MARKET-BASED LAND REFORM AND FARM EFFICIENCY IN COLOMBIA: A DEA APPROACH

This paper uses Data Envelopment Analysis to measure scale and technical efficiencies of 925 farms in rural Colombia and a Tobit model to identify the effects of land market characteristics on efficiency. Findings indicate that although larger farms are more scale efficient, they are not more technical efficient than small farms. Participation in land markets increases technical efficiency, indicating a positive potential role for market-based land reform. Further results show that intensity of violence in rural areas results in increased scale efficiency, allegedly through consolidation of land ownership.Industrial Organization, Productivity Analysis,

Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A Haldane-Shastry spin chain of BC_N type in a constant magnetic field

We compute the spectrum of the trigonometric Sutherland spin model of BC_N type in the presence of a constant magnetic field. Using Polychronakos's freezing trick, we derive an exact formula for the partition function of its associated Haldane-Shastry spin chain.Comment: LaTeX, 13 page

The exactly solvable spin Sutherland model of B_N type and its related spin chain

We compute the spectrum of the su(m) spin Sutherland model of B_N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BC_N counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of B_N type is equivalent to that of a suitable vertex model, as is the case for its A_{N-1} counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.Comment: Typeset in LaTeX (24 pages, 4 figures). arXiv admin note: text overlap with arXiv:0909.296

Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In particular, we prove that (normalizable) exactly-solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the $k$-th moment grows like the $k$-th power of a constant as $k$ tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.Comment: 22 pages, plain TeX. Please typeset only the file orth.te