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location Washington, DC
age 61
visits member for 3 years, 3 months
seen 21 hours ago

I am a math professor at Georgetown University, with broad mathematical interests.

Check out the textbook "Mathematics and Climate" by Hans Kaper and me, published in October 2013 by SIAM.


21h
comment Reverse Cauchy Schwarz for integrals
Use $f^2(x) = f(x) \cdot g(x) \cdot \frac{f(x)}{g(x)} \le f(x) \cdot g(x) \cdot \frac{M_1}{m_2}$ and a similar inequality for $g^2(x)$.
Jul
25
comment Prove two solutions of differential equation are the same
Note that we can assume $C_2 = 0$ or $C_3 = 0$, since both are additive constants.
Jul
25
comment Prove two solutions of differential equation are the same
Have you tried to plot the two functions for different choices of $C1, \dots C_4$ - just to check that these are really the same?
Jul
20
comment How to transform a maximizing objective function which contains a max operator to a standard LP form
This is the right start, however, $z$ should not be restricted to be a binary variable. In particular, this is no longer a linear program (it's an integer program) and it is possible that with this approach the problem no ponger has feasible solutions.
Jul
17
answered Let $A = \{1/2 < |z| < 2\}.$ Is there an analytic function $f$ on $\mathbb{C} \setminus \{0\}$ so that $Im(f) < −1$ on $∂A$ and $f(1) = 0$?
Jul
16
comment Distribution of reversed k-th order statistics
First off, your distribution function assumes that $X_i \sim U(0,1)$ (which is not a big restriction). As to your question, if, say, $n = 5$ and $Y_{(2)} = .3$, what do you think is $Y_4$ (using descending order)? Do you see what is going on?
Jul
16
reviewed Close Proof of Gram-Schmidt
Jul
16
reviewed Close Sum of series with triangular numbers
Jul
16
reviewed No Action Needed recurrence relation dependent inversly on n
Jul
16
reviewed Leave Open Dimension of R over Q without cardinality argument.
Jul
15
comment Number of ways to win chocolate game
could you please phrase the question clearly and precisely? Are you interested in the number of ways that the game can be played or in the number of ways in which Alice or Bob can win or in something else?
Jul
15
comment Number of ways to win chocolate game
This is the game of Nim. Its solution is well understood. en.wikipedia.org/wiki/Nim
Jul
15
comment Determinant of the sum of an orthogonal and a singular matrix
@jdizzle - $\det O x x^T = 0$ since this is a rank 1 matrix. Or is there a misprint?
Jul
15
comment Is the subset $\{P\in C[0,1]: P \text{ is polynomial and} P(0)=P'(0)=0 \}$ dense in $L^1[0,1]$?
Take $f(x) = 1$ and $p_n(x) = 1 - (1-x)^n$. Then $p_n(0) = 0$ for all $n$ and $\|p_n - f\|_{L^1} = \frac{1}{n+1}$.
Jul
15
answered Determinant of the sum of an orthogonal and a singular matrix
Jul
14
comment Linear Constraints Solution Existence
You can always take $t$ to be the zero vector. So what is the non-trivial version of your question?
Jul
14
reviewed Close How to find Inverse function value at given point?
Jul
14
comment How to calculate $\int_{-\infty}^\infty\frac{x^2+2x}{x^4+x^2+1}dx$?
First factor the denominator into something like $x^4 + x^2 + 1 = (x^2 + ax + 1)(x^2 + bx + 1)$. You will have to find $a$ and $b$. Then use partial fractions. The integrand will be of the form $$\frac{x^2 + x}{(x^2 + ax + 1)(x^2 + bx + 1)} = \frac{Ax + B}{x^2 + ax + 1} + \frac{Cx + D}{x^2 + bx + 1}$$ and you will have to find $A,B,C,D$ next. After that it's two standard integrals.
Jul
14
comment checking the solution of PDE
Do you understand how $v$ is defined?
Jul
14
comment checking the solution of PDE
Let $v = u_{x_1x_1}$, for example. Compute $\Delta v$!