Existence of a Unique Solution
... be linearly dependent on an interval I if there exist constants c1 , c2 ,.......cn , not all zero, such that c1 f1 ( x) c2 f 2 ( x) ...... cn f n ( x) 0 for every x in the interval. If the set of functions is not linearly dependent on the interval, it is said to be linearly independent. ...
... be linearly dependent on an interval I if there exist constants c1 , c2 ,.......cn , not all zero, such that c1 f1 ( x) c2 f 2 ( x) ...... cn f n ( x) 0 for every x in the interval. If the set of functions is not linearly dependent on the interval, it is said to be linearly independent. ...
exam2.pdf
... exam. In preparing your solutions, you may consult our text [Gallian’s Contemporary Abstract Algebra (any edition)], your class notes, any papers/solutions handed out in (our...) class, and your (Math 417) instructor. No other sources may be consulted, and if you run into any information in the norm ...
... exam. In preparing your solutions, you may consult our text [Gallian’s Contemporary Abstract Algebra (any edition)], your class notes, any papers/solutions handed out in (our...) class, and your (Math 417) instructor. No other sources may be consulted, and if you run into any information in the norm ...
(5 points) Problem 2c Solution (5 points)
... this DFA to decide Lk+1 : For each accepting state of this DFA, change it to an unaccepting state, remove its outgoing transitions, and create two new accepting states for it to transition to (one for a 1 and one for a 0). Since the old accepting state accepted strings with 1 in the k th -to-last po ...
... this DFA to decide Lk+1 : For each accepting state of this DFA, change it to an unaccepting state, remove its outgoing transitions, and create two new accepting states for it to transition to (one for a 1 and one for a 0). Since the old accepting state accepted strings with 1 in the k th -to-last po ...
Sample Solutions
... with no two queens on the same row, column, or diagonal. Come up with a value function and use hill climbing to try to solve the problem by minimizing this value function, starting with the configuration given below. Generate the successors of a state by moving a single queen vertically. ...
... with no two queens on the same row, column, or diagonal. Come up with a value function and use hill climbing to try to solve the problem by minimizing this value function, starting with the configuration given below. Generate the successors of a state by moving a single queen vertically. ...
Lecture 2 Structure Charts
... Problem Analysis Charts – a beginning analysis of the problem Structure Charts – shows the overall structure IPO Chart – shows the input, the processing and the output Algorithm – show the sequence of instructions comprising the solution Flowcharts – graphic representations of the algorithms ...
... Problem Analysis Charts – a beginning analysis of the problem Structure Charts – shows the overall structure IPO Chart – shows the input, the processing and the output Algorithm – show the sequence of instructions comprising the solution Flowcharts – graphic representations of the algorithms ...
x, t
... – Thus the probability density for momentum is independent of t, a very strong form of conservation of momentum. Integrating over ξ ∈ Rn shows that the L2 (Rn )-norm of u is independent of time. – Thus the requirement (4) is satisfied as soon as itR is satisfied at t = 0. – The conservation of tot ...
... – Thus the probability density for momentum is independent of t, a very strong form of conservation of momentum. Integrating over ξ ∈ Rn shows that the L2 (Rn )-norm of u is independent of time. – Thus the requirement (4) is satisfied as soon as itR is satisfied at t = 0. – The conservation of tot ...
The Efficient Outcome Set of a Bi-criteria Linear Programming and
... This paper is concerned with the Bi-criteria linear programming problem MAX{Cx , x ∈ X}, (BP) where C is a 2 × n matrix with rows c1 , c2 and X ⊂ IRn is a nonempty compact polyhedron. It is well known that while the efficient solution set XE for Problem (BP ) is also always a connected set, generall ...
... This paper is concerned with the Bi-criteria linear programming problem MAX{Cx , x ∈ X}, (BP) where C is a 2 × n matrix with rows c1 , c2 and X ⊂ IRn is a nonempty compact polyhedron. It is well known that while the efficient solution set XE for Problem (BP ) is also always a connected set, generall ...
Nonlinear Thermal Conduction
... This assignment is about practical aspects of solving sparse systems of nonlinear equations F(U ) = 0 ...
... This assignment is about practical aspects of solving sparse systems of nonlinear equations F(U ) = 0 ...
Honors Linear Algebra (Spring 2011) — Homework 5
... • Problems marked with [M] involve the use of MATLAB. You must submit the commands you use as well as all output from MATLAB as part of the answer to such a problem. You are welcome to email me these commands and output files. If you do email me, name the file(s) using your first and last names. For ...
... • Problems marked with [M] involve the use of MATLAB. You must submit the commands you use as well as all output from MATLAB as part of the answer to such a problem. You are welcome to email me these commands and output files. If you do email me, name the file(s) using your first and last names. For ...
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.