List of the sub-journals at: journals.aps.org/browse

Theory that atoms exist, i.e. matter is not continuous.

Much before atoms were thought to be "experimentally real", chemists from the 19th century already used "conceptual atoms" as units for the proportions observed in macroscopic chemical reactions, e.g. $2H_2+O_2\leftrightarrow H_{2}O$. The thing is, there was still the possibility that those proportions were made up of something continuous that for some reason could only combine in the given proportions, so the atoms could only be strictly consider calculatory devices pending further evidence.

Subtle is the Lord by Abraham Pais (1982) chapter 5 "The reality of molecules" has some good mentions. Notably, physicists generally came to believe in atoms earlier than chemists, because the phenomena they were most interested in, e.g. pressure in the ideal gas law, and then Maxwell-Boltzmann statistics just scream atoms more loudly than chemical reactions, as they saw that these phenomena could be explained to some degree by traditional mechanics of little balls.

Confusion around the probabilistic nature of the second law of thermodynamics was also used as a physical counterargument by some. Pais mentions that Wilhelm Ostwald notably argued that the time reversibility of classical mechanics + the second law being a fundamental law of physics (and not just probabilistic, which is the correct hypothesis as we now understand) must imply that atoms are not classic billiard balls, otherwise the second law could be broken.

Pais also mentions that a big "chemical" breakthrough was isomers suggest that atoms exist.

Very direct evidence evidence:

Less direct evidence:

Subtle is the Lord by Abraham Pais (1982) page 40 mentions several methods that Einstein used to "prove" that atoms were real. Perhaps the greatest argument of all is that several unrelated methods give the same estimates of atom size/mass:

Hello! I'm the official admin account for the OurBigBook Project!

Proof: docs.ourbigbook.com/ourbigbook-admin

Only certain battery voltages exist, because this voltage depends intrinsically on the battery's chemical composition.

learn.sparkfun.com/tutorials/battery-technologies/all (CC BY-SA) has a very good summary list, reordered from lowest to highest voltage:

Bibliography:

In the context of abstract algebra, the term "derivative algebra" often does not refer to a specific well-established area like group theory or ring theory, but it may relate to a couple of concepts in algebra associated with derivatives. One such area is the study of derivations in algebraic structures, particularly in the context of rings. ### Derivations in Algebras 1.

The Fox derivative is a mathematical concept related to fractional calculus and special functions. It generalizes the notion of derivatives to fractional orders, allowing for the differentiation of functions with non-integer orders. This concept is often used in areas such as signal processing, control theory, and other applied mathematics fields. In essence, the Fox derivative is defined using the framework of the Fox H-function, which is a general class of functions that encompasses many special functions used in mathematics and applied sciences.

Linear topology, also referred to as a **linear order topology** or **order topology**, is a concept in topology that arises from the properties of linearly ordered sets. The primary idea is to define a topology on a linearly ordered set that reflects its order structure.

A **quadratic Lie algebra** is a certain type of Lie algebra that is specifically characterized by the nature of its defining relations and structure. More precisely, it can be defined in the context of a quadratic Lie algebra over a field, which can be associated with a bilinear form or quadratic form.