Salesforce contracting under model uncertainty

This paper considers a firm's salesforce contracting problem under model uncertainty. Based on the notion of multiplier preferences, we capture model uncertainty and explicitly characterize the structure of the optimal contract. Our findings provide guidelines on the design of salesforce compensation contracts in practical situations.     

Universality of deep convolutional neural networks

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. Deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. This answers an open question in learning theory. Our quantitative estimate, given tightly in terms of the number of free parameters to be computed, verifies the efficiency of deep CNNs in dealing with large dimensional data. Our study also demonstrates the role of convolutions in deep CNNs.     

Iridium-Catalyzed Enantioselective Hydrogenation of Oxocarbenium Ions: A Case of Ionic Hydrogenation

Ionic hydrogenation has not been extensively explored, but is advantageous for challenging substrates such as unsaturated intermediates. Reported here is an iridium-catalyzed hydrogenation of oxocarbenium ions to afford chiral isochromans with high enantioselectivities. A variety of functionalities are compatible with this catalytic system. In the presence of a catalytic amount of the Brønsted acid HCl, an α-chloroether is generated in situ and subsequentially reduced. Kinetic studies suggest first-order kinetics in the substrate and half-order kinetics in the catalyst. A positive nonlinear effect, together with the half kinetic order, revealed a dimerization of the catalyst. Possible reaction pathways based on the monomeric iridium catalyst were proposed and DFT computational studies revealed an ionic hydrogenation pathway. Chloride abstraction and the cleavage of dihydrogen occur in the same step.     

Reverse Thinking of the Aggregation-Induced Emission Principle: Amplifying Molecular Motions to Boost Photothermal Efficiency of Nanofibers**

Using reverse thinking of the aggregation-induced emission (AIE) principle, we demonstrate an ingenious and universal protocol for amplifying molecular motions to boost photothermal efficiency of fibers. Core–shell nanofibers having the olive oil solution of AIE-active molecules as the core surrounded by PVDF-HFP shell were constructed by coaxial electrospinning. The molecularly dissolved state of AIE-active molecules allows them to freely rotate and/or vibrate in nanofibers upon photoexcitation and thus significantly elevates the proportion of non-radiative energy dissipation, affording impressive heat-generating efficiency. Photothermal evaluation shows that the core–shell nanofibers with excellent durability can reach up to 22.36 % of photothermal conversion efficiency, which is 26-fold as the non-core–shell counterpart. Such a core–shell fiber can be used for photothermal textiles and solar steam generation induced by natural sunlight with green and carbon-zero emission.     

Free vibration analysis of cracked beams by using rigid segment method

This paper deals with the analysis of influence of crack parameters to the modal characteristics of beams at various boundary conditions by using rigid segment method. The beam was discretized by a number of rigid segments which were connected by elastic joints with three degrees of freedom, while the crack was described by cracked element based on fracture mechanics. This model allows detection of coupling between the axial and transverse vibrations under the special boundary conditions. The proposed approach covers both the Euler–Bernoulli and Timoshenko beam model. The efficiency of the method was shown through the few numerical examples.