The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Trading HIV for sheep: Risky sexual behavior and the response of female sex workers to Tabaski in Senegal

We use a cohort of female sex workers (FSWs) in Senegal to show how large anticipated economic shocks lead to increased risky sexual behavior. Exploiting the exogenous timing of interviews, we study the effect of Tabaski, the most important Islamic festival celebrated in Senegal, in which most households purchase an expensive animal for sacrifice. Condom use, measured robustly via the list experiment, falls by between 27.3 percentage points (pp) (65.5%) and 43.1 pp (22.7%) in the 9 days before Tabaski, or a maximum of 49.5 pp (76%) in the 7 day period preceding Tabaski. The evidence suggests the economic pressures from Tabaski are key to driving the behavior change observed through the price premium for condomless sex. Those most exposed to the economic pressure from Tabaski were unlikely to be using condoms at all in the week before the festival. Our findings show that Tabaski leads to increased risky behaviors for FSWs, a key population at high risk of HIV infection, for at least 1 week every year and has implications for FSWs in all countries celebrating Tabaski or similar festivals. Because of the scale, frequency, and size of the behavioral response to shocks of this type, policy should be carefully designed to protect vulnerable women against anticipated shocks

Causal relations between knowledge-intensive business services and regional employment growth

This paper studies the causal relations between regional employment growth in Knowledge-Intensive Business Services (KIBS) and overall regional employment growth using German labour-market data for the period 1999-2012. Adopting a recently developed technique, we are able to estimate a structural vector autoregressive model in which the causal directions between KIBS and other sectors are examined including various time lags. One main finding holds that although regional growth has a negative short-term effect on KIBS, KIBS growth has a long-term positive effect on the whole regional economy. This result confirms the claim that KIBS can play a key role in regional policies. Distinguishing between financial and non-financial KIBS, we find that financial KIBS have a procyclical effect on regional growth underlining the potential de-stabilizing effect of a large financial sector

Exact solutions for a class of integrable Henon-Heiles-type systems

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills

Supergravity backgrounds dual to a class of exactly marginal deformations of N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N=1 theories at strong 't Hooft coupling as marginal deformations of N=4 Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrodinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.Comment: 43 pages, Latex, 2 figures. v2: References added. v3: small typos corrected, published versio

Finite-gap systems, tri-supersymmetry and self-isospectrality

We show that an n-gap periodic quantum system with parity-even smooth potential admits $2^n-1$ isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N=4 supersymmetry. We conjecture that any finite-gap system having antiperiodic singlet states admits a self-isospectral tri-supersymmetric extension with the partner potential to be the original one translated for a half-period. Applying the theory to a broad class of finite-gap elliptic systems described by a two-parametric associated Lame equation, our conjecture is supported by the explicit construction of the self-isospectral tri-supersymmetric pairs. We find that the spontaneously broken tri-supersymmetry of the self-isospectral periodic system is recovered in the infinite period limit.Comment: 40 pages, published versio