9,524 research outputs found

    Initialization Strategy for Nonlinear Systems

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    The Study Group was asked to provide some hints concerning a choice of initial values to be used for nonlinear algebraic systems. The group has considered the available options and outlined the pros and cons of various methods and provided some recommendations

    A Medical Waste Sterilizer

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    Sterilization of medical waste is very important for the environment, as the exposition may result in various diseases because of viral or bacterial content of the waste. There are devices developed for this purpose aiming to sterilize the waste in a form called batch process, meaning that a certain amount of waste is placed into the system and subjected to a sterilization procedure for a while and removed from the system afterwards. The procedure is repeated by the next set of waste till the whole set is sterilized. Our aim, however, is to design a device, a rotating cylindrical container having tubular lights attached to the walls inside, through which the waste is exposed to ultraviolet light as it gets rotated and moved towards the exit. The process will continue till the whole set is fed into the system. Such a device would be more effective as compared to batch processing types. The study group is asked to develop a mathematical model to analyse the effect of the number and location of tubes which will lead to maximal exposure during certain amount of time, which also needs an estimate, the sample will reside in the device before it gets discharged

    The Fine Moduli Space of Representations of Clifford Algebras

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    Given a fixed binary form f(u,v)f(u,v) of degree dd over a field kk, the associated \emph{Clifford algebra} is the kk-algebra Cf=k{u,v}/IC_f=k\{u,v\}/I, where II is the two-sided ideal generated by elements of the form (αu+βv)df(α,β)(\alpha u+\beta v)^{d}-f(\alpha,\beta) with α\alpha and β\beta arbitrary elements in kk. All representations of CfC_f have dimensions that are multiples of dd, and occur in families. In this article we construct fine moduli spaces U=Uf,rU=U_{f,r} for the irreducible rdrd-dimensional representations of CfC_f for each r2r \geq 2. Our construction starts with the projective curve CPk2C \subset \mathbb{P}^{2}_{k} defined by the equation wd=f(u,v)w^d=f(u,v), and produces Uf,rU_{f,r} as a quasiprojective variety in the moduli space M(r,dr)\mathcal{M}(r,d_r) of stable vector bundles over CC with rank rr and degree dr=r(d+g1)d_r=r(d+g-1), where gg denotes the genus of CC.Comment: Final version. To appear in Int. Math. Res. Not. IMR
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