Letter from Gordon Pringle Dallas of Edinburgh inquiring about the reputation of Jarvis, Conklin and Co.

Letter from Gordon Pringle Dallas of Edinburgh inquiring about the reputation of Jarvis, Conklin and Co. The letter is addressed to S.D. Woodruff, Sept. 4, 1884.

Letter to Gordon Pringle Dallas of Edinburgh ensuring him that Conklin, Jarvis and Co.

Letter to Gordon Pringle Dallas of Edinburgh ensuring him that Conklin, Jarvis and Co. “act under strict business principles”. The letter is signed S.D. Woodruff, Sept. 20, 1884.

Does the Barro-Gordon Model Explain the Behavior of US Inflation? a Reexamination of the Empirical Evidence

This paper tests the predictions of the Barro-Gordon model using US data on inflation and unemployment. To that end, it constructs a general game-theoretical model with asymmetric preferences that nests the Barro-Gordon model and a version of Cukierman’s model as special cases. Likelihood Ratio tests indicate that the restriction imposed by the Barro-Gordon model is rejected by the data but the one imposed by the version of Cukierman’s model is not. Reduced-form estimates are consistent with the view that the Federal Reserve weights more heavily positive than negative unemployment deviations from the expected natural rate.

Gordon the warden.

Cumple con los requisitos del currículo de Inglaterra, Gales y Escocia aportando los conocimientos básicos relacionados con el aprendizaje de la lectura y la escritura en niños de seis y siete años. El texto sirve de base para conocer e identificar los sonidos en las palabras. En esta historia, se trata el sonido 'or' de 'Gordon', el guardia que se encuentra muy satisfecho con su emocionante trabajo de dirigir el tráfico.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.