Any non-complete orthonormal system in a Hilbert space can be transformed into basis by small perturbations.

Automatic assembly is a promising research topic in 3D computer vision and robotics. Existing works focus on generating (e.g., IKEA furniture) from scratch with set of parts, namely part assembly. In practice, there are higher demands for the robot to take over finish an incomplete half-assembled off-the-shelf toolkit, especially human-robot multi-agent collaborations. Compared assembly, it mor...

We introduce a new type of dcpo-completion of posets, called D-completion. For any poset P , the D-completion exists, and P and its Dcompletion have the isomorphic Scott closed set lattices. This completion is idempotent. A poset P is continuous (algebraic) if and only if its D-completion is continuous(algebraic). Using the D-completion, we construct the local dcpocompletion of posets, that rev...

We consider the task of collaborative preference completion: given a pool of items, a pool of users and a partially observed item-user rating matrix, the goal is to recover the personalized ranking of each user over all of the items. Our approach is nonparametric: we assume that each item i and each user u have unobserved features xi and yu, and that the associated rating is given by gupfpxi, y...

In multiuser wireless networks, opportunistic scheduling can improve the system throughput and thus reduce the total completion time. In this paper, we explore the possibility of reducing the completion time further by incorporating traffic information into opportunistic scheduling. More specifically, we first establish convexity properties for opportunistic scheduling with file size informatio...

We consider two single-machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing or decreasing functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum...

Crystallization of Aluminum fluoride at atmospheric pressure has been considered. Structure, size and shape of crystals formed during the crystallization process have been investigated. By applying the direct analysis method for the existed aluminum in solution, the aluminum fluoride nucleation process has been detected as a concentration valley at the outset of crystallization process. The...