Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping set I(f) is unbounded. This provides a partial answer to a question of Eremenko.

Chemical reduction of a tripodal Cu(II)-F complex containing pendent hydroxyl groups results in the partial dissociation of a F(-) ligand from Cu. The resulting Cu(I) complex is characterized as containing an outer sphere F(-) anion 'captured' by hydrogen bonds. The pendent hydroxyl groups were found to be crucial for reductive stability.

Bohrification defines a locale o f hidden variables internal in a topos. We find that externally this is the space o f partial measurement outcomes. By considering the ——sheafification, we obtain the space o f measurement outcomes which coincides with the spectrum for commutative C*-algebras.

Slice Fueter-regular functions, originally called slice Dirac-regular are generalized holomorphic functions defined over the octonion algebra \({\mathbb {O}}\), recently introduced by M. Jin, G. Ren and I. Sabadini. A function \(f:\Omega _D\subset {\mathbb {O}}\rightarrow {O}}\) is (quaternionic) if, given any quaternionic subalgebra {H}}_{\mathbb {I}}\) of generated a pair {I}}=(I,J)\) orthogo...

Kinetic models of chemical reaction systems are typically represented in terms of state variables, such as concentrations, temperature and partial pressures [1]. These state variables in turn depend on the underlying reactions, transfer phenomena, and transport due to the inlet and outlet flows. Kinetic models are derived from first principles – material and energy balances – and are expressed ...

This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to homotopy). This yields an invariant of sm...

We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. specify some recent results and constructions second named author to show that those non-trivial elements in homotopy groups ◂f()▸π∗⁡◂()▸(B⁢Diff∂⁢(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ are lifted moduli space h$h$-cobordisms ◂f()▸π∗⁡◂()▸(B⁢Diff⊔⁢(Dd×I))⊗Q$\pi _*(B\mathrm{...

Type Directed Partial Evaluation (TDPE) is a new development in partial evaluation that has two properties that make it attractive for formal investigation: First, it is concise; it is deened in about six lines Dan96b]. Second, it is easy to implement; the deenition can be coded directly in a functional language like Scheme, yielding a demonstrably eecient and eeective partial evaluator DV96, V...

Let G = (V, E) be a simple graph. A vertex labeling f : V → {0, 1} induces a partial edge labeling f ∗ : E → {0, 1} defined by f ∗(uv) = f(u) 84 KWONG, LEE, LO, SU AND WANG if and only if f(u) = f(v). For i = 0, 1, let vf(i) = |{v ∈ V : f(v) = i}|, and ef (i) = |{e ∈ E : f ∗(e) = i}|. A graph G is uniformly balanced if |ef (0)−ef (1)| ≤ 1 for any vertex labeling f that satisfies |vf(0)−vf (1)| ...

We study the functor `2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its ...