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1. Work done by a distributed force on a string

Hi All I'd like to know how I could calculate the work done by a distributed force on a string. Let's say the force at a point x at a time t is given by F(x,t). Now the instantaneous amplitude of the string is given by y(x,t), say I think that the work done by the force in...
2. Including Dissipation in Kinetic Energy of Lagrangian

Hi all I've found a way to include dissipation in the kinetic energy of the lagrangian for simple systems and I want to know if its ok to do this. My understanding is that dissipation is typically included using the Rayleigh dissipation function which is seperate from the Lagrangian. The...
3. Uncontrollable States in State Space

Hi Guys/Gals If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix...
4. Godel and Fuzzy Sets

Hello all Does Godel's incompleteness theorem still hold true for fuzzy sets? My feeling is that it doesn't since the http://en.wikipedia.org/wiki/Law_of_excluded_middle" [Broken]no longer applies. Is this reasoning correct?
5. Proof: All Blind-Memoryless search strategies are equivalent

Hi All Is there a proof that all blind-memoryless search strategies are equivalent? By equivalent I mean that no blind-memoryless search strategy can outperform any other in terms of time to goal and domain coverage. It seems to me that this is intuitively true. How would I go about...

Hello Everyone :) Do any of you know of a floating point Analogue to Digital converter that can handle mega-hertz sampling frequencies? I need a really precise angular acceleration transducer which I'll integrate digitally to get angular velocity. Im using an FPGA to do the integration...
7. Lost at MIT probability

Homework Statement You are lost in the campus of MIT, where the population is entirely composed of brilliant students and absent-minded professors. The students comprise two-thirds of the population, and any one student gives a correct answer to a request for directions with probability...
8. ASCII from COM port to be used as 'keyboard' inputs

Hi guys an gals Do any of you know an elegant way to take ascii values from the com port and interpret them as keyboard input in another program? If I may be more clear, we've gotten it right to read in ascii from a microprocessor into matlab but we would like to read in values which are...
9. Proof with regards to cumulative distribution function

Hey guys I'd like a steer in the right direction with this problem. I would like to show that P\{x_1\leq X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1^{-})\quad(1) Where: X is a random variable. F_{X}(x) \equiv P\{X \leq x \} is its cumulative distribution function...

Hello ladies and gentlemen Why can't flows in phase space cross? Would it imply that the system may be at the same state at some future time and then follow a different trajectory? That is to say that the identical initial condition gives a different final condition. To my mind, flows in...
11. Arclength, Surface Area and Volume

I was just thinking: If \iint dS is the surface area of a level surface, S, and \iiint dV is the volume of an enclosed solid, V, shouldn't \int df be the arclength of a function f(x)? Lets say that our surface is given implicitly by \Phi For the surface area we get: \iint dS =...
12. Integration of inverse function

Hello Integration is the 'area under the curve' for a one dimensional function. Say we have a function f(x)=x^2, if we compute the integral of this function between two limits we get the area under it between the two limits on the x axis. What if we wanted to find the area between two...
13. Scalar Function on a Surface

Hi guys and gals This is a conceptual question. Lets say I have a scalar function, f(x,y,z) defined throughout \mathbb{R}^3. Further I have some bounded surface, S embedded in \mathbb{R}^3. How would I find the function f, defined on the surface S? Would it be the inner product of f...
14. Diagrammatic Notation

Hi guys I was first introduced to diagrammatic notation in Roger Penrose's book "Road to Reality". I wanted to know if any of you are familiar with diagrammatic notation for tensors? As such, is it worthwhile learning? Its certainly alot clearer (for me anyway :P) than index notation for...