Several Inequalities of Gronwall and Their Proofs

It is well known that integral inequalities play a very important role in studying the properties of solutions to ordinary differential equations and integral equations. In 1919, Gronwall established a class of basic integral inequalities when he studied the dependence of differential equations on parameters, which is called Gronwall's inequalities. Gronwall's inequality play a very important role in ordinary differential equations, and it is also an important tool to study the properties of differential equations and integral equation solutions. There are several proofs of Gronwall's inequality, in particular, Agarwal, Deng and Zhang studied the Gronwall-Bellman inequality with multiple nonlinear terms, which made the adaptability of the Gronwall-Bellman inequality widely. Gronwall's inequality has various generalization forms and different proving methods, which is also a good tool for solving many mathematical problems. Different kinds of Gronwall's inequalities and their proofs are discussed in this paper. By researching the induction of Gronwall's inequality forms and their proofs, this paper aims to solve the problems of inequality as much as possible

Improved Attribute-based Encryption with Fpga for Automatic Appliance Control Application in Smart Grid

In this thesis, the author describes the privacy violation issues in smart grid with Automatic Appliance Control applications, and explains the security threats related to it. The smart grid is a sensitive and sophisticated system in real life operation. A mass of data including the remote control commands and users’ energy consumptions is transmitted between the utility companies and other devices in the smart grid such as the substations, smart meters, smart home appliances and much more. Without efficient cryptographic methods, an adversary may hack into the data or the remote control commands and extrapolates a resident’s activity model. Therefore, the Attribute-Based Encryption (ABE) is proposed to provide protection through generating the secret key of user based on a set of attributes which is used to identify different users in the smart grid. And the ciphertext, which is the encrypted remote command, obtains the access policy for decryption. However, ABE algorithm requires long computational time especially a large quantity of attributes are required in a smart grid. The idea of improved ABE system with FPGA is proposed to solve the problem. But the FPGA is only conceptual idea in this thesis and future work of it will be done by other co-worker

Characterization of the Semi-Permeable Layer in Seed of \u3cem\u3eElymus nutans\u3c/em\u3e

A semi-permeable layer of the seed coat exists in many species which allows controlled water uptake and gas ex-change, while preventing solute transport (Beresniewicz et al. 1995). This layer could act as a barrier to apoplastic permeability and radicle emergence (Salanenka et al. 2009). It could also restrict the tetrazolium viability test and the electrical conductivity vigour test applied to evaluate seed quality (Yan and Wang 2008; Zhou and Wang 2012). An earlier study reported that semi-permeable layers exist in grass species, but recently research has shown that the layer was not found in seeds of oat (He 2011) or tall fescue (Yan 2008). This paper reports the location and chemical composition of a semi-permeable layer and its relationship to the electrical conductivity vigour tests in seeds of Elymus nutans, an important forage grass species widely distributed in Northwestern alpine grasslands China