The generalization of Meyer-König and Zeller operators by generating functions

In this paper, theorems are proved concerned with some approximation properties of generating functions type Meyer-König and Zeller operators with the help of a Korovkin type theorem. Secondly, we compute the rates of convergence of these operators by means of the modulus of continuity, Peetre's K-functional and the elements of the modified Lipschitz class. Also we introduce the rth order generalization of these operators and we obtain approximation properties of them. In the last part, we give some applications to the differential equations.     

Synchronization of the unified chaotic systems via active control

This paper investigates the synchronization of coupled unified chaotic systems via active control. The synchronization is given in the slave–master scheme and the controller ensures that the states of the controlled chaotic slave system exponentially synchronize with the state of the master system. Numerical simulations are provided for illustration and verification of the proposed method.     

An SQP method for optimal control of weakly singular Hammerstein integral equations

We investigate local convergence of an SQP method for nonlinear optimal control of weakly singular Hammerstein integral equations. Sufficient conditions for local quadratic convergence of the method are discussed.     

Fabrication of three-component composition spread thin film with controlled composition and thickness

A novel method for the fabrication of three-component composition spread thin films was developed and used for the combinatorial exploration of materials. The composition and the thickness of the films could be precisely controlled during deposition. Any desired part of a complete ternary diagram could be deposited onto a single substrate by sequentially ablating target materials using a pulsed laser. Atomic mixing among compositions is achieved by adjusting the amount of target material deposited in each deposition step. The system could be especially useful in the search for new functional multi-component ultra-thin film materials, such as gate dielectrics. PACS 81.15.Fg; 81.30.Bx; 81.05.Je; 77.84.Bw     

Integrable Equations of the Form q t =L 1(x,t,q,q x,q xx )q xxx +L 2(x,t,q,q x,q xx )

Integrable equations of the form q _t =L ₁(x,t,q,q _x ,q _xx )q _xxx +L ₂(x,t,q,q _x ,q _xx ) are considered using linearization. A new type of integrable equations which are the generalization of the integrable equations of Fokas and Ibragimov and Shabat are given.     

A new enhancement of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem

In this work we are concerned with the Clarke–Wright savings method for the classical capacitated vehicle routing problem. This is an NP-hard problem and numerous heuristic solution methods have been proposed. They can be classified as the classical ones and metaheuristics. Recent developments have shown that classical heuristics do not compare with the best metaheuristic implementations. However, some of them are very fast and simple to implement. This explains the popularity of the Clarke–Wright savings method in practice and the motivation behind its enhancements. We follow this line of research and propose a new enhancement which differs from the previous ones in its saving criterion: Customer demands are considered in addition to distances. Based on the extensive computational experiments we can say that the new method is not only very fast but also very accurate.     

Synthesis and in vitro antioxidant evaluation of new bis(α-aminoalkyl)phosphinic acid derivatives

Diamines were added to arylaldehydes in ethanol, which resulted in corresponding diimines. Novel bis-1-aminophosphinic acid compounds were synthesized through the interaction of diimines and hypophosphorous acid. The new compounds were characterized by elemental analyses, FT-IR and ¹H, ¹³C and ³¹P NMR techniques. The in vitro antioxidant activity of the newly synthesized compounds were measured and found to exhibit significantly higher antioxidant activity than the standard.     

Fast determination of anthocyanins and free pelargonidin in fruits,fruit juices,and fruit wines by high‐performance liquid chromatography using a core–shell column

Anthocyanins are water‐soluble pigments that are liable for colors ranging from red to blue of most fruits, vegetables, and flowers. A novel and fast method was developed for the determination of five anthocyanins and free pelargonidin by high‐performance liquid chromatography coupled to photodiode array detection. A 10% formic acid and acetonitrile mixture was employed as mobile phase in the gradient elution mode. Mobile phase composition, column temperature, flow rate, injection volume, and column conditioning time were optimized by employing a stepwise strategy. Using a C₁₈ core–shell column (100 × 4.6 mm, 2.7 μm), the separation of six analytes was accomplished in less than 9.5 min with a run‐to‐run analysis time of 19 min. The developed method was validated with respect to linearity (r > 0.9999), limit of detection, limit of quantification, intra‐/interday precision (<2%), accuracy (98.6–104.4%), and specificity. Afterwards, the method was applied to the determination of anthocyanins present in 15 different samples including fruits, fruit juices, and fruit wines.     

Poly(p‐phenylene) with Poly(ethylene glycol) Chains and Amino Groups as a Functional Platform for Controlled Drug Release and Radiotherapy

Conventional cancer treatments such as chemotherapy, radiotherapy, or combination of these two result in side effects, which lower the quality of life of the patients. To overcome problems with these methods, altering the drug properties by conjugating them to carrier polymers has emerged. Such polymeric carriers also hold the potential to make tumor cells more sensitive to radiation therapy. Herein, poly(p‐phenylene) (PPP) polymer with poly(ethylene glycol) (PEG) chains and primary amino groups (PPP‐NH₂‐g‐PEG) is synthesized and conjugated with anticancer drug Doxorubicin (DOX). pH dependent drug release experiments are performed at pH 5.3 and pH 7.4, respectively. Cell viability studies on human cervix adenocarcinoma cells show that lower doses of DOX inhibit cell proliferation when conjugated with nontoxic doses of PPP‐NH₂‐g‐PEG polymer. Additionally, PPP‐NH₂‐g‐PEG/Cys/DOX bioconjugate significantly increases radiosensitive properties of DOX. It is possible to use lower doses of DOX when conjugated to PPP‐NH₂‐g‐PEG in combination with radiotherapy.