We introduce a R “Dual” transform which relates Quantum Field Theory and Quantum String regimes, both in a curved background. This operation maps the characteristic len gth of one regime into the other and, as a consequence, mass domains as well. The Hawking-Gibbons tempe rature and the string maximal or critical temperature are dual of each other. If back reaction of quan tum matter is include...

This paper studies a method of shifting poles of linear constant systems via LQ optimal feedback. By making use of a solution to the so-called inverse regulator problem, this method enables us to shift poles successively by pairs while maintaining the well-known advantages of LQ regulators. Polynomial fractional representation is effectively used both to characterize the maximal pole-assignable...

This paper considers the problems of estimating the stability region (domain of attraction) and controller design for uncertain linear continuous-time systems with input saturationwhen linear quadratic (LQ) optimal controller is used. By exploiting the structure of the LQ controller and the property of saturation functions, it is established that the estimation of stability region can be obtain...

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

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The performance of the linear consensus algorithm is studied by using a Linear Quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting an analogy between Markov Chains and electrical resistive networks. Indeed, this permits to uncover the relation between the LQ performance cost and the average effective resist...

Let Pn be the collection of all polynomials of degree at most n with real coefficients. A subtle Bernstein-type extremal problem is solved by establishing the inequality ‖U (m) n ‖Lq(R) ≤ (cm)n‖Un‖Lq(R) for all Un ∈ e Gn, q ∈ (0,∞], and m = 1, 2, . . . , where c is an absolute constant and e Gn := ( f : f(t) = N X j=1 Pmj (t)e −(t−λj )2 , λj ∈ R , Pmj ∈ Pmj , N X j=1 (mj + 1) ≤ n ) . Some relat...

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