Modeling the behavior of a prototype cantilevered X-ray adaptive mirror (held from one end) demonstrates its potential for use on high-performance X-ray beamlines. Similar adaptive mirrors are used on X-ray beamlines to compensate optical aberrations, control wavefronts and tune mirror focal distances at will. Controlled by 1D arrays of piezoceramic actuators, these glancing-incidence mirrors can provide nanometre-scale surface shape adjustment capabilities. However, significant engineering challenges remain for mounting them with low distortion and low environmental sensitivity. Finite-element analysis is used to predict the micron-scale full actuation surface shape from each channel and then linear modeling is applied to investigate the mirrors' ability to reach target profiles. Using either uniform or arbitrary spatial weighting, actuator voltages are optimized using a Moore–Penrose matrix inverse, or pseudoinverse, revealing a spatial dependence on the shape fitting with increasing fidelity farther from the mount.

A brace for a wall-mounted toilet, particularly useful for wall-mounted porcelain toilets in hospitals and other health care facilities. The brace a weight receiving structure supported by cantilevered struts that attach the brace to the wall, preferably using the same bolts that attach the toilet to the wall. The weight receiving structure may be seat portion that overlies the rim of the toilet bowl, so that the weight of the user is transmitted from the toilet seat to the seat structure and then to the walls through the struts. Alternately, the weight receiving structure may include an under-bowl support that extends underneath the toilet bowl so that the user's weight is transmitted from the bowl to the wall through the struts. Thus, the cantilevered brace increases the weight-bearing capacity of the wall-mounted toilet. A plastic shroud may be included for enclosing the brace and toilet bowl.