# lithium barbie doll

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# 87 Questions

 9 Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$ 7 Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ 7 Is it Possible to have Two Distinct Analytic Functions with the Same Real Part? 7 Show bounded harmonic function on $\mathbb{C}$ is constant. 6 For $I,J$ ideals, show that $IJ\subseteq (I\cap J)(I+J)$

# 1,291 Reputation

 +15 The semifinite portion of a measure $\mu$ +5 Counterexample to upper continuity +5 Questions regarding the use of Index Calculus for finite fields and elliptic curves +5 Hidden Markov Model Coin Toss Problem

 4 Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$ 3 Accidents of small $n$ 2 Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$ 0 Complex Analytic Proof of the Gaussian Integral $\int_{-\infty}^{\infty}e^{-z^2}dz=\sqrt{\pi}$ 0 Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$

# 67 Tags

 4 abstract-algebra × 18 2 homework × 10 4 commutative-algebra × 3 0 real-analysis × 11 3 examples-counterexamples × 2 0 number-theory × 8 3 big-list 0 group-theory × 6 2 complex-analysis × 26 0 measure-theory × 6

# 5 Accounts

 Mathematics 1,291 rep 29 Cryptography 143 rep 4 Stack Overflow 106 rep 2 Programmers 106 rep 2 Japanese Language & Usage 101 rep