Voronovskaya Type Theorems in Weighted Spaces

In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity.     

RNA-sensitive N-isopropylacrylamide/vinylphenylboronic acid random copolymer

Random copolymers of N-isopropylacrylamide (NIPA) and 4-vinylphenylboronic acid (VPBA) were obtained by solution polymerization using 2,2′-azobisizobutyronitrile as the initiator in ethanol at 65 °C. NIPA-co-VPBA copolymer exhibited both temperature- and pH-sensitivity. Thermally reversible phase transitions were observed both in the acidic and alkaline pH region for the copolymers produced with different VPBA/NIPA feed ratios. The pH dependency of the lower critical solution temperature (LCST) was stronger for the copolymers produced with higher VPBA feed concentrations. RNA was selected as a model biomolecule having vicinal-diol and amino groups that were potentially reactive with the boronic acid groups of NIPA-co-VPBA copolymer. The effect of RNA concentration on the LCST of NIPA-co-VPBA copolymer was investigated in aqueous media at different pHs. Although no significant effect was observed at pH 4, 7 or 10.5, the LCST decreased linearly with increasing RNA concentration at a pH approximately equal to the pK_a of boronic acid. This behavior was explained by considering the binding of RNA onto the copolymer chains to occur via two types of complex formation. For the formation of these complexes, the amino and vicinal-diol groups of RNA should react with the boronic acid groups of the copolymer in the tetrahedral anionic form. The results indicated that NIPA-co-VPBA copolymer could be utilized as a new reagent for the determination of RNA concentration in aqueous media. The proposed method was valid for the RNA concentration range of 0–4 g · mL⁻¹.

The schematical representation of the possible interactions between NIPA-co-VPBA copolymer and RNA. (A) A typical structure of single-stranded RNA. (B) Tetrahedral anionic form of boronic acid groups. (C) The interaction between the amino groups of the unpaired bases of RNA and the boronic acid groups of the copolymer. (D) Cyclic borate ester formation by the interaction between vicinal diol groups located at the 3′-end of RNA and boronic acid groups of the copolymer.     

Ion‐exchanger synthesis using reversible addition‐fragmentation chain transfer polymerization

An ion‐exchanger with polyanionic molecular brushes was synthesized by a “grafting from” route based on “surface‐controlled reversible addition‐fragmentation chain transfer polymerization” (RAFT). The RAFT agent, PhC(S)SMgBr was covalently attached to monodisperse‐porous poly(dihydroxypropyl methacrylate‐co‐ethylene dimethacrylate), poly(DHPM‐co‐EDM) particles 5.8 μm in size. The monomer, 3‐sulfopropyl methacrylate (SPM), was grafted from the surface of poly(DHPM‐co‐EDM) particles with an immobilized chain transfer agent by the proposed RAFT protocol. The degree of polymerization of SPM (i. e. the molecular length of the polyanionic ligand) on the particles was controlled by varying the molar ratio of monomer/RAFT agent. The particles carrying polyanionic molecular brushes with different lengths were tested as packing material in the separation of proteins by ion exchange chromatography. The columns packed with the particles carrying relatively longer polyanionic ligands exhibited higher separation efficiency in the separation of four proteins. Plate heights between 130–200 μm were obtained. The ion‐exchanger having poly‐(SPM) ligand with lower degree of polymerization provided better peak‐resolutions on applying a salt gradient with higher slope. The molecular length and the ion‐exchanger group content of polyionic ligand were adjusted by controlling the degree of polymerization and the grafting density, respectively. This property allowed control of the separation performance of the ion‐exchanger packing.     

A bicriteria parallel machine scheduling with a learning effect of setup and removal times

In studies on scheduling problems, generally setup times and removal times of jobs have been neglected or by including those into processing times. However, in some production systems, setup times and removal times are very important such that they should be considered independent from processing times. Since, in general jobs are done according to automatic machine processes in production systems processing times do not differ according to process sequence. But, since human factor becomes influential when setup times and removal times are taken into consideration, setup times will be decreasing by repeating setup processes frequently. This fact is defined with learning effect in scheduling literature. In this study, a bicriteria m-identical parallel machines scheduling problem with a learning effect of setup times and removal times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and total tardiness. A mathematical programming model is developed for the problem which belongs to NP-hard class. Results of computational tests show that the proposed model is effective in solving problems with up to 15 jobs and five machines. We also proposed three heuristic approaches for solving large jobs problems. According to the best of our knowledge, no work exists on the minimization of the weighted sum of total completion time and total tardiness with a learning effect of setup times and removal times.     

