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  1. E

    Proving something is bounded

    I'm not sure what you are trying to prove - is it given that u,v are harmonic & uv>=0 ?
  2. E

    Stochastic differential equation problem

    This will turn into a standard equation of the type dv/dt=kv+ noise after a change of variable. For some general methods for solving SDEs, I hope the following link will be of much help -
  3. E

    Bounded Lebesgue integrals

    Proceed by indirect method : if the integral over E is strictly > e ,then the integral over E_k should also exceed e for sufficiently large k.
  4. E

    Solving Uxx - Uy - Ux =0

    Does the equation look familiar if you put x+y=t ?
  5. E

    Does anyone know the name of this type of map

    How about calling this a 'hyperinvolution'?
  6. E

    Commuting derivative/Integral (not FTC or Leibniz)

    I don't see any simple relation between the two.Although L is periodic, its second order derivatives may not be so.
  7. E

    What to read after Understanding Analysis

    Have you come across Korner's ' A Companion to analysis'? I find it a good second course, even after having studied Rudin's & Apostol's books. Separate textbooks on complex analysis & on differential geometry would help , as these have much special attributes. An overview of books...
  8. E

    Brownian Motion 1 (birth-death)

    The value of c follows from the varience of the process.( Note that this has to be a 1-dimensional random walk).
  9. E

    Need help w/ Fibonnaci and Golden Ratio proof

    Just use the formula for nth fibonacci number.
  10. E

    Fixed Point Iteration Convergence

    Try to find bounds on x_(n+1) in terms of x_n ,y_n ( for instance, when it's less than x_n).
  11. E

    Oscillator with and without damping - Need help please

    It won't be simply the sum of the two. It will consist of alternate pieces of the graphs of the two. We must consider the time intervals in which x>0 & x<0 separately.
  12. E

    Two general questions about differential equations.

    Have you tried 'Differential Equations' by Simmons? It's a good book & contains many problems in physics. For a course in PDEs, you must be familiar with calculus of several variables & a little functional analysis.
  13. E

    What is the physical meaning of curvature?

    The curvature of potential energy is definitely related to distribution function, but the dependence is weird.I can't give any physical meaning to curvature which might suit the dependence.
  14. E

    Interesting contour integral

    Let a+ib =c^2, so that the integrand has poles at +-c.Integrate along a semicircle which contains a part of the real axis and loops around +-c.
  15. E

    Lie derivative with respect to anything else

    I can't think of a definition of the lie derivative with respect to a covector off my head. However, we may talk about the lie derivative with respect to a totally contravariant tensor.We could define it as the tensor product of component-wise lie derivatives. Such a quantity could be another...
  16. E

    Weird statement in my book about (measure theoretic) conditional expectation

    Think of a sigma algebra as 'containing information'.Since G is the trivial sigma algebra, it contains no intrinsic information & doesn't affect the expectation. I must admit that this terminology is vague & nearly metaphorical. It's perfectly fine if you stash this terminology if it...
  17. E

    Best bound for simple inequality

    Yes,1 is the best possible. Try the functions f_n(x)=x^n.
  18. E

    Higher Order derivative representation

    The geometric interpretation of the second derivative can be convexity at that point, but I have no clue about higher derivatives.
  19. E

    Value of the infinite sum of fourier coefficients?

    I don't see why the series should converge, let alone the exact sum.
  20. E

    Finding Surface Area Cone through integration

    Let a surface be X=(x(u,v),y(u,v),z(u,v)) . The element of area will be the cross product of Xu & Xv ( Xu is the partial derivative with respect to u &c.).Integrate this within the limits.
  21. E

    Measurability of a function f which is discontinuous only on a set of measure 0.

    (a) Let M be the upper bound for f & consider the sets O_n={x in D |2M/(n+1)<=Of(x)<=2M/n} n=1,2,.. Do you see why each O_n must be closed & their union is D? (b)If D is a null set,f would be riemann integrable(& hence measurable) as it is bounded .
  22. E

    Negative Binomial random variable

    E[X]/Var = p and k=pE[X]/(1-p).
  23. E

    Homogeneous DE solution?

    The equation becomes dx/x =[(vtanv-1)/2v]dv on simplification.
  24. E

    Solving specific PDE

    This looks like the heat equation.So, I suggest seperating variables.
  25. E

    When can I change the order of plim and Lim?

    We must check whether all the limits exist in the first place.Although the general question is difficult to answer,I have a counterexample for the second ( where the second limit doesn't exist).
  26. E

    Isolated points are equal to boundary points

    No, a boundary point may not be an accumulation point.Since an isolated point has a neighbourhood containing no other points of the set, it's not an interior point. The boundary is, by definition , A\intA & hence an isolated point is regarded as a boundary point.
  27. E

    Does the Weierstrass M-Test work for all spaces?

    I think the codomain must be a complete metric space for the series to converge pointwise (otherwise the convergence wouldn't make sense).
  28. E

    How to verify a uniform distribution on n-sphere

    Divide the sphere into many parts & count the no. of dots in each part. If they're roughly equal,the distribution is close to being uniform.