10,265 research outputs found
Derivation of the Camassa-Holm equations for elastic waves
In this paper we provide a formal derivation of both the Camassa-Holm
equation and the fractional Camassa-Holm equation for the propagation of
small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic
medium. We first show that the equation of motion for the nonlocally and
nonlinearly elastic medium reduces to the improved Boussinesq equation for a
particular choice of the kernel function appearing in the integral-type
constitutive relation. We then derive the Camassa-Holm equation from the
improved Boussinesq equation using an asymptotic expansion valid as
nonlinearity and dispersion parameters tend to zero independently. Our approach
follows mainly the standard techniques used widely in the literature to derive
the Camassa-Holm equation for shallow water waves. The case where the Fourier
transform of the kernel function has fractional powers is also considered and
the fractional Camassa-Holm equation is derived using the asymptotic expansion
technique.Comment: 15 page
WhÄriki : beyond simple : an exhibition report presented as partial fulfilment of the requirements for the degree of Masters of MÄori Visual Arts, Massey University, Palmerston North, New Zealand
This thesis/exhibition report is an explication of the significance and relationship of Kai
rÄranga, rÄranga whÄriki and their relationship with whÄnau, hapÅ« and iwi. It explores the
impetus behind and relationships important in, and to the production of whÄriki.
Through the exploration of these relationships the necessity for whÄriki wÄnanga throughout
Aotearoa and having wÄnanga as the preferred medium of imparting knowledge pertaining to
rÄranga whÄriki and for continuity in the production of whÄriki is emphasised.
It touches on the MÄori convention of tono that facilitates interaction between the Kai rÄrangaresearcher
and the Kai tono-researched negating the sometimes invasive convention of ethics
approval and formalised contractual obligations.
It follows the pathway of author and Kai rÄranga, Te Hemo Ata Henareās, coming to be of her
mahi whÄriki practice. It is an intimate account that extends from function and technique to
foundational connectivity to the wider roopu whÄriki and those who have preceded us with
templates of excellence that recognise the importance of the whakapapa of MÄori whakaaro,
our epochs and eons of transcendent time and the interconnectedness of all things in and
through these patterned processes (Jackson, 2013; Marsden, 2003; Tamanui, 2013). As
Karani Sonny PÄpuni said;
āā¦you take this whÄriki home with you and then a piece of us will always be
with your whÄnauā (Mate ki TÄtahi [Sonny] PÄpuni, personal communication,
May 17 1991).
A clear objective emerging out of this research exercise was to produce a body of work in the
form of an exhibition of whÄriki and to produce a pictorial and written explication of the process
and praxis of whÄriki wÄnanga. However, through the research process, I was returned; i hoki
atu ki te timatatanga Å oku mahi, so I could come to know and be.
The theme that emerges through rÄranga whÄriki is the inseparability and the multiplicity of
whakapapa and/or whanaungatanga that the Kai rÄranga embodies essential for the
continuation of the praxis of rÄranga whÄriki that can only be described as extraordinarily
āBeyond Simpleā
Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies
We consider a class of open stochastic processing networks, with feedback
routing and overlapping server capabilities, in heavy traffic. The networks we
consider satisfy the so-called complete resource pooling condition and
therefore have one-dimensional approximating Brownian control problems.
We propose a simple discrete review policy for controlling such networks.
Assuming 2+\epsilon moments on the interarrival times and processing times,
we provide a conceptually simple proof of asymptotic optimality of the proposed
policy.Comment: Published at http://dx.doi.org/10.1214/105051604000000495 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Multilevel poetry translation as a problem-solving task
Poems are treated by translators as hierarchical multilevel systems. Here we propose the notion of āmultilevel poetry translationā to characterize such cases of poetry translation in terms of selection and rebuilding of a multilevel system of constraints across languages. Different levels of a poem correspond to different sets of components that asymmetrically constrain each other (e.āg., grammar, lexicon, syntactic construction, prosody, rhythm, typography, etc.). This perspective allows a poem to be approached as a thinking-tool: an āexperimental labā which submits language to unusual conditions and provides a scenario to observe the emergence of new patterns of semiotic behaviour as a result. We describe this operation as a problem-solving task, and exemplify with Augusto de Camposā Portuguese translation of John Donneās poem āThe Expiration.
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