Academic literature on the topic 'Yao's principle'

We offer efficient and practical solutions of Yao’s millionaires’ problem without using any one-way functions. Some of the solutions involve physical principles, while others are purely mathematical. One of our solutions (based on physical principles) yields a public-key encryption protocol secure against (passive) computationally unbounded adversary. In that protocol, the legitimate parties are not assumed to be computationally unbounded.

The elliptical trainer is a widely used piece of equipment for fitness and rehabilitation. An elliptical trainer with seven links and eight joints, and two degrees of freedom, can have its range of motion adjusted to match the user's stature, and the user can obtain different athletic effects. It allows for more adjustment than an elliptical trainer with one degree of freedom. In this paper, we refer to the present patents that specify the design requirements and constraints for an elliptical trainer. We then use Yan's creative mechanism design methods, which include generalized principles, number synthesis, specialization, and particularization, to obtain a practicable structure for an elliptical trainer with two degrees of freedom. We obtained five alternative kinds of mechanism. We chose one of them for a simulated kinematic analysis, and manufactured the prototype. This paper can serve not only as a reference for the development of fitness equipment but also as a teaching tool for creative mechanism design courses.

This paper investigates the size-dependent nonlinear bending of functionally graded carbon nanotube-reinforced (FG-CNTR) nanobeams. Chen–Yao’s surface elasticity and modified couple stress theories are adopted to describe surface effects and couple stress effects, respectively. These nanobeams, in which the carbon nanotube (CNT)-reinforced phases are assumed to be distributed in a gradient along the thickness, are subjected to a uniform pressure and rest on a nonlinear elastic foundation. In accordance with the Euler–Lagrange variational principle, the governing equations and boundary conditions for the FG-CNTR nanobeams, which involve geometric nonlinearity due to the von Kármán strain relations, are obtained. Then, with the assistance of the two-step perturbation technique, the load-deflection relationship is determined for nanobeams subjected to simply supported (SS) and clamped–clamped (CC) boundary conditions. Finally, the impacts of various factors, including surface properties, characteristic material length, elastic foundation, geometric factors, layout type and volume fraction of CNTs, on the mechanical behaviors of CNT-based nanobeams are examined. The numerical results reveal that the combination of surface effects and couple stress helps to enhanceq the stiffness of the nanobeams. Furthermore, the size-dependent nonlinear bending of the FG-CNTR nanobeam is markedly affected by the content and layout type of the reinforcements.