numerical iterative scheme is suggested to solve the Euler equations in two and three dimensions. The step of the iteration procedure consists of integration over the velocity which is here carried out by three di erent approximate integration methods, and in particular, by a special Monte Carlo technique. Regarding the Monte Carlo integration, we suggest a dependent sampling technique whic...

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. Af...