From 6987dcbd64f3d4b3c3c43a8fd96a03a0ce5b56eb Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Mon, 12 Sep 2022 21:46:01 +0200
Subject: Post "Revisiting my email server in 2022"

---
 content/know/concept/calculus-of-variations/index.pdc    | 6 ++++--
 content/know/concept/pulay-mixing/index.pdc              | 2 +-
 content/know/concept/rayleigh-plesset-equation/index.pdc | 2 +-
 3 files changed, 6 insertions(+), 4 deletions(-)

(limited to 'content/know')

diff --git a/content/know/concept/calculus-of-variations/index.pdc b/content/know/concept/calculus-of-variations/index.pdc
index a8861cb..26c5753 100644
--- a/content/know/concept/calculus-of-variations/index.pdc
+++ b/content/know/concept/calculus-of-variations/index.pdc
@@ -14,7 +14,7 @@ markup: pandoc
 # Calculus of variations
 
 The **calculus of variations** lays the mathematical groundwork
-for Lagrangian mechanics.
+for [Lagrangian mechanics](/know/concept/lagrangian-mechanics/).
 
 Consider a **functional** $J$, mapping a function $f(x)$ to a scalar value
 by integrating over the so-called **Lagrangian** $L$,
@@ -28,6 +28,8 @@ If $J$ in some way measures the physical "cost" (e.g. energy) of
 the path $f(x)$ taken by a physical system,
 the **principle of least action** states that $f$ will be a minimum of $J[f]$,
 so for example the expended energy will be minimized.
+In practice, various cost metrics may be used,
+so maxima of $J[f]$ are also interesting to us.
 
 If $f(x, \varepsilon\!=\!0)$ is the optimal route, then a slightly
 different (and therefore worse) path between the same two points can be expressed
@@ -238,7 +240,7 @@ $$\begin{aligned}
 
 ## Constraints
 
-So far, for multiple functions $f_1, ... f_N$,
+So far, for multiple functions $f_1, ..., f_N$,
 we have been assuming that all $f_n$ are independent, and by extension all $\eta_n$.
 Suppose that we now have $M < N$ constraints $\phi_m$
 that all $f_n$ need to obey, introducing implicit dependencies between them.
diff --git a/content/know/concept/pulay-mixing/index.pdc b/content/know/concept/pulay-mixing/index.pdc
index 4e7a411..476932d 100644
--- a/content/know/concept/pulay-mixing/index.pdc
+++ b/content/know/concept/pulay-mixing/index.pdc
@@ -125,7 +125,7 @@ $$\begin{aligned}
 You might be confused by the absence of any $\rho_m^\mathrm{new}$
 in the creation of $\rho_{n+1}$, as if the iteration's outputs are being ignored.
 This is due to the first assumption,
-which states that $\rho_n^\mathrm{new}$ are $\rho_n$ are already similar,
+which states that $\rho_n^\mathrm{new}$ and $\rho_n$ are already similar,
 such that they are basically interchangeable.
 
 Speaking of which, about those assumptions:
diff --git a/content/know/concept/rayleigh-plesset-equation/index.pdc b/content/know/concept/rayleigh-plesset-equation/index.pdc
index 9325f3f..75feb13 100644
--- a/content/know/concept/rayleigh-plesset-equation/index.pdc
+++ b/content/know/concept/rayleigh-plesset-equation/index.pdc
@@ -20,7 +20,7 @@ inside an incompressible liquid.
 Notably, it leads to [cavitation](/know/concept/cavitation/).
 
 Consider the main
-[Navier-Stokes equations](/know/concept/navier-stokes-equations/)
+[Navier-Stokes equation](/know/concept/navier-stokes-equations/)
 for the velocity field $\va{v}$:
 
 $$\begin{aligned}
-- 
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