This paper considers the stabilization of a heat‐ODE system cascaded at a boundary point and an intermediate point. The stabilizing feedback control law is designed by the backstepping method. Based on a novel transformation, we prove that all the kernel functions in the forward and inverse transformations are of the class C2. Moreover, the effectiveness of controller design is shown with a numerical simulation. Finally, we show the coherence between the controllability assumption of the main theorem in this paper and the known one for a special case with λ=0.
This paper studies a three-echelon supply chain consisting of a commercial bank, an e-commerce platform, and a capital-constrained online retailer. Due to limited creditworthiness, the retailer can only obtain a restricted bank loan, while the remaining needs to resort to the e-commerce platform to fund its business. We formulate a three-echelon Stackelberg game in which the bank is a leader, the e-commerce platform is a subleader, and the retailer is a follower. We analytically derive the optimal interest rates of the bank and the ecommerce platform and the optimal order quantity of the retailer. Compared with the nonfinancing case, we characterize the regions of the interest rates charged by the bank and the e-commerce platform under which Pareto improvement can be achieved. We also present the retailer's financing preference under equilibrium and show how the initial capital affects the retailer's financing selection. Numerical examples demonstrate that the retailer's order quantity and expected profit increase with the bank's loan ratio.
Molecular docking aims to predict possible drug candidates for many diseases, and it is computationally intensive. Particularly, in simulating the ligand-receptor binding process, the binding pocket of the receptor is divided into subcubes, and when the ligand is docked into all cubes, there are many molecular docking tasks, which are extremely time-consuming. In this study, we propose a heterogeneous parallel scheme of molecular docking for the binding process of ligand to receptor to accelerate simulating. The parallel scheme includes two layers of parallelism, a coarse-grained layer of parallelism implemented in the message-passing interface (MPI) and a fine-grained layer of parallelism focused on the graphics processing unit (GPU). At the coarse-grain layer of parallelism, a docking task inside one lattice is assigned to one unique MPI process, and a grouped master-slave mode is used to allocate and schedule the tasks. Meanwhile, at the fine-gained layer of parallelism, GPU accelerators undertake the computationally intensive computing of scoring functions and related conformation spatial transformations in a single docking task. The results of the experiments for the ligand-receptor binding process show that on a multicore server with GPUs the parallel program has achieved a speedup ratio as high as 45 times in flexible docking and as high as 54.5 times in semiflexible docking, and on a distributed memory system, the docking time for flexible docking and that for semiflexible docking gradually decrease as the number of nodes used in the parallel program gradually increases. The scalability of the parallel program is also verified in multiple nodes on a distributed memory system and is approximately linear.
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