Based on a course taught by the author and aimed primarily at engineering students, the book explains concepts effectively and efficiently, uncovering the “shortcut” to understanding each topic, enabling readers to quickly grasp the underlying essence. The book is divided into two main parts; the first part provides a general introduction to key topics encountered in superconductivity, illustrated using COMSOL simulations based on time-dependent Ginzburg-Landau equations and avoiding any deeply mathematical derivations. It includes numerous worked examples and problem sets with tips and solutions."

]]>A Boolean semilattice is a Boolean magma where ·* *is associative, commutative, and square-increasing. Let SL be the class of semilattices and let **S**(SL^{+}) be all subalgebras of complex algebras of semilattices. All members of **S**(SL^{+}) are Boolean semilattices and we investigate the question of which Boolean semilattices are representable, i.e., members of **S**(SL^{+}). There are 79 eight-element integral Boolean semilattices that satisfy a list of currently known axioms of **S**(SL^{+}). We show that 72 of them are indeed members of **S**(SL^{+}), leaving the remaining 7 as open problems.

For a positive idempotent element p in a relation algebra A, the double division conucleus image* p*/A/*p* is an (abstract) weakening relation algebra, and all representable weakening relation algebras (RWkRAs) are obtained in this way from representable relation algebras (RRAs). The class S(dRA) of subalgebras of {*p*/A/*p*∶ A ϵ RA; 1 ≤ p^{2} = p ϵ A} is a discriminator variety of cyclic involutive GBI-algebras that includes RA. We investigate *S*(dRA) to find additional identities that are valid in all RWkRAs. A representable weakening relation algebra is determined by a chain if and only if it satisfies 0 ≤ 1, and we prove that the identity 1 ≤ 0 holds only in trivial members of S(dRA).

This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.

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