On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation

2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hierarquia mKdV e sinh-Gordon supersimétrica com N = 1

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Bäcklund and Darboux transformations for the Tzitzéica model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Extreme Sports: A positive transformation in courage and humility

Extreme sports and extreme sports participants have been most commonly explored from a negative perspective, for example the “need to take unnecessary risks.” This study explored what can be learned from extreme sports about courage and humility - two positive psychology constructs. A phenomenological method was used via unstructured interviews with 15 extreme sports participants and other first hand accounts. The extreme sports included B.A.S.E. jumping, big wave surfing, extreme skiing, waterfall kayaking, extreme mountaineering and solo rope-free climbing. Results indicate that humility and courage can be deliberately sought out by participating in activities that involve a real chance of death, fear and the realisation that nature in its extreme is far greater and more powerful than humanity.

Creative industries in China : four perspectives on social transformation

In late 2004, the concept of the creative industries arrived in China. It was warmly welcomed in Shanghai then subsequently adopted with some degree of caution in Beijing. In the years since, officials, scholars, practitioners, entrepreneurs and developers have exploited of the idea of creative industries, and a range of associated terms, to construct an alternative vision of an emerging China. In 2009, Li Wuwei, the Director of the Shanghai Creative Industries Association, himself a leading player in national political reform, released a book titled Creativity is Changing China (Chuangyi gaibian Zhongguo), subsequently translated as Creative Industries Are Changing China in English. The paper investigates the uptake of the creative industries in China and asks: can they really change China, or are they just rearranging the cultural landscape in some cities?

Applied theatre and organisational transformation

Applied Theatre is an umbrella term for a range of drama-based techniques, all of which align with a lineage of pedagogical theory and practice: (e.g.) Freire, Moreno, Heathcote. It encompasses methods and forms including Drama Education (O’Neill); Forum Theatre (Boal); and Process Drama (Haseman, O’Toole). Applied theatre often occurs in non-theatrical settings (schools, hospitals, prisons) with the aim of helping participants address issues of local concern. Increasingly, Applied Theatre practices are utilised in the corporate environment. Appied Theatre adopts artistic principles in production, but posits a practical utility beyond simple entertainment.

Dynamics of transformation and fragmentation of composite liquid nano-particles

Recent research on particle size distributions and particle concentrations near a busy road cannot be explained by the conventional mechanisms for particle evolution of combustion aerosols. Specifically they appear to be inadequate to explain the experimental observations of particle transformation and the evolution of the total number concentration. This resulted in the development of a new mechanism based on their thermal fragmentation, for the evolution of combustion aerosol nano-particles. A complex and comprehensive pattern of evolution of combustion aerosols, involving particle fragmentation, was then proposed and justified. In that model it was suggested that thermal fragmentation occurs in aggregates of primary particles each of which contains a solid graphite/carbon core surrounded by volatile molecules bonded to the core by strong covalent bonds. Due to the presence of strong covalent bonds between the core and the volatile (frill) molecules, such primary composite particles can be regarded as solid, despite the presence of significant (possibly, dominant) volatile component. Fragmentation occurs when weak van der Waals forces between such primary particles are overcome by their thermal (Brownian) motion. In this work, the accepted concept of thermal fragmentation is advanced to determine whether fragmentation is likely in liquid composite nano-particles. It has been demonstrated that at least at some stages of evolution, combustion aerosols contain a large number of composite liquid particles containing presumably several components such as water, oil, volatile compounds, and minerals. It is possible that such composite liquid particles may also experience thermal fragmentation and thus contribute to, for example, the evolution of the total number concentration as a function of distance from the source. Therefore, the aim of this project is to examine theoretically the possibility of thermal fragmentation of composite liquid nano-particles consisting of immiscible liquid v components. The specific focus is on ternary systems which include two immiscible liquid droplets surrounded by another medium (e.g., air). The analysis shows that three different structures are possible, the complete encapsulation of one liquid by the other, partial encapsulation of the two liquids in a composite particle, and the two droplets separated from each other. The probability of thermal fragmentation of two coagulated liquid droplets is discussed and examined for different volumes of the immiscible fluids in a composite liquid particle and their surface and interfacial tensions through the determination of the Gibbs free energy difference between the coagulated and fragmented states, and comparison of this energy difference with the typical thermal energy kT. The analysis reveals that fragmentation was found to be much more likely for a partially encapsulated particle than a completely encapsulated particle. In particular, it was found that thermal fragmentation was much more likely when the volume ratio of the two liquid droplets that constitute the composite particle are very different. Conversely, when the two liquid droplets are of similar volumes, the probability of thermal fragmentation is small. It is also demonstrated that the Gibbs free energy difference between the coagulated and fragmented states is not the only important factor determining the probability of thermal fragmentation of composite liquid particles. The second essential factor is the actual structure of the composite particle. It is shown that the probability of thermal fragmentation is also strongly dependent on the distance that each of the liquid droplets should travel to reach the fragmented state. In particular, if this distance is larger than the mean free path for the considered droplets in the air, the probability of thermal fragmentation should be negligible. In particular, it follows form here that fragmentation of the composite particle in the state with complete encapsulation is highly unlikely because of the larger distance that the two droplets must travel in order to separate. The analysis of composite liquid particles with the interfacial parameters that are expected in combustion aerosols demonstrates that thermal fragmentation of these vi particles may occur, and this mechanism may play a role in the evolution of combustion aerosols. Conditions for thermal fragmentation to play a significant role (for aerosol particles other than those from motor vehicle exhaust) are determined and examined theoretically. Conditions for spontaneous transformation between the states of composite particles with complete and partial encapsulation are also examined, demonstrating the possibility of such transformation in combustion aerosols. Indeed it was shown that for some typical components found in aerosols that transformation could take place on time scales less than 20 s. The analysis showed that factors that influenced surface and interfacial tension played an important role in this transformation process. It is suggested that such transformation may, for example, result in a delayed evaporation of composite particles with significant water component, leading to observable effects in evolution of combustion aerosols (including possible local humidity maximums near a source, such as a busy road). The obtained results will be important for further development and understanding of aerosol physics and technologies, including combustion aerosols and their evolution near a source.

The Federal circuit in Bilski : the machine-or-transformation test

In a much anticipated judgment, the Federal Circuit has sought to clarify the standards applicable in determining whether a claimed method constitutes patent-eligible subject matter. In Bilski, the Federal Circuit identified a test to determine whether a patentee has made claims that pre-empt the use of a fundamental principle or an abstract idea or whether those claims cover only a particular application of a fundamental principle or abstract idea. It held that the sole test for determining subject matter eligibility for a claimed process under § 101 is that: (1) it is tied to a particular machine or apparatus, or (2) it transforms a particular article into a different state or thing. The court termed this the “machine-or-transformation test.” In so doing it overruled its earlier State Street decision to the extent that it deemed its “useful, tangible and concrete result” test as inadequate to determine whether an alleged invention recites patent-eligible subject matter.