1,721,084 research outputs found
Optimal contracting under adverse selection: The implications of mentalizing
Get PDFWe study a model of adverse selection, hard and soft information, and mentalizing ability-the human capacity to represent others' intentions, knowledge, and beliefs. By allowing for a continuous range of different information types, as well as for different means of acquiring information, we develop a model that captures how principals differentially obtain information on agents. We show that principals that combine conventional data collection techniques with mentalizing benefit from a synergistic effect that impacts both the amount of information that is accessed and the overall cost of that information. This strategy affects the properties of the optimal contract, which grows closer to the first best. This research provides insights into the implications of mentalizing for agency theory
Classification of traveling waves for a class of nonlinear wave equations
No full textWe classify the weak traveling wave solutions for a class of one-dimensional non-linear shallow water wave models. The equations are shown to admit smooth, peaked, and cusped solutions, as well as more exotic waves such as stumpons and composite waves. We also explain how some previously studied traveling wave solutions of the models fit into this classification
Classification of all travelling-wave solutions for some nonlinear dispersive equations
No full textWe present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa-Holm or the Degasperis-Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles
Riemannian geometry on the diffeomorphism group of the circle
No full textThe topological group D-k(S) of diffeomorphisms of the unit circle 5 of Sobolev class H-k, for k large enough, is a Banach manifold modeled on the Hilbert space H-k(S). In this paper we show that the H-1 right-invariant metric obtained by right-translation of the H-1 inner product on TidDk(S)similar or equal to H-k(S) defines a smooth Riemannian metric on D-k(S), and we explicitly construct a compatible smooth affine connection. Once this framework has been established results from the general theory of affine connections on Banach manifolds can be applied to study the exponential map, geodesic flow, parallel translation, curvature etc. The diffeomorphism group of the circle provides the natural geometric setting for the Camassa-Holm equation - a nonlinear wave equation that has attracted much attention in recent years - and in this context it has been remarked in various papers how to construct a smooth Riemannian structure compatible with the H-1 right-invariant metric. We give a self-contained presentation that can serve as a detailed mathematical foundation for the future study of geometric aspects of the Camassa-Holm equation
Traveling wave solutions of the Degasperis–Procesi equation
No full textAbstractWe classify all weak traveling wave solutions of the Degasperis–Procesi equation. In addition to smooth and peaked solutions, the equation is shown to admit more exotic traveling waves such as cuspons, stumpons, and composite waves
Stability for the periodic Camassa-Holm equation
No full textWe use integrability to prove the stability of smooth periodic solutions of the Camassa-Holm equation. In particular, the smooth periodic traveling wave solutions are shown to be orbitally stable
Conservation laws of the Camassa-Holm equation
No full textWe use the bi-Hamiltonian structure of the Camassa-Holm equation to show that its conservation laws H-n[m] are homogeneous with respect to the scaling m --> lambdam. Moreover, a direct argument is presented proving that H-1, H-2,..., are of local character. Finally, simple representations of the conservation laws in terms of their variational derivatives are derived and used to obtain a constructive scheme for computation of the H(n)s
Semiclassical limit of a non-polynomial q-Askey scheme
No full textPublisher Copyright: © 2025 The Author(s)We prove a semiclassical asymptotic formula for the two elements M and Q lying at the bottom of the recently constructed non-polynomial hyperbolic q-Askey scheme. We also prove that the corresponding exponent is a generating function of the canonical transformation between pairs of Darboux coordinates on the monodromy manifold of the Painlevé I and III3 equations, respectively. Such pairs of coordinates characterize the asymptotics of the tau function of the corresponding Painlevé equation. We conjecture that the other members of the non-polynomial hyperbolic q-Askey scheme yield generating functions associated to the other Painlevé equations in the semiclassical limit.Peer reviewe
A multigrid Krylov method for eigenvalue problems.
No full textWe are interested in computing eigenvalues and eigenvectors of matrices derived from differential equations. They are often large sparse matrices, including both symmetric and non symmetric cases. Restarted Arnoldi methods are iterative methods for eigenvalue problems based on Krylov subspaces. Multigrid methods solve differential equations by taking advantage of the hierarchy of discretizations. A multigrid Krylov method is proposed by combining Arnoldi and multigrid methods. We compare the new approach with other methods, and explore the theory to explain its efficiency
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