G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that g-frames share many useful properties with frames. We also give a generalized version of Riesz bases and orthonormal bases. As an application, we get atomic resolutions for bounded linear operators.

The self-assembly of nanoparticles at the fluid/fluid interface (Pickering emulsions) in the breath figures (BF) method have been explored to direct nanoparticles onto BF microarrays and adjust the BF assembly in microsize. Circular rings of nanoparticle-decorated honeycomb-structured polymeric film can be obtained by a one-step process. The combination of Pickering emulsions and capillary flow in the BF method may be responsible for the formation of this intriguing structure.

Kinetics of iron carbonate layer formation in carbon dioxide corrosion has been investigated using a direct method-the corrosion layer weight-change method. The experiments were conducted in a glass cell at the temperatures from 60°C to 90°C, within an iron carbonate supersaturation range from 10 to 350. It was found that the calculated results obtained by the previous kinetics expressions, which were based on the traditional dissolved ferrous ion concentration change method, are one to two orders of magnitude higher than the experimental reaction rates obtained in the present study. Based on the new data, a more appropriate equation is developed to describe iron carbonate layer growth on the steel surface. The experimental results further suggest that the main source of the ferrous ions, which are involved in the formation of the protective iron carbonate layer, is the iron dissolution process. It has been clearly demonstrated that the formation of iron carbonate is directly related to the conditions at the steel surface, which frequently can be very different from the one in the bulk fl uid. CORROSION SCIENCE SECTION CORROSION-Vol. 64, No. 4 335 FIGURE 17. Comparison of scaling tendency (ST) in pure CO 2 corrosion under the following conditions: initial Fe 2+ concentration = 50 ppm (which then drifted down); pH 6.6; T = 60°C, 70°C, 80°C, and 90°C; and stagnant solution.

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A mechanistic model of uniform hydrogen sulfide (H 2 S) and hydrogen sulfide/carbon dioxide (H 2 S/CO 2 ) corrosion of mild steel is presented that is able to predict the rate of corrosion with time. In the model, the corrosion rate of mild steel is primarily affected by H 2 S concentration, temperature, velocity, and the protectiveness of the mackinawite surface layer. The amount of mackinawite retained on the steel surface changes with time and depends on the layer formation rate as well as the layer damage rate. The layer formation may occur by corrosion and/or precipitation, while the layer damage can be by mechanical or chemical means. The model predictions were compared with a very broad set of experimental results and good agreement was found. The current version of the model does not yet include iron sulfide precipitation effects, nor hydrodynamic effects on film damage, which will be addressed in future work.