The oxidation of As(III) to As(V) by K-birnessite was examined at different temperatures, pHs, and birnessite/As(III) ratios. Experiments ranged in duration from 5 to 64 hr, and solution and solid products were determined at several intervals. All experiments showed that the reaction produced large amounts of K+ to solution and very little Mn2+. As(V) was released to solution and incorporated into the K-birnessite. The oxidation was initially rapid and then slowed. The oxidation of As(III) was probably facilitated initially by autocatalytic Mn-As(V) reactions occurring mostly in the interlayer, in which large amounts of As(V) and K+ could be easily released to solution. The reaction also slowed when interlayer Mn was exhausted by forming Mn-As(V) complexes. Mn(IV) could only be acquired from the octahedral sheets of the birnessite. The two-stage reaction process proposed here depended on the layered structure of birnessite, the specific surface, and presence of exchangeable cations in K-birnessite.

The solubility of four different gibbsite preparations was measured, including two commercial hydrated aluminas produced by Alcoa, a Fisher ACS-grade Al(OH)3, and a laboratory preparation. The Alcoa samples and the laboratory-prepared sample had been studied previously by other investigators but without using a long-term acid treatment. Scanning electron microscopy showed globular surface material that was removed by a 14-day, 0.1 M HCl treatment. Solubility was determined at pH 4 from both over-and undersaturation with continuous agitation for 228 days. The acid treatment correlated with a decrease in log*Kso[*KSO = (Al3+)/(H+)3] of about 0.5 units. The mean solubility of the three acid-treated commercial gibbsite samples was log*Kso = 7.55 ± 0.055 (*Kso = 3.5 × 107). The solubility of the acid-treated laboratory preparation was log*Kso = 7.86 (*Kso = 7.2 × 107). The greater solubility of the laboratory-prepared gibbsite is attributed to a greater concentration of structural defects in the crystals.

Most of the world's sepiolite-palyg orskite precipitates in lacustrine and perimarine environments. Although these minerals can transform from precursor minerals, the most common formation mechanism involves crystallization from solution. In this study, equilibrium activity diagrams are calculated for sepiolite-palygorskite in the seven component system MgO-CaO-Al2O3-SiO2-H2O-CO2-HCl, employing available thermodynamic data for related minerals, aqueous species and water. Stability fields are illustrated graphically on plots of log $[a_{{\text{Mg}}^{2+}}\text{/}{(a_{{\text{H}}^{+}})}^2]$vs. log $[a_{{\text{H}}_{\text{4}}{\text{SiO}}_{\text{4}}}{}^{\text{o}}]$, using the activities for log $[a_{{\text{Al}}^{3+}}\text{/}{(a_{{\text{H}}^{+}})}^3]$ defined by an arbitrarily chosen value and the approximate saturation limits of pyrophyllite + amorphous silica, kaolinite + amorphous silica, kaolinite + pyrophyllite, pyrophyllite + quartz and gibbsite. The formation of sepiolite-palygorskite from solution is more favored in the presence of amorphous silica than quartz. Lower aqueous aluminum activities favor the non-aluminum phases sepiolite and kerolite relative to the aluminum-containing phases palygorskite and saponite. The stability ranges of worldwide associations of magnesite and dolomite with sepiolite and palygorskite are also illustrated as a function of aluminum activity.

We establish a boundary Schwarz lemma for solutions to nonhomogeneous biharmonic equations.

Solution-processed CuInGaS2 (CIGS) thin-film solar cells are promising for large-scale commercialization due to their economic process although the efficiency still needs to be improved to compete with vacuum-based materials. Systematic studies were performed to optimize the series and shunt resistance of hydrazine-based CIGS solar cells. Optimization was achieved through compositional adjustment of copper (Cu) near the p–n junction and gallium (Ga) near the back contact. Cu adjustments optimized the shunt resistance between 4000 and 5000 Ω cm2. Ga adjustments optimized the series resistance to 2 Ω cm2. Shunt and series resistance play vital roles in the fill factor. Fill factor was hence improved upward of 0.80 with the optimization of Cu and Ga. Chemical etching was also conducted to investigate the durability of the materials and to remove small crystals near the interface. Device conversion efficiencies were improved up to 12.4%. This study provides the implications for improving the device performance of chalcogenide solar cell materials.

Functions are important in designing. However, several issues hinder progress with the understanding and usage of functions: lack of a clear and overarching definition of function, lack of overall justifications for the inevitability of the multiple views of function, and scarcity of systematic attempts to relate these views with one another. To help resolve these, the objectives of this research are to propose a common definition of function that underlies the multiple views in literature and to identify and validate the views of function that are logically justified to be present in designing. Function is defined as a change intended by designers between two scenarios: before and after the introduction of the design. A framework is proposed that comprises the above definition of function and an empirically validated model of designing, extended generate, evaluate, modify, and select of state-change, and an action, part, phenomenon, input, organ, and effect model of causality (Known as GEMS of SAPPhIRE), comprising the views of activity, outcome, requirement–solution–information, and system–environment. The framework is used to identify the logically possible views of function in the context of designing and is validated by comparing these with the views of function in the literature. Describing the different views of function using the proposed framework should enable comparisons and determine relationships among the various views, leading to better understanding and usage of functions in designing.

In this paper, we investigate a semilinear elliptic equation that involves multiple Hardy-type terms and critical Hardy–Sobolev exponents. By the Moser iteration method and analytic techniques, the asymptotic properties of its nontrivial solutions at the singular points are investigated.

We deal with a singular quasilinear elliptic problem, which involves critical Hardy-Sobolev exponents and multiple Hardy terms. Using variational methods and analytic techniques, the existence of ground state solutions to the problem is obtained.