On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Theatricality, irony and artifice in Gustave Courbet's self-portraits

This article considers the role of theatre as a questioning of Realism in the art of Gustave Courbet

Social determinants of older adults' awareness of community support services in Hamilton, Ontario

Community support services (CSSs) have been developed in Canada and other Western nations to enable persons coping with health or social issues to continue to live in the community. This study addresses the extent to which awareness of CSSs is structured by the social determinants of health. In a telephone interview conducted in February-March 2006, 1152 community-dwelling older adults (response rate 12.4%) from Hamilton, Ontario, Canada were made to read a series of four vignettes and were asked whether they were able to identify a CSS they may turn to in that situation. Across the four vignettes, 40% of participants did name a CSS as a possible source of assistance. Logistic regression was used to determine factors related to awareness of CSSs. Respondents most likely to have awareness of CSS include the middle-aged and higher-income groups. Being knowledgeable about where to look for information about CSSs, having social support and being a member of a club or voluntary organisations are also significant predictors of awareness of CSSs. Study results suggest that efforts be made to improve the level of awareness and access to CSSs among older adults by targeting their social networks as well as their health and social care providers. © 2011 Blackwell Publishing Ltd.

Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).