Intereting Posts

Does there exist a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
Multiplicative Functions
Categorification of the (co-)induced topology
Find the Polar of a set.
Maximal ideal in commutative ring
Uses of step functions
A general element of U(2)
Monotone Convergence Theorem – clarification on measurable set.
When is a Markov process independent-increment?
Existence proof of the tensor product using the Adjoint functor theorem.
Negation of quantifiers
History of the Concept of a Ring
Topological properties of symmetric positive definite matrices
Definition of definition
Prove the empty set is closed for a metric space (X,d).

I tried to characterize mathematically what makes a function *bell-shaped*. I found the following:

Definition. A $C^\infty$-function $f:\Bbb R\to\Bbb R$ is calledbell-shapedif its $n$-th derivative has exactly $n$ zeros (counted with multiplicity) for all $n\in\Bbb N_0$.

I do not claim that any intuitively bell-shaped curve is included (e.g. non-smooth functions), but I felt pretty confident that there are no intuitively non-bell-shaped curves in this class. However, my imagination is limited, so I want to ask whether anyone can find a pathological example of some curve in this class for which it might be debatable to call it bell-shaped in an intuitive sense. Upside down or asymmetric bells are okay for me.

- Not every metric is induced from a norm
- Example of two open balls such that the one with the smaller radius contains the one with the larger radius.
- Why is this weaker then Uniform Integrability?
- Set of zeroes of the derivative of a pathological function
- Give an example of a bounded, non-convergent real sequence $(a_n)$ s.t. $a_n-a_{n-1}\rightarrow 0$
- Intersection of finite number of compact sets is compact?

Also, is it true that any such function must be bounded? I would consider an unbounded function as a counterexample. Then the next question would be whether it suffices to extend the definition by the predicate “bounded”.

- X,Y are independent exponentially distributed then what is the distribution of X/(X+Y)
- If a sub-C*-algebra does not contain the unit, is it contained in a proper ideal?
- absolute minimum of function
- Example of an increasing, integrable function $f:\to\mathbb{R}$ which is discontinuous at all rationals?
- Definition of Sinc function
- Help finding this set
- If the set of values , for which a function has positive derivative , is dense then is the function increasing?
- What are some easy to understand applications of Banach Contraction Principle?
- Constructing a quasiconvex function
- Is every real valued function on an interval a sum of two functions with Intermediate Value Property?

- What is the family of generating functions for the *rows* of this Stirling-number matrix for whose columns they are $\exp(\exp(x)-1)-1 $?
- Is a single point boundaryless?
- Cardinality of sum-set
- $$ is not true or false
- Interpreting the Cayley-Hamilton theorem
- Counterexamples to “Naive Induction”
- Frobenius coin problem
- Is it true that $\mathbb{E}+|\mathbb{E}\rvert\geq\mathbb{E}\rvert]+\mathbb{E}\rvert]$?
- Prove that $\{\frac 1 n \mid n \in \mathbb N\} \cup \{0\}$ is closed in $\mathbb R$
- Is the root of $x=\cos(x)$ a transcendental number?
- Square free finite abelian group is cyclic
- Finding a polynomial with a given shape
- How to determine highest power of $2$ in $3^{1024}-1$?
- Second derivative criteria for maxima and minima.
- Contractive mapping on compact space