Notes and symbols whilst attempting to tidy up unfinished publications

1. 𝜧/𝝁 The Möbius function is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832.[i][ii][2] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula. Following work of Gian-Carlo Rota in the 1960s, generalizations of the Möbius function were introduced into combinatorics, and are similarly denoted .𝝁(n).

The Möbius function is defined by[3]

The Möbius function can alternatively be represented as

where is the Kronecker delta, is the Liouville function, is the number of distinct prime divisors of , and is the number of prime factors of , counted with multiplicity.

In coordination chemistry, hapticity is the coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms.[1] The hapticity of a ligand is described with the Greek letter η ('eta'). For example, η2 describes a ligand that coordinates through 2 contiguous atoms. In general the η-notation only applies when multiple atoms are coordinated (otherwise the κ-notation is used). In addition, if the ligand coordinates through multiple atoms that are not contiguous then this is considered denticity[2] (not hapticity), and the κ-notation is used once again.[3] When naming complexes care should be taken not to confuse η with μ ('mu'), which relates to bridging ligands.[4][5]

Enantiomers having helicity may labeled by using the prefix notation (P) ("plus") or Δ (from Latin dexter, "right") for a right-handed helix, and (M) ("minus") or Λ (Latin levo, "left") for a left-handed helix.[5][3][9]

The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non-SI unit named debye in his honor.

In 1934, an experiment showed that when natural 209Bi is bombarded with neutrons, 210Bi is created, which then decays to 210Po via beta-minus decay. By irradiating certain bismuth salts containing light element nuclei such as beryllium, a cascading (α,n) reaction can also be induced to produce 210Po in large quantities.[58] The final purification is done pyrochemically followed by liquid-liquid extraction techniques.[59] Polonium may now be made in milligram amounts in this procedure which uses high neutron fluxes found in nuclear reactors.[57] Only about 100 grams are produced each year, practically all of it in Russia, making polonium exceedingly rare.[60][61]

Distortions in gaseous XeF6 are caused by its non-bonding lone pair, according to VSEPR theory.

Hexafluoroarsenate is relatively inert, being the conjugate base of the notional superacid hexafluoroarsenic acid (HAsF6).

Proton emission (also known as proton radioactivity) is a rare type of radioactive decay in which a proton is ejected from a nucleus.

The tetraneutron is considered an unbound isotope with a lifetime around 10-22 seconds.[1]: 275  The stability of this cluster of four neutrons is not supported by current models of nuclear forces.[2]Bertulani and Zelevinsky proposed that, if it existed, the tetraneutron could be formed by a bound state of two dineutron systems.[9]

Researchers from Australia have said they had identified a variation of the fine-structure constant across the observable universe.[57][58][59][60][61][62]

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interactionbetween elementary charged particles.

It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula 4πε0ħcα=  𝑒². Its numerical value is approximately 0.0072973525643 ≈ ⁠1/137.035999177⁠, with a relative uncertainty of 1.6×10−10.[1]

Definition

n terms of other physical constants, α may be defined as:[4]

             𝑒²    𝑒²

ɑ = ⏤ = ⏤       

2𝛆₀hc 4𝝅𝛆ℏc

where

• e is the elementary charge (1.602176634×10−¹⁹ C[5]);

• h is the Planck constant (6.62607015×10−³⁴ J⋅Hz−¹[6]);

• ħ is the reduced Planck constant, ħ = h/2π (1.054571817...×10−³⁴ J⋅s[7])

• c is the speed of light (299792458 m⋅s−¹[8]);

• ε0 is the electric constant (8.8541878188(14)×10−¹²  F⋅m−¹[9]).

Since the 2019 revision of the SI, the only quantity in this list that does not have an exact value in SI units is the electric constant (vacuum permittivity).

 According to Chung (Peter) Chieh (Professor Emeritus, Chemistry @ University of Waterloo) via LibraTexts: 2.2.2.9: Water Physics: Electric Dipole Moment and Dielectric Constant the symbol D is a cgs-esu unit of measure called debye where 1 D = 1e-18 esu cm

https://bio.libretexts.org/Courses/Coastline_College/ENVS_C100%3A_Environmental_Science_(Hoerer)/02%3A_Environmental_Chemistry/2.02%3A_Supplemental_Modules_(Environmental_Chemistry)/2.2.02%3A_Aquatic_Chemistry/2.2.2.09%3A_Water_Physics

The debye (/dɪˈbaɪ/ dib-EYE,[1] Dutch: [dəˈbɛiə]; symbol: D)

the fluoridopolyhalogenates [F(ClF)3]− and [F(Cl2)3]− anions show planar D3h molecular structures at the CCSD(T)/aug-cc-pVTZ level, indicating that the pyramidal structure of the title compound in the solid state is most likely due to the formation of hydrogen bonds to the counter ion. [39]

Note, very recently a quantum-chemical investigation has been published which predicts a planar tetracoordinated structure of a fluorine atom in e.g. [FIn4]+ or [FTl4]+.[40] {39]

Reverse-phase HPLC was used to fractionate 40S ribosomal proteins from human placenta. Application of a C4 reverse-phase column allowed us to obtain 27 well- resolved peaks. The protein composition of each chromatographic fraction was established by two-dimensional polyacrylamide gel electrophoresis and N-terminal sequencing. N-terminally blocked proteins were cleaved with endoproteinase Lys- C, and suitable peptides were sequenced. All sequences were compared with those of ribosomal proteins available from data bases. This allowed us to identify all proteins from the 40S human ribosomal subunit in the HPLC elution profile. By matrix-assisted laser-desorption ionization mass spectrometry the masses of the 40S proteins were determined and checked for the presence of post-translational modifications. For several proteins differences to the deduced sequences and the calculated masses were found to be due to post-translational modifications [2].

According to the Medicinal Chemistry of Anticancer Drugs, 2nd edt. (2015) A radical (sometimes called free radical) is a chemical species that contains one or more unpaired electrons and is sufficiently stable for independent existence. [52]. Unfortuantly, there is no shortage of ignorant fear from people with control issues regarding free radicals too often accompanied with recklessly dangerous arrogant attempts to further violate nature for the sake of arrogance and comercial interests [53][54]. However, despite the mess of western medicine and complications that creates for the subject, there is growing interest in the essential functional actions free radicals are capable of facilitating. [55][56][57] and others cautioning the critical nature of how such complex chemical interrelationships are interpreted [58].

⎲aʸ ˳ªº¹²³ʰ ˣ ʲʸʳˢ     ʳʸ𝑃 ͭ ͥ ͭ ͪ ͫ ħ ℏ  ∑ ∏

⎳ ≠ ≡ ≣ ∈ ⎷⎸⎹⋂⋃⋀⊂⊃π 𝛆 𝚫𝚪𝛀𝛴𝟂𝞿𝝅𝇇 ˉ ⎺ɑ= ⏤⎺ ⋋⋌≞ ⁿ㎥ ⨧ ₑ e²¹⁹³⁴¹²

              𝑒²    𝑒²

ɑ = ⏤ = ⏤       

2𝛆₀hc 4𝝅𝛆ℏc