Academic literature on the topic 'Yao's principle'

We introduce the compound interest rate into the continuous version of the online leasing problem and discuss the generalized model by competitive analysis. On the one hand, the optimal deterministic strategy and its competitive ratio are obtained; on the other hand, a nearly optimal randomized strategy is constructed and a lower bound for the randomized competitive ratios is proved by Yao's principle. With the help of numerical examples, the theoretical results show that the interest rate puts off the purchase date and diminishes the uncertainty involved in the decision making.

AbstractIn this paper, we deal with complete hypersurfaces immersed with bounded higher order mean curvatures in steady state-type spacetimes and in hyperbolic-type spaces. By applying a generalised maximum principle for the Yau's square operator [11], we obtain uniqueness results in each of these ambient spaces.

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.

We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly---it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs