A capacitor changes, then resists being charged further. Their rules work opposite to resistors.

capacitor in series

\begin{equation} \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \end{equation}

and yet,

capacitor in parallel

\begin{equation} C_{eq} = C_1 + C_2 + C_3 \end{equation}

energy stored by a capacitor

\begin{equation} E = \frac{1}{2} CV^{2} \end{equation}

where, \(E\) is the energy stored, \(C\) the capacitance, and \(V\) the voltage across the capacitor.

Which, subbing the formula below:

A cancer drug to synthesize Fluoropyrimidine.

CAPM is a method of portfolio selection analysis which focuses on maximizing return given some fixed variance.

It deals with optimal Capital Market Line, given here:

\begin{equation} E[R_{p}] = r_{f}+\frac{\sigma_{p}}{\sigma_{T}}\qty(E[R_{T}]-r_{f}) \end{equation}

Which describes \(E[R_{p}]\), the expected return of an optimal portfolio in a market, given, \(R_{T}\) is the market return, \(r_{f}\) is the risk-free rate, \(\sigma_{p}\) is the portfolio returns, and \(\sigma_{t}\) is standard-deviation of the market returns.

Sharpe Ratio

The Sharpe Ratio is a measure of the risk-adjusted performance of an asset—given the rate of return of some risk-free asset.

Pitfalls

The bytes remains the same despite copying, so you can get too funky:

int v = -12345;
unsigned int uv = v;

printf("v = %d, uv = %d\n", v, uv);

This prints “v = -12345, uv=4294954951”. As in: when you copy rvalues, the bit pattern gets copied and not the numerical number itself; so, it will overflow.

You can use U to force an signed quantity to be unsigned:

unsigned int uv = -12345U;

sign promotion

If you have the nerve of putting a comparing things of different types (don’t), then, the signed quantities gets promoted to be unsigned.

categorical grammar is a grammar in the language of categories.

constituents

• \(A\), a set of “expressions”
• \(C\), a set of categories of “syntax”
• \(\varphi: A \to Pow( C)\), assigning each \(a \in A\) to a set of categories \(c \subset C\)
• \(G\): a family of sets of n-place operations where \(n=1, 2, \ldots\) (what does a “3-place” op mean? idk)
• \(R\): a set of rules encoded as tuples: \((f; \{c_1, \dots c_{k}\}; c_{k+1})\), where \(f\) is a \(k\) place operation, and \(c_{j} \in C\)

requirements

The operations of this grammar behaves like so: