Constructing and evaluating alternative frames of discernment

We construct alternative frames of discernment from input belief functions. We assume that the core of each belief function is a subset of a so far unconstructed frame of discernment. The alternative frames are constructed as different cross products of unions of different cores. With the frames constructed the belief functions are combined for each alternative frame. The appropriateness of each frame is evaluated in two ways: (i) we measure the aggregated uncertainty (an entropy measure) of the combined belief functions for that frame to find if the belief functions are interacting in interesting ways, (ii) we measure the conflict in Dempster’s rule when combining the belief functions to make sure they do not exhibit too much internal conflict. A small frame typically yields a small aggregated uncertainty but a large conflict, and vice versa. The most appropriate frame of discernment is that which minimizes a probabilistic sum of the conflict and a normalized aggregated uncertainty of all combined belief functions for that frame of discernment.     

Formation of tryptanthrin compounds upon Oxone-induced dimerization of indole-3-carbaldehydes

Tryptanthrin is a natural product with numerous important pharmacological properties. Tryptanthrin and its analogs are commonly prepared by condensation of isatoic anhydride and isatin. In this Letter we investigate the formation of tryptanthrin derivatives upon Oxone-induced oxidative dimerization of indole-3-carbaldehydes.     

Fluorescence Signal Enhancement Using Double Pass Cell Configurations

Abstract

A simple and reproducible method for increasing the sensitivity of fluorescence measurements by a factor of 2.0–2.5 is presented. Data are presented to explain: the deviation from the expected theoretical increase in sensitivity of 4.0; wavelength dependency and subsequent problems arising from enhanced inner filtering effects.     

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.