Common fixed point results for new Ciric-type rational multivalued <Emphasis Type="Italic">F</Emphasis>-contraction with an application

In this article, common fixed point theorems for a pair of multivalued mappings satisfying a new Ciric-type rational F-contraction condition in complete dislocated metric spaces are established. An example is constructed to illustrate our results. An application to the system of integral equations is presented to support the usability of proved results. Our results combine, extend and infer several comparable results in the existing literature.     

Separation of no-carrier-added radioactive scandium from neutron irradiated titanium

In this work, sorption of Ni(II) from aqueous solution to goethite as a function of various water quality parameters and temperature was investigated. The results indicated that the pseudo-second-order rate equation fitted the kinetic sorption well. The sorption of Ni(II) to goethite was strongly dependent on pH and ionic strength. A positive effect of HA/FA on Ni(II) sorption was found at pH < 8.0, whereas a negative effect was observed at pH > 8.0. The Langmuir, Freundlich, and D-R models were applied to simulate the sorption isotherms at three different temperatures of 293.15 K, 313.15 K and 333.15 K. The thermodynamic parameters (ΔH ⁰, ΔS ⁰ and ΔG ⁰) were calculated from the temperature dependent sorption, and the results indicated that the sorption was endothermic and spontaneous. At low pH, the sorption of Ni(II) was dominated by outer-sphere surface complexation or ion exchange with Na⁺/H⁺ on goethite surfaces, whereas inner-sphere surface complexation was the main sorption mechanism at high pH.     

One-pot synthesis of α,β-epoxy ketones by palladium-catalyzed epoxidation-oxidation of terminal allylic alcohols

Described herein is a one-pot synthesis of α,β-epoxy ketones using a palladium-catalyzed epoxidation-oxidation sequence. Functionalized terminal allylic alcohols are treated with m-CPBA under mild reaction conditions to obtain the α,β-epoxy ketones. The main benefit of this approach is that the epoxidation of the terminal double bond and the oxidation of the secondary alcohol occured in the same reaction under mild reactions and both electron-donating and electron-withdrawing functionalities are tolerated in the reaction sequence.     

Viscosity Results for a Class of Evolution Inclusions with Maximal Monotone Operators

In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton–Jacobi–Bellman equations related to control problems subject to evolution inclusions governed by time-dependent maximal monotone operators with Young measures.     

Synthesis and properties ofN-substituted azacalix[n]arenes

Side arm modifications of hexahomotriazacalix[3]arene (1) were achieved by simple synthetic methods. Compound5 has picolyl side arms and liquid-liquid extraction experiments showed that the alkali cation affinity of5 is much stronger than that of1. A chiral group was also introduced into the azacalixarene structure. Calix[4]arene was converted into dihomoazacalix[4]arene (2) in 8% yield. Clathrate formation of2 with various solvents is described. MM3 calculations were carried out onp-substituted analogs of2. The self-filled structure, in which the benzyl side arm is placed in its cavity, is the most stable structure when thep-positions of the aromatic rings carry small substituents. Strong hydrogen bonds between nitrogen and phenolic hydroxyl groups in dihomoazacalix[4]arene (2) were observed at low temperatures. The¹H-NMR signals of phenolic hydroxyl groups appeared as six singlets in the range of 9.817.1 ppm at –70°C.This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

First natural urease inhibitor from Euphorbia decipiens

Three new diterpene esters with a myrsinol-type skeleton have been isolated from Euphorbia decipiens BOISS. & BUHSE. The structure elucidation of the isolated compounds was based primarily on two-dimensional (2D)-NMR techniques including correlation spectroscopy (COSY), heteronuclear multiple quantum coherence (HMQC), heteronuclear multiple bond correlation (HMBC) and nuclear Overhauser effect spectroscopy (NOESY) experiments. Compounds 1 and 3 are active against prolyl endopeptidase and compound 2 showed inhibitory activity against urease enzyme.     

Conformational structure of peptides containing dehydroalanine: Formation of β‐bend ribbon structure

α,β‐Unsaturated amino acids (dehydroamino acids) have been found in naturally occurring antibiotics of microbial origin and in some proteins. Due to the presence of the C_αC_β double bond, the dehydroamino acids influence the main‐chain and the side‐chain conformations. The lowest‐energy conformational state of the model tripeptides, Ac–X–ΔAla–NHMe, (X=Ala, Val, Leu, Abu, or Phe) corresponds to ϕ₁=−30°, ψ₁=120° and ϕ₂=ψ₂=30°. This structure is stabilized by the hydrogen bond between CO of the acetyl group and the NH of the amide group, resulting in the formation of a 10‐membered ring. In the model heptapeptide containing ΔAla at alternate position with Ala, Abu, and Leu, the lowest‐energy conformation corresponds to ϕ=−30° and ψ=120° for all the Ala, Abu, and Leu residues and ϕ=ψ=30° for all ΔAla residues. A graphical view of the molecule in this conformation reveals the formation of three hydrogen bonds involving the CO moiety of the ith residue and the NH moiety of the i+3th residue, resulting in a 10‐membered ring formation. In this structure, only alternate peptide bonds are involved in the intramolecular hydrogen‐bond formation unlike the helices and it has been named the β‐bend ribbon structure. The helical structures were predicted to be the most stable structures in the heptapeptide Ac–(Aib–ΔAla)₃–NHMe with ϕ=±30°, ψ=±60° for Aib residues and ϕ=ψ=±30° for ΔAla residues. The computational results reveal that the ΔAla residue does not induce an inverse γ‐turn in the preceding residue. It is the competitive interaction of small solvent molecules with the hydrogen‐bonding sites of the peptide which gives rise to the formation of an inverse γ‐turn (ϕ₁=−54°, ψ₁=82°; ϕ₂=44°, ψ₂=3°) in the preceding residue to ΔAla. The computational studies for the positional preference of ΔAla in the peptide containing one ΔAla and nine Ala residues reveals the formation of a 3₁₀ helical structure in all the cases with the terminal preferences for ΔAla, consistent with the position of ΔAla in the natural antibiotics. The extended structures is found to be the most stable for poly‐ΔAla. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 15–23, 1999     

Asymptotic Normality of a Combined Regression Estimator

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.