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.Pareto Efficiency;Cooperative Differential Games;Infinite Horizon Optimal Control;LQ theory

Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model

Abstract: In this article we analyze how the presence of thresholds influences multi agent decision making situations. We introduce a class of discounted autonomous optimal control problems with threshold effects and discuss tools to analyze these problems. Later, using these results we investigate two types of threshold effects; namely, simple and hysteresis switching, in the canonical model of the shallow lake. We solve the optimal management and open loop Nash equilibrium solutions for the shallow lake model with threshold effects. We establish a bifurcation analysis of the optimal vector field. Further, we observe that modeling with threshold effects simplifies this analysis. To be precise, the bifurcation scenarios rely on simple rules (inequalities) which can be verified easily. However, the qualitative behavior of the switching vector field is similar to the smooth case.Optimal control;Differential games;Threshold effects;Discontinuous dynamics;Shallow lake

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.

Acetylacetonates of Nickel( 11) and Copper( 11) as Accelerators for the Epoxy Resin System

The acetylacetonates of nickel(II) and copper(II) serve as accelerators for the anhydride-curable epoxy resin system. An appreciable lowering in the cure gel time and a substantial increase in the rate of curing is observed with enhanced concentrations of the metal chelates. Cure kinetic studies and cure schedules have been followed using a differential scanning calorimeter. The thermal and electrical insulation characteristics of the cured epoxy system are little affected by the variation of temperature, voltage, and aging under UV radiation. (C) 1994 John Wiley & Sons, Inc

The Importance of Data Visualization in Exploratory Data Analysis

Data analysis or data science is the most talked about and buzz world in recent time it is also the most research area. Exploratory data analysis also popularly known as EDA is a statistical method or process which helps you to get a better understanding of the data or dataset which you are working on. Exploratory data analysis is considered an essential process in any data science project life cycle. The better you understand your data the better report you will provide or you will able to build more robust and better models. The EDA is consisting of several steps or is a process of several steps that you need to perform on your dataset. The data visualization technics help you a better representation of your data. There n-numbers of way to visualize your data. In this work, we are going to see the importance of data visualization in exploratory data analysis and the graphs you look for in any EDA. There are many paperwork and books available on exploratory data analysis and the steps involved in it. But here we will only try to focus on the different types of visualization techniques involved in the EDA. All the examples we going to see here are built by using python. There many tools available in the market to perform exploratory data analysis but in python where you write your own code to perform anything and python is widely used in the data science field. We will segregate each and every stage of EDA and see the important role plays by data visualization in order to understand the data you are working on

Lyapunov stochastic stability and control of robust dynamic coalitional games with transferable utilities

This paper considers a dynamic game with transferable utilities (TU), where the characteristic function is a continuous-time bounded mean ergodic process. A central planner interacts continuously over time with the players by choosing the instantaneous allocations subject to budget constraints. Before the game starts, the central planner knows the nature of the process (bounded mean ergodic), the bounded set from which the coalitions' values are sampled, and the long run average coalitions' values. On the other hand, he has no knowledge of the underlying probability function generating the coalitions' values. Our goal is to find allocation rules that use a measure of the extra reward that a coalition has received up to the current time by re-distributing the budget among the players. The objective is two-fold: i) guaranteeing convergence of the average allocations to the core (or a specific point in the core) of the average game, ii) driving the coalitions' excesses to an a priori given cone. The resulting allocation rules are robust as they guarantee the aforementioned convergence properties despite the uncertain and time-varying nature of the coaltions' values. We highlight three main contributions. First, we design an allocation rule based on full observation of the extra reward so that the average allocation approaches a specific point in the core of the average game, while the coalitions' excesses converge to an a priori given direction. Second, we design a new allocation rule based on partial observation on the extra reward so that the average allocation converges to the core of the average game, while the coalitions' excesses converge to an a priori given cone. And third, we establish connections to approachability theory and attainability theory

Transition metal chelates as accelerators for epoxy resin systems—studies with cobalt (III) acetylacetonate

Cobalt(III)acetylacetonate serves as an accelerator for anhydride curable epoxy resin system and the rate of curing is found to increase with enhanced concentrations of the metal chelate. There is also an appreciable reduction in the cure gel time. Kinetic studies based on thermal analytical techniques reveal that the overall curing process follows first order kinetics. Based on the kinetic results a cure schedule has been proposed. It is also observed that the electrical, mechanical, and thermal properties of the cured epoxy system are not altered by the presence of the metal chelate at the concentration studied

Synthesis and structural studies of first row transition metal complexes of N-(2-nitro)-benzilidine-3-hydrazino quinoxaline-2-one

Cr(III), Mn(II), Fe(III), Co(II), Ni(II) and Cu(II) complexes of N-(2-nitro)-benzilidene-3-hydrazino quinoxaline-2-one (NBHQO) have been synthesized and characterized by elemental analysis, conductance, thermal, spectral and magnetic data. NBHQO acts as a bidentate ON donor in all the complexes except in Ni(II) complex in which it acts as a tridentate ONO donor. Octahedral geometries have been proposed for all the complexes except for Cu(II) complex to which the square planar geometry is assigned. KEY WORDS: Metal complexes, N-(2-nitro)-benzilidene-3-hydrazino quinoxaline-2-one, ON donor  Bull. Chem. Soc. Ethiop. 2008, 22(3), 385-390