Hamilton-Jacobi Theory in k-Symplectic Field Theories

In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework

The Bank of Canada's Management of Foreign Currency Reserves

This article describes the Bank's management of the liquid foreign currency portion of the government's official reserves. It broadly outlines the operations of the Exchange Fund Account (EFA), the main account in which Canada's reserves are held. It then briefly reviews the evolution of the objectives and management of the EFA over the past 25 years, particularly in light of the changing level of reserves and developments in financial markets. The EFA is funded by Canada's foreign currency borrowings in capital markets. The article focuses on the comprehensive portfolio framework used to manage the Account, which matches assets and liabilities. Under this framework, funds are invested in assets that match, as closely as possible, the characteristics of foreign currency liabilities issued, helping to immunize the portfolio against currency and interest rate risks.

Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

Guide to the classics: Don Quixote, the world’s first novel – and one of the best

Completed by Cervantes when he was in prison, Don Quixote is the tale of a man so passionate about reading he leaves home to live the life of his fictional heroes

Singular Lagrangians and precontact Hamiltonian Systems

In this paper we discuss singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac-Bergman algorithm). We also construct the Hamiltonian counterpart and prove the equivalence with the Lagrangian side. A Dirac-Jacobi bracket is constructed similar to the Dirac bracket