We show that in simple environments, a bidding ring operating at a firstprice sealed-bid auction cannot achieve any gains relative to non-cooperative bidding if the ring is unable to control the bids that its members submit at the auction. This contrasts with results for the case in which the ring can control its members’ bids or prevent all but one of the ring members from participating in the...

In this paper, the stabilization problem in switched linear systems with time-varying delay under constrained state and control is investigated. The synthesis of bounded state-feedback controllers with memory ensures that a closed-loop state is positive and stable. Firstly, synthesis with a sign-restricted (nonnegative and negative) control is considered for general switched systems; then, the ...

This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...

New tests for checking asymptotic stability of positive 1D continuous-time and discrete-time linear systems without and with delays and of positive 2D linear systems described by the general and the Roesser models are proposed. Checking of the asymptotic stability of positive 2D linear systems is reduced to checking of suitable corresponding 1D positive linear systems. It is shown that the stab...

The minimum energy control problem for the positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...

In this article, the problem of determining the shape of a thin wing for minimum drag has been examined. In order to determine the optimal shape, we have extended a measure theory-based method. Using an embedding procedure, the problem of finding the optimal shape is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated ...

In this paper, a numerical scheme based on the three-dimensional block-pulse functions is proposed to solve the three-dimensional fractional Poisson type equations with Neumann boundary conditions. The differential operational matrices of fractional order of the three-dimensional block-pulse functions are derived from one-dimensional block-pulse functions, which are used to reduce the original ...

We consider partitions of a finite set whose elements are associated with a single numerical attribute. For each partition we consider the vector obtained by taking the sums of the attributes corresponding to the elements in the parts (sets) of the partition, and we study the convex hulls of sets of such vectors. For sets of all partitions with prescribed number of elements in each set, we obta...