Radical Cyclization/ipso‐1,4‐Aryl Migration Cascade: Asymmetric Synthesis of 3,3‐Difluoro‐2‐propanoylbicyclo[3.3.0]octanes

A novel method for the asymmetric synthesis of 3,3‐difluoro‐2‐propanoylbicyclo‐[3.3.0]octanes involves an unprecedented intramolecular radical cyclization/ipso‐1,4‐aryl migration cascade.     

A hybrid projective method for solving system of equilibrium problems with demicontractive mappings applicable in image restoration problems

In this paper, we propose a general iterative scheme based on CQ projection method for finding a common solution of system of equilibrium problems and the fixed point set of a finite family of demicontractive mappings. We also prove strong convergence of the scheme to a common element of the two above-described sets. We then give a numerical example to justify our main result. An example is given in an infinite dimensional space for supporting our main result. Moreover, we apply our main result to solve the unconstrained image restoration problems with a finite family of blurring operators. Our results extend and improve some existing results in the literature.     

An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces

This work is concerned with the strong convergence of an approximating common fixed point sequence of a finite family of multi-valued mappings in a uniformly convex and smooth Banach space using an implicit iteration scheme introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].     

An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces

In this work, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. For solving this problem, we propose an inertial forward–backward splitting algorithm involving an extrapolation factor. We then prove its strong convergence under some mild conditions. Finally, we provide some applications including the numerical experiments for supporting our main theorem.     

Solidification of floating organic droplet microextraction for determination of seven insecticides in fruit juice,vegetables and agricultural runoff using gas chromatography with flame ionization and mass spectrometry detection

Liquid microextraction employing solidification of the floating organic droplet, with vortexing and heating to optimize extraction efficiency, was developed for the determination of seven insecticides in fruit juice, vegetables, and agricultural runoff water. The extracts were analyzed by gas chromatography with both flame ionization and mass spectrometry detection for the determination of chlorpyrifos, prothiofos, profenofos, ethion, λ‐cyhalothrin, permethrin, and cypermethrin, respectively. Using 20 μL of 1‐undecanol in 10 mL of aqueous solution containing 1% w/v sodium chloride provided preconcentration factor of 500. The enrichment factor of the analytes was in the range of 355 to 509 with extraction recovery >71%. The linearity ranges were 4–200 μg/kg for gas chromatography with flame ionization detection and 1–100 μg/kg for gas chromatography with mass spectrometry, with limits of detection ranging from 0.04 to 1.2 μg/kg, which are lower than the international maximum residue limits for vegetables and fruit juice. Intra‐day and inter‐day precisions are less than 5.4 and 7.0% relative standard deviation, respectively. The method was successfully applied to the determination of the seven insecticides in samples of vegetables, fruit juice and agricultural runoff, with recoveries ranging from 61.7 to 120.8%. The extraction method is simple, efficient and environmentally friendly.     

Existence and Convergence Theorems for Global Minimization of Best Proximity Points in Hilbert Spaces

In order to solve global minimization problems involving best proximity points, we introduce general Mann algorithm for nonself nonexpansive mappings and then prove weak and strong convergence of the proposed algorithm under some suitable conditions in real Hilbert spaces. Furthermore, we also provide numerical experiment to illustrate the convergence behavior of our proposed algorithm.

     

Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings

In this paper, we prove a weak convergence theorem for the modified Mann iteration process for a uniformly Lipschitzian and asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two new kinds of monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and asymptotically quasi-nonexpansive mappings in a Hilbert space. The results of this paper improve on and extend corresponding ones announced by many authors.     

A modified forward-backward splitting methods for the sum of two monotone operators with applications to breast cancer prediction

This work proposes a modified forward-backward splitting algorithm combining an inertial technique for solving the monotone variational inclusion problem. The weak convergence theorem is established under some suitable conditions in Hilbert space, and a new step size is presented for our algorithm to speed up the convergence. We give an example and numerical results for supporting our main theorem in infinite dimensional spaces. We also provide an application to predict breast cancer by using our proposed algorithm for updating the optimal weight in machine learning. Moreover, we use the Wisconsin original breast cancer data set as a training set to show efficiency comparing with the other three algorithms in terms of three key parameters, namely, accuracy, recall, and precision.