Structure and lining: A review

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Robust Separation:A search for a generic framework to simplify registration and trading of interests in natural resources

This report is about the search for an economically efficient and equitable system of defining, allocating, and managing use of natural resources that proves to be robust. Robust in the sense that the fundamental principles and foundations upon which it is based remains unchanged over time. We focus on the notion of “interests” in natural resources, and obligations associated with use. We search for a generic robust approach to the definition of interests, rights and use obligations that sits comfortably within an economically efficient trading system. Pricing and charging issues and the question of how to convert from existing systems to the proposed one are left for subsequent reports.audit;Australia;natural resource management

Robust Reform: Implementing robust institutional arrangements to achieve efficient water use in Australia

The focus of this report is on implementing institutional arrangements for the efficient allocation and management of water. Water is an input into human use including economic production and recreation activities that generate many externalities. It also provides many valuable ecosystem services only partially captured in the market. Institutional arrangements are required that are dynamically efficient and low cost, and robust enough to withstand the test of time. Robust administrative arrangements are characterised by the lack of a need for change.water reform;institutional;trading;Australia

Trace Identities for the Topological Vertex

The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It encodes the combinatorics of 3D partitions, the action of vertex operators on Fock space, the Donaldson-Thomas theory of toric Calabi-Yau threefolds, or the open string partition function of $\mathbb{C}^3$. We prove several identities in which a sum over terms involving the topological vertex is expressed as a closed formula, often a product of simple terms, closely related to Fourier expansions of Jacobi forms. We use purely combinatorial and representation theoretic methods to prove our formulas, but we discuss applications to the Donaldson-Thomas invariants of elliptically fibered Calabi-Yau threefolds at the end of the paper.Comment: 21 pages. Published versio

Managing Change: Australian structural adjustment lessons for water

The purpose of this report is to search Australia's extensive experience in running and reviewing structural adjustment programs for insights of relevance to water reform.Water;Australia;Water reform;structural adjustment;rural;agricultural;policy.

Carath\'eodory extremal functions on the symmetrized bidisc

We show how realization theory can be used to find the solutions of the Carath\'eodory extremal problem on the symmetrized bidisc $$G \stackrel{\rm{def}}{=} \{(z+w,zw):|z|<1, \, |w|<1\}.$$ We show that, generically, solutions are unique up to composition with automorphisms of the disc. We also obtain formulae for large classes of extremal functions for the Carath\'eodory problems for tangents of non-generic types.Comment: 24 pages, 1 figure. This version contains some minor changes. It is to appear in a volume of Operator Theory: Advamces and Applications, Birkhause

Nevanlinna representations in several variables

We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.Comment: 37 pages. In this version we have added some references and expanded the introductio

Operator monotone functions and L\"owner functions of several variables

We prove generalizations of L\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$ matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone