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Feb
10
comment Prove that $a+\frac{1}{b}>2$ or $b+\frac{1}{a}>2$ for two strict positive numbers
@ByronSchmuland Did the answer get vandalized?
Feb
10
answered Matrices and diagonalization.
Feb
9
comment convolution is well-defined and differentiable for continuous $f$ and differentiable $g$ with compact support
I think the term "well-defined" here has a different meaning. I think you're supposed to show that the integral is finite for every $x$.
Feb
9
comment Differentiability of PDE with respect to parameters
Oh I understand what you mean now. In that case, I tend to believe the answer is positive. You have the same differential operator acting on $u$ and $\frac{\partial u}{\partial y}$ (and all its higher $y$ derivatives), and the non-homogeneous term seems to possess the same type of regularity.
Feb
9
comment Differentiability of PDE with respect to parameters
I'm not sure what the second equation means. (Are there typos? Zero on the left-hand side maybe?) Anyway, I suspect that smoothness of $a_{\alpha}$ with respect to $y$ might not be enough. I believe zeros of some $a_{\alpha}$ might cause irregularity, but I could be wrong.
Feb
9
comment Injectivity in the zero homology
You can write up your own answer and accept it. (You can make it community's answer too, I believe.)
Feb
9
comment Write expressions w/out quantifiers (convert to AND/OR expressions)
I think you're thinking about the right method, but for a), there's a mistake in the first pair of brackets, and in c), you should have only three terms.
Feb
9
comment Finding the maximum value of a divergent series
If you can prove that the sum is smaller than a particular value, then it will converge because the sequence of partial sums is monotonically increasing. The question that you mentioned involves a finite sum.
Feb
9
comment Appropriate distribution for set of probabilities $p_1 ,…, p_n$
How about uniform distribution in the given region?
Feb
9
comment Why would an equation switch signs when something becomes independent of time? (Traffic Flow)
I think you might have misread something. Equation (10) involves $\frac{\partial q}{\partial x}$, not $\frac{\partial\rho}{\partial t}$
Feb
9
comment Conditional pdf of a random variable that is a function of other random variables
The pdf of $g(x, Z)$ will be related to $f(y \mid x)$, but not necessarily equal. You can even take a simpler example, like $Y = 2Z$.
Feb
9
comment If a and b are negative , then can we use the same method we are taught for solving the equation y'' + ay' + by=0 ,
@Leth I think you must have missed some details in those statements that you remembered. For example, maybe it was more like what macroland said?
Feb
9
comment How to derive the equation of tangent to an arbitrarily point on a ellipse?
I'm not sure if you understand implicit differentiation correctly but your notation seems off. Your $\frac{d}{dx}$ should be just $dx$ (and the same with $dy$).
Feb
9
answered Eigenvector of a matrix of ones associated with $\lambda =0$
Feb
9
comment If a and b are negative , then can we use the same method we are taught for solving the equation y'' + ay' + by=0 ,
@Leth Those methods will work regardless of the signs of $a$ and $b$. (What makes you think they might not work?)
Feb
9
comment If a and b are negative , then can we use the same method we are taught for solving the equation y'' + ay' + by=0 ,
What method were you taught? The method I know doesn't really care much about the signs of $a$ and $b$.
Feb
9
comment Functions between metric spaces (and how they relate to closures of sets)
Yes. It has something to do with the fact that $X$ is not compact.
Feb
8
answered Vanishing Integral of a differential form without using Stokes' Theorem
Feb
8
comment Solve this system of nonlinear differential equations
The fraction can be simplified to a constant, namely $\frac{k_1}{k_2}$.
Feb
8
revised Chance of drawing 4 red marbles out of a big bag.
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