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Everything posted by alext87

  1. Is this correct? Let G be a group and H a subgroup of G. Suppose that G acts on the (non-empty) set A. Then there exists an element of A which has H as its stabilizer? The converse is easily shown. As if G acts on a set A and then pick any w belonging to A then the the stabilizer of w is a subgroup of G. I.e. it there a one-one correspondence between the subgroups of G and the stabilizers of the elements of A? Any help would be great cheer.s
  2. Can anybody describe to be "in basic" terms what is a Platonic solid? And why are there only five? Also what does it mean to say that the faces, angles and edges are all congruent? Thanks
  3. To clear up the confusion. It is not actually a theorem by it is called the Banach–Tarski paradox. And it is a consequence of accepting the axiom of choice.
  4. I have worked out how to do it now. There was no need to work out the integral (in fact it cannot be done analytically). You need to note that the bivariate normal distribution is centrally symmetric about the origin if X and Z are independent and N(0,1). Hence the angle was proportion to the angle the area made with the origin. Thanks for your help. AT
  5. Does anybody know of a one-one homomorphism from A4 (alternating group) into the symmetric group S6 which is not a consequence of a natural embedding of S4 into S6? Does one even exist?? AT
  6. Okay I can show that they are independent... That they are N(0,1) comes from the marginal distributions. I need to integrate over the first quadrant but the integration is what I am struggling on... One method I tried was to change variables to x and z and then separate as they are independent. However, I can't get the answer. Do you what the limits are of z? Do you know a substitution I can make in the integrand for z?
  7. Let (X,Y) have a bivariate normal pdf with correlation coefficient p and variance 1 for both X and Y. So the joint density is: f(x,y) = (1/((2*PI)SQRT(1-p^2)))*exp(-0.5*(1-p^2)^-1 * (x^2-2pxy+y^2)) Show that X and Z=(Y-pX)/SQRT(1-p^2) are independent N(0,1) variables, and deduce that P(X>0,Y>0) = 1/4 +arcsin(p)/((2*PI)) ?? Does anybody know how to do this!?
  8. For every n-dimensional vector space there does exist a basis consisting of semi-definite matrices. Proof: Take the canonical basis of the vector space. This is where we have matrices {E11,E12,...,E1n,E21,E22,...,E2n,...,...,En1,En2,...,Enn} where Eij is a matrices with all zero elements except the (i,j) entry. All these matrices are semi-definite. As the characteristic polynomial is x^n for all Eij where i is not equal to j and the characteristic poly is x^(n-1) * (x-1) for Eii 1<=i<=n. Now all eigenvalues of a matrix are the roots of the characteristic poly i.e (in this case) just 0 and 1. So the matrices are all semi-definite. Hope this helps. AT
  9. A particle is dropped from the top of a tower on the Earth's equator. As a result of the Earth's rotation, does it land slightly to the east, or slightly to the west of the tower?
  10. Can anybody explain how to and solve the equation: d2005y/dx2005 - y = 0 for y? I have tried ancillary equs but are there complex roots. I know the ans it y=exp(x) but need to be able to show it.
  11. This is like the question does 0/0=0 as 0/n=0; or 0/0=1 as n/n=1; or 0/0=infinite as n/0=infinite. This questions hardly have a definite answer but I like to think that the answer is all three at the same time - its more fun that way!!!!
  12. Yx - aYx-1 = cx + d This is one of the different equations and the particular function is rather complicated! Have a go at solving it please. Thanks!
  13. I am having a bit of problem with finding the particular function for linear difference equations. The method of finding the particular function is similar to the method for finding the particular integral in linear differiational equations. Can anybody help?
  14. Geometric problem traingle.doc
  15. I have just looked at the gamma function and am wondering what it tells us and what is the point in the function?
  16. i think I may have found the answer but it is quite tricky. I will scan in the solution tomo. But the ratio ended up being 7:1? Can you verify this or check the worked solution tomo once I have posted it.
  17. science forum probs.doc Here is the solution:-)
  18. k is 5 as this is the minimum found by equating the derivative to zero and rearranging. The range is greater than or equal to 4 as this is the value min y value. It is one-one in this case. One-many does not exist as a name! but only one-one function has inverses!?-is this what you mean!?
  19. There are two similar triangles. Which means the angles must be the same. so from the diagram drawn. tanθ=(x-1)/6 and tanθ=6/(y-6) so 1/6xy - y - x + 6 = 6 x+y = 1/6xy also known is x2 +y2 = 400 therefore: 400 - 2xy = 1/36(xy)2 Solving this quadratic give xy = -36 + 12(SQRT109) = 89.28 sub in x= {-36 + 12(SQRT109)}/y this gives the quadratic y4 -400y2 +16992-864(SQRT109)=0 solving this gives: y=19.47 so x=4.59 (3dp) OR y=4.59 so x = 19.47 (2dp)
  20. I thought the current thinking was that a person had to have the schizophrenic gene and then be exposed to a event that caused the symptoms. However, I dont think this is backed up by extensive research as the problem was with identifying the event which caused the symptoms as the person may not be aware of the traumatic experience. Therefore some people believe that the gene is triggered in some people by an event but in other is as a result of a hormone imbalence through puberty.
  21. I have managed to work out some general solution for multiple angled trig equations which a number of people have checked and told me are good enough to publish as the work is completely orignal. How do I begin to get this work published and insure that the journal/magazine is at the right level for the work? Any ideas? Alex
  22. We will make some simplifying assumptions for this new planetary system: the orbit of the planet is circular (e = 0) the mass of the star is 1 solar mass the mass of the planet is much, much less that of the star we are viewing the system nearly edge on we express everything in terms of the mass and period of Jupiter We make these assumptions to simplify the equations we have to use for determining the mass of the planet. The equation we must use is: Mass of planet = (P/12)^(1/3) x (K/13) x Mass of jupiter P is orbiting time, K is the amplitude of radial velocity change. P should be expressed in years (or fraction of a year), and K in m/s. Twelve years is the approximate orbital period for Jupiter and 13 m/s is the magnitude of the "wobble" of the Sun due to Jupiter's gravitational pull. Not all calculators will take the cube root of a number. Get help if yours does not. Put in your values for P and K and calculate the mass of this new planet in terms of the mass of Jupiter. That is, your calculations will give the mass of the planet as some factor times the mass of Jupiter (for example: Mplanet = 4 MJupiter). Can anybody show me how to get to this equation?
  23. i need help when differiation of function in the form a^x. For example how to i work out the differiational of 2^x and 3^x?
  24. The definition of co-ordination of a complex ion is the number of atoms datively bonded to the central ion. It there a situation where one atom in a ligand can donate two lone pairs of electrons to the central ion?
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