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Let Q_0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0^{-1}=0. Q_0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q_0(s ,sqrt) of the signed rationals in which every number has a unique square root.
A meadow is a commutative ring with a total inverse operator satisfying 0^{-1}=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a corollary, we obtain a unique representation of minimal finite meadows in terms of finite prime fields.
Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by putting add
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set ${x Leftarrow 0, x Leftarrow 1, xLeft
The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favour of the square root voting system, where th
We prove the Kato conjecture for elliptic operators, $L=- ablacdotleft((mathbf A+mathbf D) abla right)$, with $mathbf A$ a complex measurable bounded coercive matrix and $mathbf D$ a measurable real-valued skew-symmetric matrix in $mathbb{R}^n$ with