Estimation of the solubility product of hydrocalumite–hydroxide,a layered double hydroxide with the formula of [Ca2Al(OH)6]OH·nH2O

From aqueous NaOH/Ca(OH)₂/NaAl(OH)₄ mixtures, after allowing short reaction times we observed the precipitation of Ca(OH)₂(s) at lower, and a mixture of Ca(OH)₂(s) and a layered double hydroxide, hydrocalumite (HC) at higher aluminate concentrations. From the maximum aluminate concentration, at which the equilibrium solid phase is still portlandite (i.e., further increase in the aluminate concentration results in HC appearing in the precipitate beside the portlandite), the concentration based solubility products of two polymorphs of HC with the formula of [Ca₂Al(OH)₆]OH·nH₂O (differing in n) has been estimated and was found to be log L_HC=−11.4 at 25 °C and −12.1 at 75 °C, respectively (where L_HC=[Ca²⁺]²[Al(OH)₄⁻][OH⁻]³) and at constant ionic strength (I=1 M NaCl). To the best of our knowledge, this is the first published estimate for the solubility product of hydrocalumite. Additionally, from the composition obtained for NaOH/Ca(OH)₂/NaAl(OH)₄ mother liquors in equilibrium with Ca(OH)₂(s), attempts were made to extract the formation constant of the ion pair CaAl(OH)₄⁺. It was found, that the effects caused by the supposed formation of this solution species are too small to be reliably determined, which allowed an upper estimate for its formation constant, K, to be suggested in the temperature range of 25–75 °C (K<200 and 40 M⁻¹ at 25 and 75 °C, respectively).     

Ion Product of Pure Water Characterized by Physics-Based Water Model

Pure water has been characterized for nearly a century, by its dissociation into hydronium (H₃O)¹⁺ and hydroxide (HO)^1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product or the product of the equilibrium concentration of the two ion species, has been extensively measured by chemists over the liquid water temper-ature and pressure range. The experimental data have been nonlinear least-squares fitted to chemical thermodynamic-based equilibrium equations, which have been accepted as the industrial standard for 35 years. In this study, a new and statistical-physics-based water ion product equation is presented, in which, the ions are the positively charged protons and the negatively charged proton-holes or prohols. Nonlinear least squares fits of our equation to the experimental data in the 0-100 ℃ pure liquid water range, give a factor of two better precision than the 35-year industrial standard.     

Application of Prins cyclization to the total synthesis of (+)-decytospolides A and B

(+)-Decytospolides A and B, natural products containing the tetrahydropyran skeleton, were synthesized via Prins cyclization as the key step.     

Functions averages over the roots of unity,cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.     

Semi-concurrent vector fields in Finsler geometry

In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold $(M,F)$, admitting a non-constant smooth function f on M such that $\frac{\partial f}{\partial x^i}\frac{\partial g^{ij}}{\partial y^k}=0$?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented.     

The impact of environmental regulations on forest product trade in China

Forest product trade plays an important role in the development of the Chinese forest industry. The trading value of forest product has shown a yearly growth rate of 12% during the last five recent years. Stringent environmental regulations in China have a profound impact on raw material supplies and industrial production in the forest sector; however, their impact on the forest product trade is still unclear. This study applies fixed and random effects models as well as a seemingly unrelated regression model to investigate the impact of environmental regulations on the trade of forest product from 2002 to 2015. The results indicate that the stringent environmental regulations promoted the import but restricted the export of forest product in general. Specifically, the stringent environmental regulations stimulated the import but had an ambiguous impact on the export of the paper product. The stringent environmental regulations had also stimulated the import of wood product but inhibited the export. In contrast, wooden furniture had been affected minimally; only export got slightly negatively affected by environmental regulations. Recommendations for resource managers:

• Trade‐offs between economic growth and environmental regulations are needed to smoothly promote the forest product trade in China.
• Paper and wooden furniture product sectors are less likely to be affected by stringent environmental regulations, because high value‐added products could compensate for environmental costs.
• The wood product sector is more likely to be negatively affected by stringent environmental regulations because environmental costs could severely impact the competitiveness of low value‐added products.

     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

Operators on Soft Inner Product Spaces

In the present paper, self-adjoint operator and completely continuous operator on soft inner product spaces have been introduced and some basic properties of such operators are studied.