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).     

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.     

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.     

我国渔业企业经济效益分析研究——以2013年我国上市渔业公司数据为例

随着居民收入水平的提高,我国水产品消费数量不断增加.水产品消费需求的增加,一方面导致水产品养殖企业数量增多,水产品养殖产业初具规模;另一方面也导致了市场竞争压力的增大,使得水产品养殖企业经济效益降低.利用2013年我国上市渔业公司财务数据,基于因子分析法研究了我国上市渔业公司经济效益水平.研究结果显示,2013年大湖股份、国联水产各公共因子及综合因子得分都较高,表明其公司盈利能力、偿债能力及运营能力较强,企业后期发展前景较好.而好当家、武昌鱼的综合因子得分较低,需要引起公司重视.最后针对2013年我国上市渔业公司的整体得分情况,提出了提高我国渔业企业经济效益水平的建议.     

Properties of mono-weakly hyponormal 2-variable weighted shifts

In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers.     

Further results on the Drazin inverse of even‐order tensors

The notion of the Drazin inverse of an even‐order tensors with the Einstein product was introduced, very recently [J. Ji and Y. Wei. Comput. Math. Appl., 75(9), (2018), pp. 3402‐3413]. In this article, we further elaborate this theory by establishing a few characterizations of the Drazin inverse and $\mathrm{??}$‐weighted Drazin inverse of tensors. In addition to these, we compute the Drazin inverse of tensors using different types of generalized inverses and full rank decomposition of tensors. We also address the solution of multilinear systems by using the Drazin inverse and iterative (higher order Gauss‐Seidel) method of tensors. Besides these, the convergence analysis of the iterative technique is also investigated within the framework of the Einstein product.     

Lie-trotter product formulas for nonlinear filtering

The nonlinear filtering problem for a diffusion process whose drift and diffusion coefficients depend parametrically on a finite-state jump process involves the solution of a vector system of linear, stochastic partial differential equations. A Lie-Trotter product formula is proven to hold for this system and a recursive implementation is discussed.