Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | Σ in the boundary condition, where ε > 0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

Mass Customisation for Zero-Energy Housing

This article describes the potential that co-design and marketing strategies have on increasing the consumption of energy-efficient dwellings. It explains how Japanese housebuilders are using ‘mass customisation’—a phenomenon that mirrors the production and marketing of the automobile sector—in order to produce zero-energy houses and how this applies to the UK. The research consisted of a comparative analysis of Japanese and UK housebuilding. It identifies how mass customisation strategies are used to drive the sales of zero-energy houses in Japan and infers how to apply these in the UK context. This research found that some housebuilders in the UK are already using production strategies that resemble Japanese practices; however, the sustainable benefits observed in the Japanese context are not present in the UK because housebuilders’ mass customisation strategies are limited to construction and not used as part of the marketing, co-design, and selling processes. Production and consumption of sustainable houses would increase in the UK if housebuilders implemented full mass customisation, meaning selecting existing robust production processes, defining an appropriate space solution, and using informative navigation tools.

An Optimized DiscretizationApproach using k-Means Bat Algorithm

This study has proposed arelatively new discretization approach using k-means and Bat algorithm in preparation phase of classification problem. In essence, bat algorithm is applied to find the best search space solution. Eventually, the best search space solution is utilized to produce cluster centroid. The cluster centroid is very useful to determine appropriate breakpoint for discretization. The proposed discretization approach is applied in the experiments with continuous datasets. Decision Tree, k-Nearest Neighbours and Naïve Bayes classifiers are used in the experiments. The proposed discretization approach is evaluated against other existing approaches: K-Means algorithm, hybrid K-Means with Particle Swarm Optimization (PSO) and hybrid K-Means with Whale Optimization Algorithm (WOA).The classification performance is evaluated in terms of accuracy, recall, f-measure and receiver operating characteristic curve (ROC). To test the performance of the proposed algorithm, nine benchmark continuous datasets are used. The proposed algorithm show the better results compare to other approaches. The proposed algorithm performs better in discretization to solve classification problems.