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ex.nihil
  • Member for 8 years, 4 months
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7 votes
2 answers
9k views

Prove that $A$ is dense if and only if any non-empty open set in $X$ has an intersection with $A$

6 votes
1 answer
1k views

Does the form $XAX^\top$ have a name?

6 votes
4 answers
2k views

Prove $R(a \times b) = Ra \times Rb$ given $R \in \mathcal{SO}(3)$ and $a,b \in \mathbb{R}^3$.

5 votes
0 answers
80 views

How far (for which $p$) can we generalize $\int x^p \mathrm{d}x=\frac{x^{p+1}}{p+1} + C,p\neq-1 $?

4 votes
0 answers
273 views

Uses of nonsmooth analysis in mathematical research

4 votes
0 answers
2k views

Prove that a cone is convex if and only if it is closed under addition.

3 votes
0 answers
65 views

Prove that the polar cone $K^\circ = \{v\in\mathbb{R}^n:Av\leq 0\}$ where $A$ is the matrix that has $x^i$ as its $i$-th row for ($i=1,\dots\,m$).

3 votes
0 answers
553 views

Prove that $X$ is a complete metric space if every closed ball in $X$ is compact.

3 votes
0 answers
154 views

At what point does a topological space become a geometric one?

3 votes
2 answers
2k views

Geometric definition of the dot product in $n$-dimensional vector spaces

2 votes
1 answer
53 views

Counterintuitive result, Expected Value of Uniform Random Variable raised to increasing powers.

2 votes
2 answers
2k views

Natural deduction proof / Formal proof : Complicated conclusion with no premise

2 votes
1 answer
816 views

Show that the function $h$ defined by $h(x)=g(f(x))$ is lower semicontinuous.

1 vote
1 answer
269 views

Prove that if $x$ is a fixed point for $g$ then its projection to $S$ minimizes $f$ over $S$.

1 vote
1 answer
2k views

Determine the normal and tangent cones $N_C (x)$ and $T_C (x)$ for all $x \in C$.

1 vote
2 answers
923 views

Find the convex subdifferential $\partial d_K$ of the distance function $d_K$ associated to a convex set $K$ at in-set points $x_0 \in K$.

1 vote
1 answer
523 views

Prove that the normal cone $N_{\text{gph}(f)}$ of the graph of the affine function $f$ has the given form.

1 vote
0 answers
83 views

Prove that the dual of the norm approximation problem has the given form.

1 vote
1 answer
329 views

Differential equations: Substitution choice.

1 vote
1 answer
51 views

Give a metric space $(X,d)$ and a function $f$ such that the topologies $T_d$ and $T_{d_f}$ are distinct.

1 vote
1 answer
2k views

In practice, what is the difference between the “nominal plant model” and the “plant model”?

1 vote
1 answer
49 views

Are most integral formulas invariant to complex-valued parameters?

1 vote
2 answers
198 views

What is the difference between feasibility and admissibility?

0 votes
0 answers
28 views

Random Variable Definition: Sample versus Event Space

0 votes
1 answer
11k views

Predicate Logic Expression: "Nobody loves anybody."

0 votes
3 answers
4k views

Duplicate - Proof by Ordinary Induction: $a^n-b^n \leq na^{n-1}(a-b)$

0 votes
1 answer
325 views

Prove that the set $\{x_n:n\in\mathbb{N}\}\cup\{a\}$ is sequentially compact using sequences

0 votes
1 answer
65 views

Verify these propositions about open and closed sets.

0 votes
4 answers
57 views

Prove that $\sum^\infty_{n\text{ = }m}\big(\frac{a}{e^{n+b}}\big)=\frac{a\,e^{1-\,b\,-\,m}}{e-1}$ [closed]

0 votes
1 answer
21 views

Is $ \max_{x\in\mathbb{R}^n} \{ f(x)+g(x) \} = \max_{x\in\mathbb{R}^n} f(x)+\max_{x\in\mathbb{R}^n} g(x) $ if $f$ and $g$ are affine in $\mathbb{R}$?