practical stability boundary
... Def 1 : x is said to be a critical point of (1) if it satisfies the condition f (x) = 0 where f (x) is the objective function assumed to be in C2(n, ).The corresponding nonlinear dynamical system is -------- Eq. (1) The solution curve of Eq. (1) starting from x at time t = 0 is called a trajector ...
... Def 1 : x is said to be a critical point of (1) if it satisfies the condition f (x) = 0 where f (x) is the objective function assumed to be in C2(n, ).The corresponding nonlinear dynamical system is -------- Eq. (1) The solution curve of Eq. (1) starting from x at time t = 0 is called a trajector ...
The Robustness-Performance Tradeoff in Markov Decision Processes
... a certain tradeoff relationship between the worst-case performance and the nominal performance, that is, if the decision maker insists on maximizing one criterion, the other criterion may decrease dramatically. On the other hand, relaxing both criteria may lead to a well balanced solution with both ...
... a certain tradeoff relationship between the worst-case performance and the nominal performance, that is, if the decision maker insists on maximizing one criterion, the other criterion may decrease dramatically. On the other hand, relaxing both criteria may lead to a well balanced solution with both ...
Clustering and routing models and algorithms for the design of
... strengthen the formulation of the problem, we also consider some valid inequalities in the preprocessing. We then incorporate the column generation algorithm with a variable fixing scheme. Computational results show that the algorithm gives high quality solutions in a short execution time. Finally, ...
... strengthen the formulation of the problem, we also consider some valid inequalities in the preprocessing. We then incorporate the column generation algorithm with a variable fixing scheme. Computational results show that the algorithm gives high quality solutions in a short execution time. Finally, ...
Complex chemical equilibrium calculations. Solution of systems of
... or division by zero. Another option to alleviate the solution of systems of algebraic equations is to convert them to a system where there is only one implicit equation, and the rest of the variables can be calculated from explicit expressions. This approach is demonstrated in Problem 6.3 although i ...
... or division by zero. Another option to alleviate the solution of systems of algebraic equations is to convert them to a system where there is only one implicit equation, and the rest of the variables can be calculated from explicit expressions. This approach is demonstrated in Problem 6.3 although i ...
chpt10examp
... Example 10.1 We will discretize the domain in Figure 10.1 using a uniform mesh of 40 by 40 square bilinear elements. The parameters are chosen as Ra = 105, Pr = 1.0 and the time step t = 10-3. Starting from uniform initial conditions T(x,y,0) = u(x,y,0) = v(x,y,0) = 0.0, the steadystate solution is ...
... Example 10.1 We will discretize the domain in Figure 10.1 using a uniform mesh of 40 by 40 square bilinear elements. The parameters are chosen as Ra = 105, Pr = 1.0 and the time step t = 10-3. Starting from uniform initial conditions T(x,y,0) = u(x,y,0) = v(x,y,0) = 0.0, the steadystate solution is ...
NGSS Engineering Practices Rubric Student
... them. We used science knowledge and could clearly articulate the science behind our design. ...
... them. We used science knowledge and could clearly articulate the science behind our design. ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.