There are many uncertainties and risks in residential electricity consumption during the economic development. Knowledge of the relationship between residential electricity consumption and its key determinant—income—are important to the sustainable development of electric power industry. Using panel data from 30 provinces for the 1995-2012 period, this study investigates how residential electricity consumption changes as incomes increase in China. Previous studies typically used linear or quadratic double-logarithmic models imposing ex ante restrictions on the indistinct relationship between residential electricity consumption and income. Contrary to those models, we employed a reduced piecewise linear model that is self-adaptive and highly flexible and circumvents the problem of “prior restrictions.” Robust tests of different segment specifications and regression methods are performed to ensure the conservatism of the research. The results provide strong evidence that the income elasticity was approximately one, and it remained stable throughout the estimation period. The income threshold at which residential electricity consumption automatically remains stable or slows has not been reached. To ensure the sustainable development of the electric power industry, introducing higher energy efficiency standards for electrical appliances and improving income levels are vital. And government should emphasize electricity conservation in industrial sector rather than in residential sector.

Only cross-sectional studies have demonstrated muscle deficits in children with spastic cerebral palsy (SCP). The impact of functional impairments on altered muscle growth remains unclear. This prospective longitudinal study modelled the morphological muscle growth in 87 children with SCP (age range 6 months to 11 years, Gross Motor Function Classification System [GMFCS] level I/II/III=47/22/18). Repeated ultrasound assessments were performed during 2-year (y) follow-up with an interval of minimal 6 months. Three-dimensional freehand ultrasound was applied to assess medial gastrocnemius muscle volume (MV), mid-belly cross-sectional area (CSA) and muscle belly length (ML). Non-linear mixed models compared trajectories of (normalized) muscle growth between GMFCS-I versus GMFCS-II&III. MV and CSA growth trajectories showed piecewise model with 2 breakpoints, with the highest growth before 2y and negative growth rates after 6-9y. Before 2y, children with GMFCS-II&III already showed lower growth rates compared to GMFCS-I. From 2-9y, the growth rates did not differ between GMFCS-levels. After 9y, a more pronounced reduction in normalized CSA was observed in GMFCS-II&III. Different trajectories in ML growth were shown between the GMFCS-level subgroups. These longitudinal trajectories could be used to monitor the SCP muscle pathology during childhood and to optimize treatment planning and goals aiming to stimulate muscle growth

Estimating the vehicle crashworthiness parameters experimentally is expensive and time consuming. For these reasons different modelling approaches are utilized to predict the vehicle behaviour and reduce the need for full-scale crash testing. The earlier numerical methods used for vehicle crashworthiness analysis were based on the use of lumped parameters models (LPM), a combination of masses and nonlinear springs interconnected in various configurations. Nowadays, the explicit nonlinear finite element analysis (FEA) is probably the most widely recognized modelling technique. Although informative, finite element models (FEM) of vehicle crash are expensive both in terms of man-hours put into assembling the model and related computational costs. A simpler analytical tool for early analysis of vehicle crashworthiness could greatly assist the modelling and save time. In this paper a simple piecewise LPM composed of a mass-spring-damper system, is used to estimate the vehicle crashworthiness parameters, focusing on the dynamic crush and the acceleration severity index (ASI). The model is first calibrated against a full-scale crash test and a FEM, post-processed with the LS-DYNA software, at an impact velocity of 56 km/h. The genetic algorithm is used to calibrate the model by estimating the piecewise lumped parameters (stiffness and damping of the front structure of the vehicle). After calibration, the LPM is applied to a range of velocities (40, 48, 64 and 72 km/h). The predictions for crashworthiness parameters from the LPM were compared with the predictions from the FEA and the results are much similar. It is shown that the LPM can assist in crash analysis, since LPM has some predictive capabilities and requires less computation time in comparison with the explicit nonlinear FEA.

Since the conventional split-merge algorithm is sensitive to the object scale variance and splitting starting point, a piecewise split-merge polygon approximation method is proposed to extract the object contour features. Specifically, the contour corner is used as the starting point for the contour piecewise approximation to reduce the sensitivity of the contour segment on the starting point; then, the split-merge algorithm is used to implement the polygon approximation for each contour segments. Both the distance ratio and the arc length ratio instead of the distance error are used as the iterative stop condition to improve the robustness to the object scale variance. Both the angle and length as two features describe the shape of the contour polygon, and affect each other along the contour order relationship. Since they have a strong coupling relationship. To improve the description correction of the contour, these two features are combined to construct a Coupled Hidden Markov Model to detect the object by calculating the probability of the contour feature. The proposed algorithm is validated on ETHZ Shape Classes and INRIA Horses standard datasets. Compared with other contour-based object detection algorithms, the proposed algorithm reduces the complexity of contour description, improves the robustness of contour features to scale variance, and has a higher object detection rate.

A complete MAPLE procedure is designed to implement effectively an algorithm for approximating the trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval-polynomial as its output that we can easily explore in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both of rational and irrational arguments as well as drawing the graph of the piecewise approximate functions will be presented. Moreover, from the approximate integration of integrands of the form $x^m\sin x$ on $[a,b]$, another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best $L^2$-approximation of the sine function in the vector space $\mathcal{P}_{\ell}$ of polynomials of degree at most $\ell$, a subspace of $L^2(a,b)$.

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigates the performance of several representative piecewise-linear (or piecewise-affine) relaxation schemes (referred to as McCormick, bm, nf5, nf6t, and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. Computational results show that applying these schemes give improved relaxation tightness than only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It is also seen that there is a limit on the number of partitions that contributes to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relation between relaxation size and tightness does not always hold for non-uniform partition sizes.