Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

Structure determination of salisomide and salisoflavan,two new secondary metabolites from Salsola imbricata,by 1D and 2D NMR spectroscopy

Chromatographic analysis of the alcoholic extract from Salsola imbricata yielded two new secondary metabolites, salisomide (1) and salisoflavan (2). Their structures were established with the help of spectroscopic techniques including COSY, HMQC and HMBC NMR experiments. Copyright © 2008 John Wiley & Sons, Ltd.     

Solubility of polycyclic aromatics in binary solvent mixtures using activity coefficient models

Polycyclic aromatic hydrocarbons (PAHs) precipitation is one of the major problems in the hydrocracking units. In this investigation, pyrene and phenanthrene were selected because they were found to be in higher concentrations in the feed to hydrocracking units. Their solubilities were investigated in toluene solvent mixture of iso-octane and heptane over a temperature range from 293 to 323 K. The experimental solubility data were used to predict the interaction parameters for seven different solid–liquid equilibrium models. The following activity coefficient models were used; Wilson, NIBS/Redlich–Kister, UNIQUAC, modified UNIFAC, modified UNIFAC (Dortmund), Flory–Huggins and Sheng. The interaction parameters were expressed as a second-order polynomial function in temperature. In order to test the models, the average absolute deviation percentage (AADP) was used. The overall AADP was found to range from approximately 7 to 14%. The models can be arranged according to their accuracy in a descending order based on AADP as follows: NIBS/Redlich–Kister, Wilson, UNIQUAC, Sheng, Flory–Huggins, modified UNIFAC (Dortmund) and finally modified UNIFAC. All models used in this work gave reasonable results; however, the group contribution models can also be used as a predictive tool for the solubility measurement of pyrene and phenanthrene in other solvents containing the same groups of the solvents used in this study.     

Weighted Cebysev-Ostrowski type inequalities

In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.     

π‐Expanded α,β‐Unsaturated Ketones: Synthesis,Optical Properties,and Two‐Photon‐Induced Polymerization

A library of π‐expanded α,β‐unsaturated ketones was designed and synthesized. They were prepared by a combination of Wittig reaction, Sonogashira reaction, and aldol condensation. It was further demonstrated that the double aldol condensation can be performed effectively for highly polarized styrene‐ and diphenylacetylene‐derived aldehydes. The strategic placement of two dialkylamino groups at the periphery of D ‐π‐A‐π‐D molecules resulted in dyes with excellent solubility. These ketones absorb light in the region 400–550 nm. Many of them display strong solvatochromism so that the emission ranges from 530–580 nm in toluene to the near‐IR region in benzonitrile. Ketones based on cyclobutanone as central moieties display very high fluorescence quantum yields in nonpolar solvents, which decrease drastically in polar media. Photophysical studies of these new functional dyes revealed that they possess an enhanced two‐photon absorption cross section when compared with simpler ketone derivatives. Due to strong polarization of the resulting dyes, values of two‐photon absorption cross sections on the level of 200–300 GM at 800 nm were achieved, and thanks to that as well as the presence of the keto group, these new two‐photon initiators display excellent performance so that the operating region is 5–75 mW in some cases.     

Selective and Simultaneous Determination of Dihydroxybenzene Isomers Based on Green Synthesized Gold Nanoparticles Decorated Reduced Graphene Oxide

In the present study, we report the simultaneous electrochemical determination of hydroquinone (HQ), catechol (CC) and resorcinol (RC) at gold nanoparticles (Au‐NPs) decorated reduced graphene oxide (RGO) modified electrode. An enhanced and well defined peak current response with a better peak separation of HQ, CC and RC is observed at RGO/Au‐NPs composite than that of RGO and Au‐NPs modified electrodes. The fabricated modified electrode shows a wide linear response in the concentration range of 3–90 µM, 3–300 µM and 15–150 µM for HQ, CC and RC, respectively. The detection limit of HQ, CC and RC is found as 0.15 µM, 0.12 µM and 0.78 µM, respectively.     

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

Thermal Decomposition Kinetics of Some Di‐ and Triorganotin(IV) Carboxylates Derived from para‐Nitrophenylethanoic Acid

Thermogravimetric (TG) investigations of organotin(IV) carboxylates with the general formula R_mSnL_4−m (where R=CH₃, C₂H₅, n‐C₄H₉, C₆H₅, cyclo‐C₆H₁₁, n‐C₈H₁₇, m=2, 3, and L=para‐nitrophenylethanoate anion) have been performed. Derivative thermogravimetry (DTG) and differential thermal analysis (DTA) techniques, Horowitz‐Metzger method and the fundamental thermodynamic relations are used to evaluate the thermokinetic parameters of each thermal degradation pattern. Results reveal that the thermal stability is functional to Sn C and Sn O bonds. In the case of R₂SnL₂, activation energy, reaction order and pre‐exponential factor associated with the bulk degradation processes increase as the alkane chain length increases. Hence, Oct₂SnL₂ is thermally more stable than Bu₂SnL₂, which in turn is more resistant to thermal dissociation than Et₂SnL₂. The same phenomenon is not observed for R₃SnL compounds because their degradation is highly irregular. Furthermore, R₂SnL₂ has larger values of kinetic parameters than those of corresponding triorganotin(IV) para‐nitrophenylethanotes. Thermodynamic parameters of these compounds also reinforce the above facts.     

Multi-stage mass spectrometric analysis of saponins in glycyrrhiza radix

The fragmentation pathways of six triterpenoid saponins from Glycyrrhiza radix were investigated using LC-MS/MS. Depending on the structure and the substitution pattern, different molecular adduct ions, [M+NH4]+ or [M+H]+, were observed in the positive ESI spectra. In the positive MSn spectra from the molecular adduct ions, characteristic product ions corresponding to the loss of dehydrated glucuronic acid or glucuronic acid were detected and they indicated the type of substitution and structural modification. Fragment ions originating from the sapogenin moiety in the positive mass spectra were predominantly provided by saponins having an 11-oxo-12-ene structure. On the other hand, the saponins gave fragment ions corresponding to the sugar moiety in the negative mass spectra. These results indicate the specific property of saponins that have the 11-oxo-12-ene structure to localize positive or negative charge in the mass spectrometric ionization and fragmentation process. Information obtained from the present study can be utilized for structural elucidation of triterpenoid saponins in the Glycyrrhiza radix by LC-MS.     

On $$\gamma $$ γ - and local $$\gamma $$ γ -vectors of the interval subdivision

Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In...