Wednesday, June 30, 2010
Consider the following set of synomyns and antonyms:
empowerment - embargo
enabler - disabler
catalyst - inhibitor
strength - weakness
able - inept
competence - incompetence
We probably all need to improve our level of competence.
Tuesday, June 29, 2010
Sunday, June 27, 2010
From the first row of the matrix equation for a and b one sees that the square of a is a linear combination of x and y but by the Pythagorean Theorem it is also the sum of the squares of x and y which enables us to show that the equation for the x and y is that of a circle.
Friday, June 25, 2010
One can eliminate the X·X term from the two equations for the circles to get a vector equation for a straight line. X can then be defined as a linear combination of ΔK and its normal ΔK' and the unknown parameters, λ and μ, can be found by substituting into the equations for the line and one of the circles.
Wednesday, June 23, 2010
The objective function, f, is the sum of the lengths of the lines and at the optimal point its variation is zero for all possible variations in position and as a consequence the variational coefficients are also zero.
These two conditions can be simplified to show that the sum of the unit vectors along the connecting lines is also zero. This means that the angles between these directions are all 120 degrees.
One can solve for the unknown lengths of two of the lines if the angle of one of them is assumed and in this way one can obtain two curves which intersect at the optimal point. The epsilons, ε, denote the unit vectors along the lines connecting at the optimal point.
Using a solve block one can easily find the optimal point. The function, r, solves for the unknown length of the lines for a given angle, θ, and the find function solves for the optimum angle yielding the solution, X.
The solution appears to be the intersection of two circles with one point of intersection at the optimal point and another point of intersection for which the distance from the common point, A, is zero. Circles are curves of constant curvature which may be due the angle between the two links being a constant.
Friday, June 18, 2010
This quote exemplifies some of the problems that we are likely to face when dealing with the challenge of containing the oil spill in the Gulf of Mexico. It is not business as usual. We are lacking the means to achieve an end. We have to create an economy practically from scratch. Wasted effort is contrary to our goal. We have to do the best that we can under the situation. We not only have to reduce the time it takes to stop the flow of oil but we also have to try to reduce the rate at which the costs accumulate. This is probably the best plan of attack. We need to look for what is missing and strive to fill the gap.
Obama's plans for change face similar problems. We don't always know in advance what difficulties we will face. There are hazards which need to be avoided and factored into the "equation." There are barriers to progress.
Tuesday, June 15, 2010
From the point of view of operations research one should try to reduce the "cost" of the oil spill. One can measure cost in terms of the monetary cost or the cost to the environment. Either way one has an objective function which one tries to minimize. There are a number of methods such as the Simplex Method and Algorithm which address the best way of proceeding when constraints are present. The basic idea involved is that of gradient descent in which one follows the path which most quickly reduces the costs. In this case containing the oil spill should be given the highest priority by all parties involved. We need to end the release of oil into the environment which could mean capturing it and placing it in containment vessels. There is probably a problem with storage capacity.
If this is an international problem then it requires an international approach with someone in charge of coordinating activities among nations to get a handle on the problem. It may be that no one has the power or resources to act alone. We need to come together on this. It is the only way to get on top of the situation.
Saturday, June 12, 2010
The question you may ask is, "Have we just recreated the 'such that' symbol?"