Sources for sub super scripts

At the request of @jiahao, I am trying to compile use cases for physics, chemistry and mathematics.

Chemistry
1. \Delta_vap*E_{m,b} is the molar energy of vaporization.   [1, p. 55]
2. \eta_{inh} is the inherent viscosity - SI Unit m^3 kg ^-1
3. Polymerization reactions require the need for the notation `P_x + P_y -> P_{x+y}` [1, p. 72]
4. Units for degree of crystallinity are `w_{c,h}`
5.  Modulated smectic mesophases SmÃ, and SmC with a tilde, which can't be currently drawn. [1, p 112]
6. Anisotropy in general requires the squiggle tilde on top of the quantity being referred to, see [1,p. 114]
7. Stochiometric equations sometimes need to describe a molecule/atom as aqueous, with the "aq" subscript.

Physics:
1. Vectors are indicated by an arrow above, Second rank tensors use a double arrow, higher order tensors use the index notation. [2, p,3] 
2. Neutrinos require the `\mu` and `\tau` subscripts [2, p.12]
3. Nuclear configuration notation require several fractions as subscripts [2, p.14]
4. The equals symbol with a tilde on top means 'corresponds to'
5. The circumflex accent  ( hat vector) can mean maximum, or minimum value, depending on where it points, whilst the squiggle tilde is used for the rms value. [2, p. 51]
6. The universal constants of vacuum permittivity and permeability require a  º symbol as a subscript. [2, p. 54]
7. The Kronecker delta \delta^i_j, Levi-Civita symbol \epsilon_ij
8. Special functions make extensive use of a a specified (n) derivative  as superscript with respect to a parameter (m) usually denoted at the bottom. See Spherical Harmonics and functions with last names [4].


Mathematics:
1. Limit, max, min, and `\Sigma`, supremum, infimum,  Unions, Intersections, and Multiplication notation have subscripts to delimit the set under consideration, or process.
2. Derivatives up to order n (and not just 1-9), with the use of a parenthesis.
3. Partial derivatives `can be annotated as \delta_xx`, and second partial derivatives may have a subscripted index number, as well as an exponent of 2.
4. Specifying the neighbourhood of a topological ball - `B_\epsilon`
5. The negative infinity sign is used as a subscript for integrals
6. X with a caret (^) on top  is used as an estimator of state X [3]
7. ...Almost half the notation index of [4] can't be expressed without super/subscripts.
8. The | bar when applied to a domain denotes with superscripts and subscripts the upper and lower bounds of evaluation - amongst many types of set restrictions.
9. In Integral Equations, a degenerate kernel requires a sum over an index j=1<=n with functions \phi_j(x) and \psi*_j(x). [4, p. 556]

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References.
[1]. [Compendium of Polymer Terminology and Nomenclature IUPAC 2008](https://www.iupac.org/cms/wp-content/uploads/2016/01/Compendium-of-Polymer-Terminology-and-Nomenclature-IUPAC-Recommendations-2008.pdf)
[2]. [Symbols, Units, Nomenclature and Fundamental Constants in Physics, IUPAP  - Commission C2 SUNAMCO 2010 reprint](http://iupap.org/wp-content/uploads/2014/05/A4.pdf)
[3]. Stochastic Differential Equations, Bernt Oksendal, Sixth Edition, Springer.
[4]. A Comprehensive Introduction to Differential Geometry, Michael Spivak, Vol. 1.
[5]. Mathematical Physics - A Modern Introduction to its Foundations, Sadri Hassani, 2013.
[4]  A Comprehensive introduction to Differential Geometry, Michael Spivak, Vol.1, p. 478, 3rd edition.