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Jan
20
comment Exponential and Logarithmic Functions: $y=2e^{-5x^2}$
Draw the graph to get an idea. It answers majority of the questions by itself. And see then how the first and second derivative tests give the same results.
Jan
10
comment an isomorphism from $L^\infty(\mathbb{T})$ to $L^\infty([-1,1],\displaystyle\frac{2}{\pi } \sqrt{1-t^2}\mathrm{d}t)$
What is the question?
Jan
7
comment Sum of the sets in $\mathbb R^2$
Compact + closed = closed. So (c) is closed with X or with Y.
Dec
30
comment Proper solution of the limit of $\sin(x)/\tan(x)$ as $x \to 0$
This looks perfectly formal to me. By definition tan=sin/cos
Dec
10
comment Prove $\operatorname{dist}(\overline{A},\overline{B}) = \operatorname{dist}(A, B)$
@ArielMarceloPardo: Infimum is an increasing function when you decrease the set of which the infimum is taken over. The intuition is that the smaller set has at least the same infimum as the ambient set, but possibly larger in case you remove the smallest values of the set when creating the subset.
Nov
19
comment Optimizing a convex combination
@michael. I know there is no answer in general, it's easy to produce counter examples even in $\mathbb{R}$, but it's also easy to find classes of functions for which it is possible, if the assumptions are strong enough. In the question I was asking for reference to literature where such problems are addressed, unless someone knows from the top of their head. Also, regarding Benjamin's post, each function is fully dependent on the same variable, most likely some nice function space in the context of my interest or the hilbert cube. But we definitely don't have an inner product in the domain.
Nov
19
comment Optimizing a convex combination
@michael. Yes. The supremum will be finite and the maximum will exist with quite mild assumptions. But I would like the maximizer to be some nice function of $x_i$, if that's possible.
Nov
19
comment Optimizing a convex combination
@BenjaminLindqvist. Not sure what you mean by that. Each $f_{i}$ is a function of the same variable. I've edited this to the question to make it more clear. This variable could be another function, a sequence of functions, a sequence of numbers, or anything else. We can assume that $X$ is a vector space for simplicity or a convex subset of such.
Nov
18
comment Optimizing a convex combination
@Surb: That is exactly the question: what properties would we want to require from each function $f_i$. I'm sure there are many different options, but if there is any literature that discusses this scenario, or if someone knows from the top of their head, I would really appreciate the input.
Aug
7
comment How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$
Have you calculated the determinant of that matrix?
Jul
7
comment How to simplify this integrand,
At first you might want to note that $e^{-2t}+4e^{-2t}=5e^{-2t}$.
Jun
7
comment How do I show that the following is a basis for the weak topology on $X$?
Maybe you'll find this thread useful: math.stackexchange.com/questions/305808/…
Jun
7
comment How do I show that the following is a basis for the weak topology on $X$?
What is $p$ and what do you mean by that set being a semi-norm?
Jun
7
comment How do I show that the following is a basis for the weak topology on $X$?
Isn't this the definition of the weak topology? What is your definition?
Jun
7
comment When is the series converges?
Remember to include the absolute values inside the root.
Jun
7
comment Is this a metric on the shift space?
Did you check the axioms of a metric space, or what makes you "think" yes? Is there some particular part that puzzles you?
Jun
7
comment Error in the reasoning?
@dietervdf. but that's the thing. $d(x,a)=r$ does not translate to $x\in \partial B(a,r)$.
Jun
5
comment Error in the reasoning?
@dietervdf: That property does hold. Note that $\overline{B}(x,r)$ is not the closure of any given set of our interest. The upper bar is just a notation here, different from closure.
Jun
2
comment Compactness of a group with a bounded left-invariant metric
right! Because it's an additive group. Thanks.
Jun
2
comment What is the topology here with three elements in sets?
@Topology: The complement of $\{b\}$ is $\{a,c\}$, which is neither an element of $\tau$, nor $\tau$ without $\{b\}$ in it.