Synthesis,photopolymerization, and adhesive properties of new bisphosphonic acid monomers for dental application

Four new monomers, 3‐(N‐methylacrylamido)propylidenebisphosphonic acid, 3‐(N‐propyl‐acrylamido)propylidenebisphosphonic acid, 3‐(N‐hexylacrylamido)propylidenebisphosphonic acid, and 3‐(N‐octylacrylamido)propylidenebisphosphonic acid, have been synthesized in good yields and fully characterized by ¹H, ¹³C, ³¹P NMR, and HRMS. The copolymerization of these monomers with N,N′‐diethyl‐1,3‐bis(acrylamido)propane (DEBAAP) has been investigated with differential scanning calorimetry. These mixtures show a higher reactivity than DEBAAP. New self‐etch dental primers, based on these acrylamide monomers, have been formulated. Dentin shear bond strength measurements have shown that primers based on these bisphosphonic acids assure a strong bond between the tooth substance and a dental composite. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5258–5271, 2009     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.     

A splitting algorithm for equilibrium problem given by the difference of two bifunctions

In this paper, we introduce a splitting algorithm for solving equilibrium problems given by the difference of two bifunctions in a real Hilbert space. Under suitable assumptions on component bifunctions, we prove strong convergence of the proposed algorithm. In contrast to most existing projection-type methods for equilibrium problems, our algorithm does not require any convexity or monotonicity conditions on the resulting bifunction. Some numerical experiments and comparisons are given to illustrate the efficiency of the proposed algorithm.     

A reduction theorem for the Alperin weight conjecture

The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.     

Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches

In this paper, we consider a task allocation model that consists of assigning a set of m unmanned aerial vehicles (UAVs) to a set of n tasks in an optimal way. The optimality is quantified by target scores. The mission is to maximize the target score while satisfying capacity constraints of both the UAVs and the tasks. This problem is known to be NP-hard. Existing algorithms are not suitable for the large scale setting. Scalability and robustness are recognized as two main issues. We deal with these issues by two optimization approaches. The first approach is the Cross-Entropy (CE) method, a generic and practical tool of stochastic optimization for solving NP-hard problem. The second one is Branch and Bound algorithm, an efficient classical tool of global deterministic optimization. The numerical results show the efficiency of our approaches, in particular the CE method for very large scale setting.