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M. Kilp, U. Knauer, A.V. Mikhalev, Monoids, Acts and Categories with Applications to Wreath Products and Graphs, De Gruyter Expositions in Mathematics vol. 29, Walter de Gruyter, 2000, ISBN 3-11-015248-7. Ronald V. Book and Friedrich Otto, String-rewriting Systems, Springer, 1993, ISBN 0-387-97965-4, chapter 7, "Algebraic Properties"
A monoid object in the category of monoids (with the direct product of monoids) is just a commutative monoid. This follows easily from the Eckmann–Hilton argument. A monoid object in the category of complete join-semilattices Sup (with the monoidal structure induced by the Cartesian product) is a unital quantale.
Many definitions and theorems about monoids can be generalised to small categories with more than one object. For example, a quotient of a category with one object is just a quotient monoid. Monoids, just like other algebraic structures, also form their own category, Mon, whose objects are monoids and whose morphisms are monoid homomorphisms. [8]
In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G 1 and G 2 and produces a graph H with the following properties: The vertex set of H is the Cartesian product V ( G 1 ) × V ( G 2 ) , where V ( G 1 ) and V ( G 2 ) are the vertex sets of G 1 and G 2 , respectively.
Congruence classes and factor monoids are the objects of study in string rewriting systems. A nuclear congruence on S is one that is the kernel of an endomorphism of S. [6] A semigroup S satisfies the maximal condition on congruences if any family of congruences on S, ordered by inclusion, has a maximal element.
Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pump, air conditioning and refrigeration systems. [1] A heat pump is a mechanical system that transmits heat from one location (the "source") at a certain temperature to another location (the "sink" or "heat sink") at a higher temperature. [2]
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Eventually you can find out from his graph that the (1) at the end is not part of his formula and instead he is citing his graph. Air and thin air and high tech vacuums, microstructure Formula Values d=1 millimeter Standard Atmospheric Pressure 0.0209 0.0235 0.0260 0.1 atmosphere 0.0209 0.0235 0.0259 0.01 atmospheres 0.0205 0.0230 0.0254 0.001 ...
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