Electronic absorption spectra and energy gap studies of Er3+ ions in different chlorophosphate glasses

Spectroscopic properties of Er3+ ions in different chlorophosphate glasses 50P2O5-30Na2HPO4-19.8RCl (R=Li, Na, K, Ca and Pb) are studied. The direct and indirect optical band gaps (Eopt) and the various spectroscopic parameters (E1, E2, E3, and \xi 4f and \alpha ) are reported. The oscillator strengths of the transitions in the absorption spectrum are parameterized in terms of three Judd-Ofelt intensity parameters (\Omega 2, \Omega 4 and \Omega 6). These intensity parameters are used to predict the transition probabilities (A), radiative lifetimes (\tau R), branching ratios (\beta) and integrated cross sections (\Sigma) for stimulated emission. Attention has been paid to the trend of the intensity parameters over hypersensitive transitions and optical band gaps. The lifetimes and branching ratios of certain transitions are compared with other glass matrices

Necessary and Sufficient Conditions for Pareto Optimality in Infinite Horizon Cooperative Differential Games

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for infinite horizon cooperative differential games. We consider games defined by non autonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case, we present an algorithm, with mild conditions on the control space, to find all the Pareto optimal solutions.

Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.