An ultradiscrete matrix version of the fourth Painleve equation

We establish a matrix generalization of the ultradiscrete fourth Painlev\'e equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.Comment: 12 pages, 12 figures, Latex2e, Submitted to J. Phys. A, corrections mad

An improved lumped parameter method for building thermal modelling

In this work an improved method for the simplified modelling of the thermal response of building elements has been developed based on a 5-parameter second-order lumped parameter model. Previous methods generate the parameters of these models either analytically or by using single objective function optimisation with respect to a reference model. The analytical methods can be complex and inflexible and the single objective function method lacks generality. In this work, a multiple objective function optimisation method is used with a reference model. Error functions are defined at both internal and external surfaces of the construction element whose model is to be fitted and the resistance and capacitance distributions are adjusted until the error functions reach a minimum. Parametric results for a wide range (45) of construction element types have been presented. Tests have been carried out using a range of both random and periodic excitations in weather and internal heat flux variables resulting in a comparison between the simplified model and the reference model. Results show that the simplified model provides an excellent approximation to the reference model whilst also providing a reduction in computational cost of at least 30%

Image Sources: A guide to finding photographs, pictures and graphics

A Library Research Guide to finding and using print, electronic and web images for use in coursewor

Film: A guide to finding information

A guide to Library resources for Film

Texas contest fiddling : what modern variation technique tells us

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