Recent content by basik156

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    Summer 2014 internships and fellowships applications

    Applied to: UC Boulder REU Rice Quantum Institute REU RISE Germany-Us exchange program Rochester REU William and Mary REU Univ of Washington REU Haven't heard back from anyone yet
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    Undergrad Do both TE and TM modes propagate if they have different speeds in a waveguide?

    Hello. Are you familiar with the idea of birefringence and the propagation of light in anisotropic media? For example if we take a crystal of calcite the two polarization states of the light will experience a different index of refraction due to the structure of the crystal provided the beam is...
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    Showing that a series of numbers has an infinite amount of composites

    I should've erased that part before I sent that last message. Thanks so much for your guidance!
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    Showing that a series of numbers has an infinite amount of composites

    When I claim n is odd haven't I taken care of all of those cases?
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    Showing that a series of numbers has an infinite amount of composites

    I must be missing something big because I can't seem to show that x+1 would be a factor. I do know that any polynomial that has a zero at say x=k has a factor of (x-k). So if x^(2k+1)+1 and by inspection , when x=-1 we have -1^n +1 where n is odd so -1^n+1 always equals zero. Thus x=-1 is a...
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    Showing that a series of numbers has an infinite amount of composites

    I understand your first two questions, so I think to answer the third I need to use prime factorization, which is what I am working on now
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    Showing that a series of numbers has an infinite amount of composites

    If I were able to prove that 10^n +1 has any proper divisor less than √10^n+1 then I have shown the claim. How to do this is where I'm at a wall...
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    Showing that a series of numbers has an infinite amount of composites

    Homework Statement Show that infinitely many of the numbers 11, 101, 1001, 10001, 100001,... are composite Homework Equations The Attempt at a Solution So by inspecting these numbers, I notice that 11, 1001, 100001 are all divisible by 11. The numbers can be represented at 10^{n}+1 and...
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    Graduate How is Coulomb's Law generalized for continuous charge distributions?

    For calculating the force on a continuous charge distribution due to another continuous charge distribution, if F=kdqdq'/r^2 would you simply integrate first over dq' and then dq?
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