## Todo

### Meta

d = 3; a = 5; r = 1/3; f[z_] = ((z + d)^a - d^a)^r; Series[f[z], {z, 0, 6}]

##### Theormodyanmics

atm. there are only some notes under On phenomenological thermodynamics . Note.

##### topoi

#### Topics

To solve $f(x)=x$ via fixedpoint iteration, one may consider the sequence $f^n(x_\text{guess})$.

However, $g(x):=\dfrac{h(x)}{h(f(x))}\cdot f(x)$ should converge to it too and $g^n(x_\text{guess})$ may converge faster.

I saw this at Omega_constant#Computation (Wikipedia) with $h(x):=1+x$.

#### Articles waiting to be created

*Type theory*

*descrete math*

*graph theory*

source . graph theory/sink . graph theory of a graph - vertices where all adjacent edges are outgoing/ingoing

directed acyclic graph - directed graph (connected?) without directed circle as subset

Boolean circuit - directed acyclic graph where all non-sink/source vertices have either 1 or 2 ingoing vertices and there is a function assigning “$\neg$” to all of the former and another symbol (out of an alphbet “\land,\lor,\dots”) to the latter.

*CS*

*logic*

*Set theory*

supremum, bounds, etc.

mnmInt :: [Int] -> Int mnmInt [] = error "empty list" mnmInt [x] = x mnmInt (x:xs) = min x (mnmInt xs)

*category theory*

Set

Category theory

Hask

several special arrows. In particular (for Natural isomorphism)

isomorphism . category theory

NOTE:

- pullbacks + terminal object ⇒ equalizers + binary products

- binary products + terminal object ⇒ all finite products

- equalizers ⇒ all finite equalizers

- finite products + finite equalizers ⇒ finitely complete (= all finite limits)

- http://math.stackexchange.com/questions/591302/show-the-following-conditions-are-equivalent-for-a-category-c

* Number theory *

*set theory, topology*

* Analysis *

TODO: make individual entries for models of ${\mathbb R},{\mathbb Q}$ and ${\mathbb C}$ and the entries called real numbers, rational numbers and complex numbers.

shift operator $T_a=\exp\left(a\frac{\partial}{\partial x}\right)$, and more generally http://en.wikipedia.org/wiki/Lagrange_reversion_theorem

* Complex analysis *

Zeidler QFT 1

p. 515: Polchinsky equation

p.514: reg $\int$

p. 512: Weierstrass product Theorem (for entire functions) - discussion: that's an infinite generalization of the factoring w.r.t. roots of a function. Similarly, I think, the infinite partial fraction decomposition is given by theMittag-Leffler's theorem.

* diffgeo, analysis *

*physics*