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    Problem in proving d(x,y)=0 implies x=y.

    Hello everyone. I am trying to prove that the in a planar domain U \subseteq C equipped with a metric \rho, the definition of the distance between P and Q, both lying in U is given by \\ \\ d_{\rho}(P,Q)=inf \left\{ L_{\rho}(\gamma): \gamma \in C_{U}(P,Q)\right\}, where C_{U}(P,Q) denotes all...
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    A complex problem

    Hi all. The problem is "Prove that a function which is analytic in the whole plane and satisfies an inequality |f(z)| < |z|^n for some n and sufficiently large |z| reduces to a polynomial." I do not understand what I need to show that the function reduces to a polynomial. Any help will be...
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    Mobius maps form a Simple group

    Hi all, How do I prove that the set of all Mobius Maps form a simple group, that is they have no non-trivial subgroup? How can I characterize a non-trivial subgroup? Hints will be welcome. Thanks
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    Galois Extension of Q isomorphic to Z/3Z

    Hi... How do I construct a Galois extension E of Q(set of rational numbers) such that Gal[E,Q] is isomorphic to Z/3Z. Thanks.
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    Isomorphism in graphs

    Hi all, If I have to prove that the graph G and its complement G' are isomorphic, then is it enough to prove that both G and G' will have the same number of edges. Intuitively its clear to me, but how do I prove this. If there's a counterexample, please post. Thanks in advance.
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    Icm 2010

    (Well I don't know if this post should be here or not. If not please move it to the appropriate place.) Hi Everyone. Next year International Congress of Mathematicians will be held in Hyderabad, India. And I am 2nd Yr undergraduate student in mathematics, and I wish to attend it. The thing I...
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    An integer between n and n+1 where n is an integer.

    hi guys.. Does this statement require a proof? It seems pretty obvious to me. "prove that there is no integer between n and n+1 where n is an integer." Also if it does require a proof, what I need to show? Just few hints will suffice. thanks jitendra
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    Colourful space

    Hi everybody, I am unable to tackle this problem, and don't know how to attack it. can someone plz help me how to attack the following problem. Q. Suppose colour every point in 3-D space is assigned one of the three colours- red,green,blue.Can i conclude the following???: 1)there must...
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    Any Hints .

    Any Hints plzzzz. hey guys can u plz give a few hints on how to solve the following diff equation--- y' = 1 + x.(cos y)^2 I have tried the substitution y = arccos x but it does not work. plz help me. thanks in advance.
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    Can a field disturb the geometry of a space?

    hI guys. Back after a vey long time. The question is-"Consider a 3-d surface on which normal Euclidean geometry is valid. Now assume that electromagnetic field is allowed to pervade the whole of the surface . Now what is the possibility that the geometry of the space will be non-euclidean, if...
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    Mass in Relativity

    [Mentor's note: this is a continuation of a thread in the Quantum Physics forum: which turned into a discussion of the various kinds of mass in relativity.] Originally Posted by Los Bobos "It is actually more consistent to say, that from...
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    Few questions on uncertainty principle

    Can we mix SR and uncertainty principle? for ex. from uncertainty principle we have \Delta x \Delta p \geq h/4\pi . Books then write m \Delta x \Delta v \geq h/4\pi with an assumption that m can be measured accurately. However form SR we know that mass depends on velocity; with mass...
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    Poll subforum

    hi mentors dont you think there should be a subforum for poll ?
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    How is your eyesight?

    Do you have four eyes:rolleyes: I meant do you wear spectacles:bugeye: .I think almost half of the PF members wear spectacles after all each of them are either mathematicians or scientists and spectacles are their trademark. Well here's a small poll, just to know how many of you are 4-eyed...
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    A quick question on coefficient of binomial expansion

    Is it always necessary that C(n,r) is an integer if n and r are integers ? Is there any proof ?Please clarify. thanks.
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    Math Teaser

    Math Teaser!! Can you solve this? [tex] \frac{4 \infty}{\sqrt{-1}} {(1+\sqrt{-1})^(1/\infty)-(1-\sqrt{-1})^(1/\infty)} [\tex] Edit: why this latex is not being generated? Anyway the "expression" is [(4*inf)/sqrt(-1)] * { [1+sqrt(-1)]^(1/inf) - [1-sqrt(-1)]^(1/inf) } where inf stands...
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    Why the tetrahedral angle is 109 deg 28 min?

    Hope my question is understood.
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    Programs How do you do Phd?

    I was just wondering at how a Phd is obtained.i know that some research work is the thesis for the phd a new one or old? please put some light on this matter.
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    How to attack an unknown problem.

    Suppose you were given a problem.How do you attack it, I mean to say how to proceed and what ideas to apply in solving that problem?
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    A hint please.

    Can anyone give me hints on the following question.I do not know how to proceed. Find all integers a,b,c,d satisfying the following relations i) 1 \leq a \leq b \leq c \leq d ii) ab+cd = a+b+c+d+3 thanks
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    Difference between = ,<=>

    Difference between "=" ,<=> It may be a little funny but what's the difference between the signs a) equals to b) implies and is implied by?
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    Learning congruences

    I am finding it very difficult in understanding congruences.i have understood what congruences are and their basic properties .But i am stuck at the next junction about residues.After that i understood euler's totient function. Well can anyone describe in detail about residues with sufficient...
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    Is SR real ?

    Is SR "real"? What I mean to say is that as SR predicts time dilation, do the biological processes also slow down? Suppose A and B are two twin of them(A) goes for a space tour in a spaceship with a velocity comparable with c, while the other(B)remains on earth. Clearly, for B...
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    Some divisibility questions

    Hi, I am going through the book on number theory by ivan niven. well its tough book though, and i am stuck with problems in the first topic divisbility.Hope some help. 1. prove that a|bc if and only if a/(b,c)|c where (b,c) is the lcm of b and c. 2. Prove that there are no positive...
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    Questions for disscussions

    I am posting some questions from my textbook.These questions are discussive in nature. However I shall also give answers to which I want that you people should judge my answers and put forward your comments and suggestions about their correctness. Looking for help from you guys. ps. the...
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    A question on potential

    Well I am not sure where to post this. But, anyway, I am finding 'potential' to be rather difficult. Afterall what is this potential? it comes popping out in different forms such as in potential energy ,potential difference ,electric potential etc. I also know ,for example, that electric...
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    Pi[x] >=loglogx

    I am going through Hardy's book on number theory.The following theorem I do not understand. theorem 10: pi[x] >= loglog x where pi[x] is the prime counting function and >= stands for greater than or equal to The arguments written in the book are very compact.please help .
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    Does magnetic field do any work

    Sorry, but while going through the article on magnetism in wikipedia I read the following which i couldn't not catch it. When a charged particle moves through a magnetic field B, it feels a force F given by the cross product: F= q V x B where is the electric charge of the particle is the...
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    Proving geometric theorems by vector method

    I am learning vectors in which there is a section in which geometric theorems are proved with the help of vectors. However while solving problems I often face difficulty on how to proceed ,where to use dot product, cross and etc.Is there any systematic manner on how to prove these ? Please...
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    Geometrical representation of the nth derivative

    The first derivative represents the slope of a tangent at a point on the function's curve. The second derivative represents the concavity of the function's curve. However I am unable to figure out what the other derivatives of a function represent either physically or geometrically. Pleae help.