Soft set theory based on its extension

In this paper, we point out a defect that the definitions of soft subset and soft intersection in Maji’s paper are partial definitions, and then we introduce extension of soft set to redefine and simplify operations between soft sets. At last, we obtain some algebraic properties of new soft operations.     

Leibniz algebras graded by finite root systems of type C l

We study Leibniz algebras graded by finite root systems of type C _l .     

An improved Pfitzinger reaction: Eco-efficient synthesis of quinaldine-4-carboxylates by TMSCl-mediated

We report herein an improved Pfitzinger reaction for the synthesis of highly functionalized quinaldines from 1,3-dicarbonyl compounds, isatins and alcohols mediated by TMSCl. This synthesis involves cyclization and esterification in one-step cascade process for the formation of a carboxylate (CO₂R) at the 4-position of quinaldine ring. Moreover, this procedure shows highly efficient, good functional group tolerance, operational simplicity, environment-friendly and feasibility of scale up.     

Studies on pharmacokinetics,body distribution,plasma protein binding rate,and excretion of 1-methyl hydantoin in rats in vivo

In this paper, plasma concentration, plasma protein binding rate, body distribution, and excretion of both oral and intravenous administration of rats were determined by high performance liquid chromatography (HPLC) combining with UV detector. The blood drug concentration of oral and intravenous administration was summarized. The bioavailability of T_1/2 was approximately 0.75?hr. At the meanwhile, the bioavailability was about 18.84?±?2.21%. The plasma protein binding rate of 1-methyl hydantoin was about 24.36?±?0.93%, belonging to low protein binding drug. The result shows that 1-methyl hydantoin can be rapidly distributed in various organs and tissues and quickly eliminated within 6?hr without accumulation in the organs. Its discharge from the urine and feces was 16.58?±?4.48% and 3.37?±?0.71%, respectively. All of the results showed that the recovery rate, liner relationship, specificity, stability, and precision of the method were good. The study also proved that 1-methyl hydantoin has been eliminated quite faster in rats.     

A “Mitsubishi emblem” tetrauclear aluminum complex containing two unsymmetric N2O2‐ligands and a symmetric NO3‐ligand as initiator for polymerization of rac‐lactide

A novel hydroxy‐, methoxy‐, and phenoxy‐bridge “Mitsubishi emblem” tetranuclear aluminum complex ( 1 ) is synthesized from an unsymmetric amine‐pyridine‐bis(phenol) N₂O₂‐ligand (H₂L¹) and a symmetric amine‐tris(phenol) NO₃‐ligand (H₂L²). Two same configuration chiral nitrogen atoms are formed in the tetranuclear Al complex upon coordination of the unsymmetric tertiary amine ligand to central Al. Complex 1 initiates controlled ring‐opening polymerization (ROP) of rac‐lactide and afford polylactide (PLA) with narrow molecular weight distributions (M_w/M_n = 1.05–1.19). The analysis of ¹H NMR spectra of the oligomer indicates that the methoxy group is the initiating group and the ring‐opening polymerization of lactide follows a coordination‐insertion mechanism. The Homonuclear decoupled ¹H NMR spectroscopy suggests the isotactic‐rich chains is preferentially formed in PLA. The study on kinetics of the ROP of lactide reveals the homopropagation rate is higher than the cross‐propagation rate, which is in agreement with the observed isotactic selectivity in the ROP of rac‐lactide. The stereochemistry of the polymerization was also supported by activation parameters. The introduction of unsymmetric ligand H₂L¹ has an effect on stereoslectivity of polymerization. This result may be of interest for the design of multinuclear metal complex catalysts containing functionalized ligands. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2084–2091     

Authors’ response to the rebuttal by A. Cushman

This is a response to the rebuttal by A. Cushman regarding our paper “Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness” (Nonlinear Dyn. doi:, 2011).     

Pricing Derivatives under a Markov Skeleton Process

In this paper, it is assumed that the underlying is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with fast Fourier transform (FFT) method, the pricing formula of derivatives under the Markov skeleton process is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives.