Reverse Beckenbach-Dresher’s Inequality

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An equivalence form of the Brunn-Minkowski inequality for volume differences

In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual Kneser-Süss inequality. © 2007 The Korean Mathematical Society.published_or_final_versio

On Hardy-Pachpatte-Copson's Inequalities

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On some opial-type inequalities

In the present paper we establish some new Opial-type inequalities involving higher-order partial derivatives. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type.published_or_final_versio

On opial-type integral inequalities

We establish some new Opial-type inequalities involving functions of two and many independent variables. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type.published_or_final_versio

On Minkowski's inequality and its application

In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.published_or_final_versio

On Lyapunov-type inequalities for two-dimensional nonlinear partial systems

We establish a new Laypunov-type inequality for two nonlinear systems of partial differential equations and the discrete analogue is also established. As application, boundness of the two-dimensional Emden-Fowler-type equation is proved. Copyright © 2010 Lian-Ying Chen et al.published_or_final_versio

Some sharp integral inequalities involving partial derivatives

The main purpose of the present article is to establish some new sharp integral inequalities in 2n independent variables. Our results in special cases yield some of the recent results on Pachpatter, Agarwal and Sheng's inequalities and provide some new estimates on such types of inequalities.published_or_final_versio

n-Type conducting P doped ZnO thin films via chemical vapor deposition

Extrinsically doped ZnO thin films are of interest due to their high electrical conductivity and transparency to visible light. In this study, P doped ZnO thin films were grown on glass substrates via aerosol assisted chemical vapour deposition. The results show that P is a successful dopant for ZnO in the V+ oxidation state and is able to reduce resistivity to 6.0 × 10−3 Ω cm while maintaining visible light transmittance at ∼75%. The thins films were characterized by X-ray diffraction studies that showed only Bragg peaks for the wurtzite ZnO phase. Fitting of the diffraction data to a Le Bail model also showed a general expansion of the ZnO unit cell upon doping due to the substitution of Zn2+ ions with the larger P5+

Transparent and Conductive Molybdenum-Doped ZnO Thin Films via Chemical Vapor Deposition

Extrinsically doped ZnO is widely used as a transparent conducting electrode and has the potential to alleviate the demand on the expensive but ubiquitous Sn-doped In2O3. Here, we report for the first time the synthesis and characterization of molybdenum-doped ZnO via a chemical vapor deposition route. Films were grown by using diethylzinc, molybdenum hexacarbonyl, toluene, and methanol. All films had visible light transmittance of ∼80% and electrical resistivity of 10–3 Ω·cm with the lowest resistivity of 2.6 × 10–3 Ω·cm observed for the 0.57 at. % Mo-doped film. X-ray photoelectron spectroscopy of the surface species and X-ray diffraction based calculations of the ZnO unit cell parameters suggest that Mo is present in the 4+ oxidation state, thus contributing two electrons for electrical conduction for every Zn2+ ion replaced in the lattice