This paper deals with the discrete-time infinite-horizon linear quadratic problem with indefinite cost criterion. Given a discrete-time linear system, an indefinite costfunctional and a linear subspace of the state space, we consider the problem of minimizing the costfunctional over all inputs that force the state trajectory to converge to the given subspace. We give a geometric characterizatio...

1. Unconstrained finite horizon linear quadratic problem 2 1.1. Critical points of quadratic functionals 2 1.2. Shooting function and Hamiltonian flow 6 1.3. Riccati equation 8 1.4. Expression of the critical value 9 1.5. Legendre forms and minima of quadratic functions 9 1.6. Spectral analysis 12 2. Infinite horizon problems 13 2.1. Setting 13 2.2. Kalman state space theory 13 2.3. The algebra...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

won{gil park [won{gil park, j. math. anal. appl., 376 (1) (2011) 193{202] proved the hyers{ulam stability of the cauchy functional equation, the jensen functional equation and the quadraticfunctional equation in 2{banach spaces. one can easily see that all results of this paper are incorrect.hence the control functions in all theorems of this paper are not correct. in this paper, we correctthes...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

an analytical equation of state by song and mason is developed to calculate the pvt properties ofmercury. the equation of state is based on the statistical-mechanical perturbation theory of hard convexbodies and can be written as a fifth-order polynomial in the density. there exists three temperaturedependentparameters in the equation of state; the second virial coefficient, an effective molecu...

in this work, the solubility of nicotine extracted from tobacco leaves, found in the north of iran, in supercritical carbon dioxide has been measured. also the effects of pressure, temperature, extraction dynamic time, and the organic co-solvent on the amount of nicotine extracted from tobacco leaves have been investigated. it should be stressed that in order to reduce significantly the number ...

a viscosity model, based on eyring’s absolute rate theory combined with a cubic pr equation of state and wong-sandler mixing rule, has been proposed in order to correlate viscosities of aqueous solutions of alkanolamine mixtures at atmospheric pressure and different temperatures. in the proposed method, the energy and size parameters in studied equation of state (eos) have been obtained using t...