On Approximate Additive–Quartic and Quadratic–Cubic Functional Equations in Two Variables on Abelian Groups

We establish the generalized Hyers–Ulam stability of the additive–quartic and quadratic–cubic mappings with two variables on abelian groups.     

Room‐Temperature Electronic Template Effect of the SmSi(111)‐8×2 Interface for Self‐Alignment of Organic Molecules

This work describes an innovative concept for the development of organized molecular systems based on the template effect of the pre‐structured semi‐conductive SmSi(111) interface. This substrate is selected because Sm deposition in the submonolayer range leads to a 8×2‐reconstruction, which is a well‐defined one‐dimensional semi‐metallic structure. Adsorption of aromatic molecules [1,4‐di‐(9‐ethynyltriptycenyl)‐benzene] on SmSi(111)‐ 8×2 and Si(111)‐7×7 interfaces is investigated by scanning tunneling microscopy (STM) at room temperature. Density functional theory (DFT) and semi‐empirical (ASED+) calculations define the nature of the molecular adsorption sites of the target molecule on SmSi as well as their self‐alignment on this interface. Experimental data and theoretical results are in good agreement.     

An algorithmic approach to the construction of homomorphisms induced by maps in homology

This paper is devoted to giving the theoretical background for an algorithm for computing homomorphisms induced by maps in homology. The principal idea is to insert the graph of a given continuous map into a graph of a multi-valued representable map . The multi-valued representable maps have well developed continuity properties and admit a finite coding that permits treating them by combinatorial methods. We provide the construction of the homomorphism induced by such that . The presented construction does not require subsequent barycentric subdivisions and simplicial approximations of . The main motivation for this paper comes from the project of computing the Conley Index for discrete dynamical systems.

     

Progress and prospect of anodic oxidation for the remediation of perfluoroalkyl and polyfluoroalkyl substances in water and wastewater using diamond electrodes

Although diamond electrodes are widely used in the field of electroanalysis and sensing, their application in the field of environmental engineering has yet to be fully realized. Many research studies have considered their potential application in water and wastewater treatment, where the in-situ electrochemical process can avoid the need for chemical additives by facilitating the oxidation of pollutants on the electrode surface or mediated by electrochemically synthesized oxidants in solution. Diamond-based electro-oxidation can effectively treat a number of organic micropollutants and is now being evaluated for the abatement of perfluoroalkyl and polyfluoroalkyl substances, which pose health concerns and are ubiquitous recalcitrant environmental contaminants. To move implementation of diamond-based electro-oxidation forward, the integration of modifications and codopants to yield more advanced electrode materials needs to be further developed and understood. The progress and current strategies associated with diamond electrode modifications for perfluoroalkyl and polyfluoroalkyl substances abatement as well as future considerations are discussed.     

The optimal sequential information acquisition structure: A rational utility-maximizing perspective

We consider a rational utility maximizer decision maker (DM) who must gather two pieces of information from a set of multidimensional products before making a choice. We analyze the resulting sequential information acquisition process where the DM tries to find the best possible product subject to his information acquisition constraint. In addition, we introduce publicly observable signals that allow the DM to update his expected utility functions following a standard Bayesian learning rule. Even though it seems intuitively plausible to assume that the transmission of positive and credible information may lead DMs to accept any product signaled more eagerly, this paper illustrates how transmitting credible positive information is not sufficient to decrease the rejection probability faced by the information sender on its set of products. A significant difference in product rejection probabilities arises depending on the characteristic on which signals are issued, as will be illustrated numerically for both risk-neutral and risk-averse DMs.     

A new chance-constrained DEA model with birandom input and output data

The purpose of conventional Data Envelopment Analysis (DEA) is to evaluate the performance of a set of firms or Decision-Making Units using deterministic input and output data. However, the input and output data in the real-life performance evaluation problems are often stochastic. The stochastic input and output data in DEA can be represented with random variables. Several methods have been proposed to deal with the random input and output data in DEA. In this paper, we propose a new chance-constrained DEA model with birandom input and output data. A super-efficiency model with birandom constraints is formulated and a non-linear deterministic equivalent model is obtained to solve the super-efficiency model. The non-linear model is converted into a model with quadratic constraints to solve the non-linear deterministic model. Furthermore, a sensitivity analysis is performed to assess the robustness of the proposed super-efficiency model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed chance-constrained DEA model and sensitivity analysis.     

Determination of the optimum conditions for the synthesis of praseodymium(III) chloride

In the present work, we have synthesized praseodymium(III) chloride, PrCl₃, from the praseodymium oxide, Pr₆O₁₁, by dry method in the presence of ammonium chloride, NH₄Cl. This study includes the establishment of an assembly synthesis under inert gas. The thermal decomposing process of pure NH₄Cl was investigated by TG–DTG. The results showed that NH₄Cl begins to lose weight at 188 °C, large loss of weight ending at 302 °C when NH₄Cl is heated at the rate of 10 °C/min under N₂ atmosphere. For chlorination, NH₄Cl participates directly in the reaction, and HCl decomposed from NH₄Cl also contributes to the chlorination reaction. The influence of various synthesis parameters (temperature, contact time and chemical composition) on the reaction yield was studied, and the optimum conditions for synthesis were, thus, determined and discussed.     

Novel Collimated Beam Setup to Study the Kinetics of VUV‐Induced Reactions

Vacuum UV (VUV) process is an incipient advanced oxidation process, which can be used for water treatment. This process relies on the formation of hydroxyl radicals through the VUV‐induced photolysis of water. In particular, the use of ozone‐generating mercury vapor lamps, which emit 10% of the radiation at 185 nm and 90% at 254 nm, is showing very promising results for the degradation of micropollutants. The kinetics of VUV process has been studied in batch‐ and flow‐through reactors, but the effect of 254 and 185 nm photons cannot be isolated, mass transfer resistances can take place and the interpretation of the results is complex. In this technical note, a new VUV collimated beam to conduct kinetic tests is presented, which offers several advantages: (1) it allows the irradiation of samples with 185, 254 nm photons, or both, (2) the concentration of reagents is uniform in the reaction volume and (3) it allows to change the fluence rate by changing the distance between the lamp and the photoreactor. Details of the geometry are presented, as well as an analysis of the collimation and uniformity of the radiation of the new VUV‐collimated beam setup.