A control model is presented which studies optimal spending for the fight against terrorism. Under the assumptions that economic damages are larger the greater the number of terrorists and that the success of counter terror operations depends on public opinion, it is demonstrated that a so-calledDNSS threshold may exist, separating the basin of attraction of optimal paths. © 2009 Elsevier B.V. ...

In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The flexibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis conditio...

We asymptotically estimate the variance of number lattice points in a thin, randomly rotated annulus lying on surface sphere. This partially resolves conjecture Bourgain, Rudnick, and Sarnak. also obtain estimates that are valid for all balls annuli not too small. Our results have several consequences: Linnik sums two squares "microsquare", Bourgain Rudnick small sphere, covering radius distrib...

The problem of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is solved. It is supposed that M probability distributions are known and each object independently of others follows to one of them. The matrix of asymptotic interdependencies (reliability– reliability functions) of all possible pairs of the error proba...

We investigate network design under volatile conditions of link failures and traffic overload. Our model is a non-simultaneous 2-commodity problem. We characterize the feasible solutions and using this characterization we reduce the size of the linear program. For 0/1 requirements we present a closed fractional optimal solution, a closed integer-capacities optimal solution, and 76 -approximatio...

With progressing technologies and new features of production, new products compete with older ones in markets. Indeed, new products initiate contest with olden ones and this process repeats in different productions lifetime several times. In this situation recycling the olden products seems to be significant for supply chains. Governments often levy special tariffs for these products as a contr...