Electrical and dielectric properties of Al/p-Si and Al/perylene/p-Si type diodes in a wide frequency range

The perylene(C20H12) layer effect on the electrical and dielectric properties of Al/p-Si(MS) and Al/perylene/p-Si(MPS) diodes have been investigated and compared in the frequency range of 0.7 kHz–2 MHz. Experimental results show that C–V characteristics give an anomalous peak for two structures at low frequencies due to interface states(Nss) and series resistance(Rs). The increases in C and G/ω at low frequencies confirm that the charges at interface can easily follow an ac signal and yield excess capacitance and conductance. The frequency-dependent dielectric constant(ε) and dielectric loss(ε) are subtracted using C and G/ω data at 1.5 V. The ε and ε values are found to be strongly dependent on frequency and voltage, and their large values at low frequencies can be attributed to the excess polarization coming from charges at traps. Plots of ln(σac)–ln(ω) for two structures have two linear regions, with slopes of 0.369 and 1.166 for MS, and of 0.077 and 1.061 for MPS, respectively. From the C 2–V characteristics, the doping acceptor atom concentration(NA) and barrier height(ΦB) for Schottky barrier diodes(SBDs) of MS and MPS types are also obtained to be 1.484 × 1015 and 1.303 × 1015cm 3, and 1.10 and 1.13 eV, respectively.     

Meir-Keeler Type Contractions for Tripled Fixed Points

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.     

Application of fuzzy optimization to a supply chain network design: A case study of an edible vegetable oils manufacturer

This study applies fuzzy sets to integrate the supply chain network of an edible vegetable oils manufacturer. The proposed fuzzy multi-objective linear programming model attempts to simultaneously minimize the total transportation costs. The first part of the total transportation costs is between suppliers and silos; and rest one is between manufacturer and warehouses. The approach incorporates all operating realities and actual flow patterns at production/distribution network with reference to demands of warehouses, capacities of tin and pet packaging lines. The model has been formulated as a multi objective linear programming model where data are modeled by triangular fuzzy numbers. Finally, the developed fuzzy model is applied for the case study, compiled the results and discussed.     

Synthesis and characterization of fully aromatic thermotropic liquid‐crystalline copolyesters containing m‐hydroxybenzoic acid units

A series of fully aromatic copolyesters based on p‐acetoxybenzoic acid (p‐ABA), hydroquinone diacetate (HQDA), terephthalic acid (TPA), and m‐acetoxybenzoic acid (m‐ABA) were prepared by a modified melt‐polycondensation reaction. The copolyesters were characterized by DSC, thermogravimetric analysis, ¹H NMR, polarized optical microscopy, X‐ray diffraction, and intrinsic viscosity measurements. The copolyesters exhibited nematic liquid‐crystalline phases in a broad temperature range of about 150 °C, when the content of linear (p‐ABA, HQDA, and TPA) units was over 67 mol %. DSC analysis of the anisotropic copolyesters revealed broad endotherms associated with the nematic phases, and the melting or flow temperatures were found to be in the processable region. The flow temperatures and crystal‐to‐nematic and nematic‐to‐isotropic transitions depend on the type of linear monomer units, and these transitions increased as the content of the p‐ABA units increased, as compared to the HQDA/TPA units. When the content of the p‐ABA units increased, as compared to other linear units (HQDA and TPA), the intrinsic viscosity and degree of crystallinity of the copolyesters also increased, implying a higher reactivity for p‐ABA in the p‐ABA/HQDA/TPA/m‐ABA polymer system. The aromatic region in the ¹H NMR spectra of the copolyesters containing equal molar compositions of p‐ABA, HQDA, and TPA units were sensitive to the sequence distribution of aromatic rings. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3263–3277, 2001