Intereting Posts

$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
Derivative at $0$ of $\int_0^x \sin \frac{1}{t} dt$
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
Bijection from finite (closed) segment of real line to whole real line
Uniqueness of Helmholtz decomposition
Show the usual Schwartz semi-norm is a norm on the Schwartz space
Do $\omega^\omega=2^{\aleph_0}=\aleph_1$?
Coin toss – probability of a tail known that one is heads
Prove that $\,\sqrt n < 1 + \sqrt{\frac{2}{n}}\,$
Translations of Kolmogorov Student Olympiads in Probability Theory
Computing class group of $\mathbb Q(\sqrt{6})$
Importance of Cayley's theorem
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$
Non-existence of irrational numbers?

From Paulus Graphs.

“The (25,2)-, (25,4)-, and (26,10)-Paulus graphs have the apparently rather unusual property of being both integral graphs (or asymmetric) and identity graphs (a graph spectrum consisting entirely of integers).”

I once quietly conjectured this was impossible, but I was proven wrong. Very wrong. Eric Weisstein was amused enough by my reaction that he added the above quote.

- Combinatorics for a 3-d rotating automaton
- Round-robin party presents (or: Graeco-Latin square with additional cycle property)
- Question regarding bipartite graphs and their subgraphs.
- Number of edge disjoint Hamiltonian cycles in a complete graph with even number of vertices.
- Spectrum of adjacency matrix of complete graph
- A sequence of $n^2$ real numbers which contains no monotonic subsequence of more than $n$ terms

Is there a smaller counterexample?

- Permutation isomorphic subgroups of $S_n$ are conjugate
- Showing that no Hamilton Circuit exists
- Automorphism of $S_4$
- Quotient of nilpotent group is nilpotent
- the image of normal subgroups
- Holomorph is isomorphic to normalizer of subgroup of symmetric group?
- What does Frattini length measure?
- Transitive subgroup of symmetric group $S_n$ containing an $(n-1)$-cycle and a transposition
- $G$ be a non-measurable subgroup of $(\mathbb R,+)$ ; $I$ be a bounded interval , then $m^*(G \cap I)=m^*(I)$?
- Numbers of ways $k - 1$ edges to be added to $k$ connected components to make the graph connected

- Modelling a Forced undamped oscillation via ODE
- Upper and Lower Bounds of $\emptyset$
- Area of Validity of Writing an Exponential Integral as Sum of IntegralSinus and -Cosinus
- upper bound on rank of elliptic curve $y^{2} =x^{3} + Ax^{2} +Bx$
- Equivalent condition for non-orientability of a manifold
- Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
- maximum size of a $k$-intersecting antichain of $$
- $\|(g\widehat{(f|f|^{2})})^{\vee}\|_{L^{2}} \leq C \|f\|_{L^{2}}^{r} \|(g\hat{f})^{\vee}\|_{L^{2}}$ for some $r\geq 1$?
- How to find the general solution of $(1+x^2)y''+2xy'-2y=0$. How to express by means of elementary functions?
- How to write down formally number of occurences?
- Do we really need embedding for this?
- Points on two skew lines closest to one another
- Show that 2S = S for all infinite sets
- Union of subgroups is subgroup
- For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$