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Deep neural networks are powerful tools to model observations over time with non-linear patterns. Despite the widespread use of neural networks in such settings, most theoretical developments of deep neural networks are under the assumption of independent observations, and theoretical results for temporally dependent observations are scarce. To bridge this gap, we study theoretical properties of deep neural networks on modeling non-linear time series data. Specifically, non-asymptotic bounds for prediction error of (sparse) feed-forward neural network with ReLU activation function is established under mixing-type assumptions. These assumptions are mild such that they include a wide range of time series models including auto-regressive models. Compared to independent observations, established convergence rates have additional logarithmic factors to compensate for additional complexity due to dependence among data points. The theoretical results are supported via various numerical simulation settings as well as an application to a macroeconomic data set., Comment: 23 pages, 18 pages, accepted for publication in Neural Information Processing Systems

Polyurethane was widely fabricated as an environmentally friendly coating in the field of infrastructure protection. In this paper, several modification methods of polyurethane coatings were reviewed, including nanoparticle modification, silicone modification, vegetable oil modification, and organic fluorine modification^^81Cetc. Based on modification the performance of polyurethane coating was greatly improved while the application scope of the polyurethane coating was extremely expanded. A versatile coating-poly urea was introduced, which gained a foothold in coatings industry.

The combustive reduction reactions induced by high-energy ball milling in some metal-oxide systems have been investigated in this article. The experimental results show that the highly exothermic nature of a reaction is only a requisite condition for initiating combustion; whether the combustion takes place or not depends on the dynamic state of the reaction system during milling. The influence of the crystalline structures of the reactants on the ignition of combustion reactions instigated by high-energy ball milling is not clear. The ignition starting points of combustive reactions trigged by heating or ball milling have nearly the same linear uptrend with the rise of melting temperatures for the reaction systems of Al/CuO, but this is not visible for the reduction of CuO with metals instigated by ball milling. It is suggested that probably the occurrence of a reduction reaction induced by mechanical force depends mainly on the disintegration of the oxide. The mechanical properties and the type of atomic bond of the reactants also have an effect on the initiation of a combustion reaction during ball milling.

The solid state reaction of Al/CuO induced by high-energy ball milling was studied systematically. When the amount of Al was 20 wt%, only reduction occurred. When the amount of Al exceeded 20 wt%, along with the reduction, a synthesis reaction occurred simultaneously. As the amount of Al increased, the reaction products were Cu9Al4, CuAl2 or a Al(Cu) solid solution, respectively. The mechanism of these two types of reactions occurring during ball milling is discussed.

The effect of molybdenum net interlayers on the thermal shock behavior of Al2O3/Nb brazed joints was investigated. The net was able to increase the thermal shock resistance of the joint considerably. When brazed with Ni5lTi49 and Cu52Ni18Ti30 solders separately and quenched into water from 700°C, the thermal shock resistance of the joints brazed with the nets was raised by more than 180% and 130% respectively, compared to those of the joints without nets. The fracture photographs of the joints with the nets were different from those without nets. It was supposed that the existence of the net could reduce the residual stress markedly.