The results reported in Chapter 3 are consistent with the premise of this dissertation that a comprehensive understanding of how ethical leadership works requires a closer look at the variation in followers’ expectations of the leader. To date, such empirical research on follower expectations of ethical leadership has been limited. However, Chapter 3 belongs to a small group of studies that rev...

We introduce an explicit diagrammatic syntax for PROs and PROPs, which are used in the theory of operads. By means of diagram rewriting, we obtain presentations of PROs by generators and relations, and in some cases, we even get convergent rewrite systems. This diagrammatic syntax is useful for practical computations, but also for theoretical results. Moreover, rewriting is strongly related to ...

This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p : (Q̃, q̃) → (Q,q). This in turn leads us to define the algebraic fundamental group π1(Q,q) := Aut(p) = {g ∈ Adj(Q)′ | qg = q}, where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected c...

Cycle-counting rook numbers were introduced by Chung and Graham [7]. Cycle-counting q-rook numbers were introduced by Ehrenborg, Haglund, and Readdy [9] and cycle-counting q-hit numbers were introduced by Haglund [14]. Briggs and Remmel [4] introduced the theory of p-rook and p-hit numbers which is a rook theory model where the rook numbers correspond to partial permutations in Cp ≀ Sn, the wre...

Cycle-counting rook numbers were introduced by Chung and Graham [8]. Cycle-counting q-rook numbers were introduced by Ehrenborg, Haglund, and Readdy [10] and cycle-counting q-hit numbers were introduced by Haglund [14]. Briggs and Remmel [5] introduced the theory of p-rook and p-hit numbers which is a rook theory model where the rook numbers correspond to partial permutations in Cp oSn, the wre...

In their 1995 paper, Jean-Benôıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β), where β is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written ...

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...

Schur's test for integral operators states that if a kernel K:X×Y→C satisfies ∫Y|K(x,y)|dν(y)≤C and ∫X|K(x,y)|dμ(x)≤C, then the associated operator is bounded from Lp(ν) into Lp(μ), simultaneously all p∈[1,∞]. We derive variant of this result which ensures acts boundedly on (weighted) mixed-norm Lebesgue spaces Lwp,q, p,q∈[1,∞]. For non-negative kernels our criterion sharp; is, only it spaces. ...

In this short note, I point out that [p, q] 6= ih̄, contrary to the original claims of Born and Jordan, and Dirac. Rather, [p, q] is equal to something that is infinitesimally different from ih̄. While this difference is usually harmless, it does provide the solution of the Born–Jordan “trace paradox” of [p, q]. More recently, subtleties of a very similar form have been found to be of fundamental...