Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Advancing the science behind human resources for health: highlights from the Health Policy and Systems Research Reader on Human Resources for Health

Health workers are central to people-centred health systems, resilient economies and sustainable development. Given the rising importance of the health workforce, changing human resource for health (HRH) policy and practice and recent health policy and systems research (HPSR) advances, it is critical to reassess and reinvigorate the science behind HRH as part of health systems strengthening and social development more broadly. Building on the recently published Health Policy and Systems Research Reader on Human Resources for Health (the Reader), this commentary reflects on the added value of HPSR underpinning HRH. HPSR does so by strengthening the multi-disciplinary base and rigour of HRH research by (1) valuing diverse research inferences and (2) deepening research enquiry and quality. It also anchors the relevance of HRH research for HRH policy and practice by (3) broadening conceptual boundaries and (4) strengthening policy engagement. Most importantly, HPSR enables us to transform HRH from being faceless numbers or units of health producers to the heart and soul of health systems and vital change agents in our communities and societies. Health workers’ identities and motivation, daily routines and negotiations, and training and working environments are at the centre of successes and failures of health interventions, health system functioning and broader social development. Further, in an increasingly complex globalised economy, the expansion of the health sector as an arena for employment and the liberalisation of labour markets has contributed to the unprecedented movement of health workers, many or most of whom are women, not only between public and private health sectors, but also across borders. Yet, these political, human development and labour market realities are often set aside or elided altogether. Health workers’ lives and livelihoods, their contributions and commitments, and their individual and collective agency are ignored. The science of HRH, offering new discoveries and deeper understanding of how universal health coverage and the Sustainable Development Goals are dependent on millions of health workers globally, has the potential to overcome this outdated and ineffective orthodoxy

Design of hierarchically structured catalysts by mordenites recrystallization: Application in naphthalene alkylation

International audienceMicro/mesoporous composite materials with different levels of micro- and mesoporosity were prepared by recrystallization of mordenite in the presence of cethyltrimethylammonium bromide. The materials were characterized by XRD, TEM, IR spectroscopy, nitrogen adsorption-desorption and NH3-TPD. The results highlight that recrystallization in mild condition results in the creation of mesopores in the zeolite crystals and their coating with thin films of mesoporous material. The increase of the degree of recrystallization leads first to the formation of composite materials MOR/MCM-41 and then to a complete transformation of mordenite in MCM-41, followed by a gradual decrease of the amount and strength of acid sites. Recrystallized materials display remarkably high activity, stability and selectivity in alkylation of naphthalene with cyclohexene. The effect is due to the improved accessibility of active sites and easier transport of bulky molecules provided by mesopores. The best catalytic performance is achieved on composite materials with intermediate degree of recrystallization. The yield of alkylnaphthalenes over these materials reaches 80%, while the yield of monoalkylnaphthalenes is up to 58%

Transalkylation of 1,4-diisopropylbenzene with naphthalene over dealuminated mordenites

International audienceThe transalkylation of diisopropylbenzene with naphthalene has been studied over two series of mordenite catalysts dealuminated by acid treatments and by combined calcination at 750°C and acid attack treatments, respectively. The nature and accessibility of the acid sites were studied by IR spectroscopy of adsorbed pyridine, 2,4,6-trimethylpyridine and 2,4,6-triethylpyridine. The highest yields of 2,6- and 2,7- diisopropylnaphtalenes and the highest stability of catalytic activity were observed over mordenites dealuminated by combined calcination and acid attack treatments. This dealumination procedure leads to the creation of a secondary mesopore network interconnecting structural micropores, which improves the acid sites accessibility, facilitates the transport of bulky reactants and products and prevents deactivation by pore blocking