mathjacks
Reputation
1,470
Next privilege 2,000 Rep.
Edit questions and answers
7 16
Impact
~22k people reached

• 0 posts edited
• 0 helpful flags
• 212 votes cast

1,470 Reputation

2 2 days ago
 +2 20:10 accept Suppose $u,v \in \mathbb{C}$ are in the open unit disk. Is $|u|^n - |v|^n \leq |u - v|^n$?
-195 Apr 27
 -200 03:00 reversal Voting corrected (learn more) +5 01:09 upvote Compute $\lim_{x \to 0} \frac{\sin(x)+\cos(x)-e^x}{\log(1+x^2)}$.
200 Apr 26
 +5 19:53 upvote Show $f_t- a x f_x + \frac{1}{2} b \sigma^2 f_{xx}=0$ has solutions of the form $f(x,t) = C(t) e^{-D(t)x^2}$ +5 19:53 upvote Is the determinant of $A$ is equal to the product of its eigenvalues for vector spaces over any field? +5 19:53 upvote If $f(z)$ maps the unit disk onto itself $k$ times, prove that f(z) must be a rational function and show that the degree of its denominator $\leq k$. +5 19:52 upvote Let $V$ be the space of complex polynomials on $[0,1]$. Is the differentiation operator self-adjoint? +5 19:52 upvote Is there a diagonalizable matrix $A \neq B$ such that $e^A = e^B$? +5 19:52 upvote Is it possible to determine if this matrix is ill-conditioned? +5 19:52 upvote How to evaluate $\lim_{(x,y)\to(0,0)}\frac{y^2\sin^2x}{x^4+y^4}$ +5 19:52 upvote Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$ +5 19:52 upvote We are given $f: X \rightarrow P(X)$, $f(x) = X\backslash\{x\}$, and $X$ is a set. Is the function injective, surjective, bijective? +5 19:52 upvote (complex variables) Show that a convergent sequence in the plane means that the corresponding points of the sequence on the Riemann sphere converges +5 19:52 upvote Show that $\log \left| z \right|$ is harmonic and find its the conjugate harmonic function. +5 19:52 upvote First four terms of the power series of $f(z) = \frac{z}{e^z-1}$? +5 19:52 upvote Find the Laurent series of $f(z) = \frac{1}{z-2} + \frac{1}{z-3}$ for $2 < |z| < 3$ and for $|z| > 3$ +5 19:52 upvote Does $\sum_{n=0}^\infty (-1)^n (e-(1+\frac{1}{n})^n)$ converge absolutely, conditionally, or diverge? +5 19:52 upvote Let $f: \mathbb{R} \to \mathbb{R}$ be a continuous function. Is $\{ x \in \mathbb{R} | 0 < f(x) \leq 1 \}$ an open or closed subset? +5 19:52 upvote Find a polynomial which approximates $f(x) = \sqrt{x}$ in the interval $(4,5)$ within $10^{-8}$ +5 19:52 upvote Using complex analysis, calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ for $I_2$ and $I_3$ +5 19:52 upvote What vectors in the plane z=x are orthogonal to $(1,-1,0)$? +5 19:52 upvote When writing the integral sign $\int$, how does one know what integral is being discussed? +5 19:52 upvote Show that $\,f(x) = \sum_{n=0}^\infty a_nx^n$, for $x \in [0,1]$, is of bounded variation +5 19:52 upvote Why does Fubini's theorem not hold/apply to this function? +5 19:52 upvote Limit of two variables, proposed solution check: $\lim_{(x,y)\to(0,0)}\frac{xy}{\sqrt{x^2+y^2}}$ +5 19:51 upvote Show that every measurable set $A$ can be written $A=B \cup C$ +5 19:51 upvote Prove that every nonempty open subset $G$ of $\mathbb{R}^n$ can be expressed as a countable union of nonoverlapping closed rectangles. +5 19:51 upvote Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$? +5 19:51 upvote Let $f(z) = z^4 - 2z^3 + z^2$. Evaluate $\frac{1}{2\pi i} \int \frac{f'}{f} dz$ and $\int \frac{zf'}{f} dz$ +5 19:51 upvote Proof involving matrix inverse of: $\|A^{-1}\|_\infty \ge \frac{\|U^{-1}\|_\infty}{n}$ +5 19:51 upvote For what values $p,q$ does the improper integral $\int_0^1 x^p (1-x^2)^q dx$ converge? +5 19:51 upvote Let $z_1$, $z_2$ and $z_3$ be complex vertices of an equilateral triangle. Show $z_1^2 + z_2^2 + z_3^2 = z_1 z_2 + z_2 z_3 + z_3 z_1$. +5 19:51 upvote Calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ using complex variables +5 19:51 upvote What conditions are necessary on $a,b,c,d$ so that the Möbius transformation $w=\frac{az-b}{cz-d}$ has only one fixed point? +5 19:51 upvote Prove if $a$ is a nonnegative real number and $n$ is a positive integer, there exists a $b \geq 0$ such that $b^n = a$ +5 19:51 upvote Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$. +5 19:51 upvote Compute $\lim_{x \to 0} \frac{\sin(x)+\cos(x)-e^x}{\log(1+x^2)}$. +5 19:51 upvote Prove $(\overline{A \cap B}) \subseteq \overline{A} \cap \overline{B}$. +5 19:51 upvote Show the level curves of $\log|f(z)|$ are orthogonal to those of $\operatorname{arg}(f(z))$. +5 19:51 upvote Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$. +5 19:51 upvote Suppose $dX_t = a(X_t) dt + b(X_t) dW_t$ and $Y_s=X_t$ where $s=t^2$. What SDE does $Y_s$ satisfy in the weak sense? +5 19:51 upvote Let $A$ be an $n \times n$ matrix over $\mathbb{C}$ or $\mathbb{R}$. Does $\det(e^A) = e^{\mathrm{tr}(A)}$ always hold? +5 19:51 upvote Describe the Riemann surface for $w=z^2-1$.
35 Apr 23
10 Apr 18
2 Apr 16
4 Apr 4
10 Apr 3
10 Mar 29
2 Mar 26
5 Mar 25
5 Mar 19
5 Mar 18
17 Feb 23
7 Feb 17
5 Feb 10
2 Feb 9
5 Feb 6
2 Feb 3
5 Feb 2
2 Feb 1
5 Jan 30
2 Jan 18
12 Jan 17
17 Jan 13
2 Jan 2
5 Jan 1
5 Dec 20 '15
2 Dec 19 '15
22 Dec 18 '15