Math

focusing properties of parabolic mirrors
Suppose we take the parabola y = x^2 and rotate it around the y axis, outside the x-y plane or "page". The result is a paraboloid surface. If the correct side of the surface is reflective, rays of light parallel to the y axis, oriented in the negative-y direction, will reflect off the surface and all pass throug... 21 Jun 2005 15:47

¬ What does this symbol mean and how is it used?
My girlfriend is trying to do some financial coursework. In the book she is reading it uses ý in the calculation. After searching around on the internet we have found it is the /neg symbol. But what does it mean and how is it used. In the book the following step is shown in a calculation. (##note## to show po... 30 Mar 2005 08:24

substitution...
What substitution do you think is convenient ? I tried arctanx=y but it doesn't lead anywhere good. Int [xe^(arctanx)]/{Sqrt[(1+x^2)^3]} dx ?? ... 14 Mar 2005 19:25

Difficult absolute value problem
Hi, At least, it's a problem that *I* am finding difficult (read "impossible")! p(x)=[abs(x-1)+x-2] / [abs(x-1)-3x] The questions read: (a) Sketch p (b) Express p(x) as a piecewise defined function without absolute values. By using the graphics calculator I have managed to sketch p! It seems that there ... 8 Mar 2005 08:41

adding probabilities
Hi, I'm kinda stuck with this problem I'm having. Maybe you can help me. Let's say we have an event A. This event can occur through two mechanisms. The probability that event A occurs through mechanism 1 is P1=0.9. The probability that event A occurs through mechanism 2 is P2=0.8. The question I'm struggli... 26 Mar 2005 11:51

Notation question
Hi, I've got a question concerning notation. Given a binary vector xi with i=1,...,n: how can I show with a notation symbol that I just want to address a part of the vector, for example the elements x3,...,x5 of this vector? Given also a boolean function: F: {0,1}^n -> {0,1} How can I for example formally... 5 Mar 2005 16:58

Possible proof of Gabriel's Theorem?
Proof of Gabriel's Theorem: What if we simplify gabriel's proof by keeping the ens fixed and using s in the definition: i.e. we let n be fixed for each of f'(x), f'(x+w/n), f'(x+2w/n), etc. In this case, the following are true: f(x + w/s) - f(x) f'(x) = Lim ---------... 13 Mar 2005 18:33

Contractible metric space
Hello, I have a problem of terminology. What is meant by "starlike" in the assertion: "every starlike metric space is contractible" ? The definition given by the book is: "A metric space M with metric d is starlike in that metric if there is a point p in M such that each other point x in M can be joined to p b... 1 Mar 2005 17:03

where can I find video lectures about statistics such as regression models, multiple regression, non-linear, etc.?
Hi all, I am looking for video lectures about statistics such as regression models, multiple regression models, non-linear regression models, etc. I have background in EE and probability... but after reading books and webpages, I still got perplexed: a lot of time the notations are different than those in E... 17 Feb 2005 03:10

base e: making negative exponents positive
is the following possibe? and if so, why? I havent looked at this stuff in a while, so its a bit confusing...and help would be great! Start with: e (to the power of) -5/t = 0.20 Then I have to change '-5/t' to '+5/t' giving: e (to the power of) +5/t = 5.00 I just dont understand, and cant find the rules... 14 Feb 2005 21:00