On the Statistical Discrepancy and Affinity of Priority Vector Heuristics in Pairwise-Comparison-Based Methods

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (w_ij), w_ij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities.     

From Colloidal Dispersions of Zeolite Monolayers to Effective Solid Catalysts in Transformations of Bulky Organic Molecules: Role of Freeze-Drying and Dialysis

We investigated the properties and catalytic activity of zeolites with MWW topology obtained by unprecedented liquid exfoliation of the MCM-56 zeolite into solutions of monolayers and isolation/reassembly of the dispersed layers by various methods, with optional purification by dialysis or ammonium exchange. The layers were recovered by flocculation with alcohol or ammonium nitrate and freeze-drying. Flocculation alone, even with ammonium nitrate, did not ensure removal of residual sodium cations resulting in catalysts with low activity. Dialysis of the solutions with dispersed monolayers proved to be efficient in removing sodium cations and preserving microporosity. The monolayers were also isolated as solids by freeze-drying. The highest BET area and pore volume obtained with the freeze-dried sample confirmed lyophilization efficiency in preserving layer structure. The applied test reaction, Friedel–Crafts alkylation of mesitylene, showed high benzyl alcohol conversion due to increased concentration of accessible acid centers caused by the presence of secondary mesoporosity. The applied treatments did not change the acid strength of the external acid sites, which are the most important ones for converting bulky organic molecules. Zeolite acidity was not degraded in the course of exfoliation into monolayers, showing the potential of such colloid dispersions for the formation of active catalysts.     

Inductive charge dispersal in the solvolysis of 2-exo- and 2-endo-norbornyl toluenesulfonates.

The effect of substituents at C4, 5, 6 and 7 on solvolysis rates and products of 2-exo- and 2-endo-norbornyl tosylates confirms that differential carbon participation is responsible for varying exo/endo rate and product ratios.     

Crystal and molecular structure of phenylbenzyl-1-(2,2,3-trimethylcyclopropyl)phosphine oxide

The title compound crystallizes in the orthorhombic space groupPna2₁, witha=15.576(2),b=19.134(3),c=5.693(1) Å andz=4. The structure was solved by direct methods, and refined to a finalR value of 0.059. This study confirms both the structure and stereochemistry of the title compound.     

Hidden symmetry and correlated states of electrons and holes in quantum dots

We describe hidden symmetry and its application to the construction of exact correlated states of electrons and holes in quantum dots. The hidden symmetry is related to degenerate single particle energy shells and symmetric interactions. Both can be engineered in a quantum dot. We focus on hidden symmetry involving spin singlet pairing of electrons and spin singlet pairing of holes. Detailed calculations for a third shell are presented to illustrate the mechanism of pairing.     

A note on the asymptotic expansion of Feynman amplitudes

Employing the technique given by Bergere and Lam, we determine the asymptotic expansion of Feynman amplitude (in the Schwinger integral representation) when the masses of any subset of internal lines tend to zero.     

Surface morphology of polyethylene glycol films produced by matrix-assisted pulsed laser evaporation (MAPLE): Dependence on substrate temperature

The dependence of the surface morphology on the substrate temperature during film deposition was investigated for polyethylene glycol (PEG) films by matrix-assisted pulsed laser evaporation (MAPLE). The surface structure was studied with a combined technique of optical imaging and AFM measurements. There was a clear difference between the films produced below and above the melting point of PEG. For temperatures above the melting point, the polymer material was distributed non-uniformly over the substrate with growths areas, where cluster-like structures merge into large islands of micrometer size. At these temperatures, the islands in the investigated growth areas cover most of the bottom layer which has a typical height of 50-150 nm.     

Complexation of lanthanide nitrates

Summary The change of the stability constantsK ⁰ ₁ of the lanthanide nitrato complexes in the lanthanide series is presented and discussed from the viewpoint of the interaction between the first and second hydration sheath of lanthanide ions.

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Komplexierung bei Lanthaniden-Nitraten

Zusammenfassung Es wird der Verlauf der StabilitätskonstantenK ⁰ ₁ von Nitrato-Komplexen in der Lanthanidenreihe vorgestellt und auf Basis von Wechselwirkungen zwischen der ersten und zweiten Hydrat-Schicht der Lanthaniden-Ionen diskutiert.