The line analog of Ramsey numbers

For positive integersr ands, f′(r, s) is defined as the smallest positive integerp such that every connected (ordinary) graph of orderp contains eitherr mutually adjacent lines ors mutually disjoint lines. It is found thatf’(r,s) =(r−1) (s−1)+2 unlessr=2 and s ≠ 1, in which casef′(2,s)=3. Definitions not given here can be found in [7, 8].     

Abel’s integral operator: sparse representation based on multiwavelets

In this work, Abel’s integral operator is represented based on Alpert’s multiwavelets as a sparse matrix and then a non-linear Abel’s integral equation of the second kind is solved by multiwavelets Galerkin method. Nonlinearity and singularity make the numerical procedure more challenging. But the proposed scheme overcomes these problems. Convergence analysis is investigated and some numerical examples validated this analysis.

     

On m-th root metrics with special curvature properties

In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.     

Micron and Submicron-Sized Whey Protein–Pectin Aggregates Generated Via Alkali-Catalyzed Chemical Crosslinking

Citric acid was used to crosslink whey proteins and sugar beet pectin at 50°C with the aid of sodium hydroxide as catalyst. The effects of the pH of biopolymers mixed solution and the duration of the crosslinking process on various characteristics of generated particles were studied. Although the majority of the generated aggregates were of submicron size, particles as small as 59 nm were present. The crosslinking duration did not affect the size of aggregates; however, the samples crosslinked at pH 4.2 were greater than those obtained at pH 7.0. Scanning electron microscopy images revealed that aggregates were not uniformly shaped; differential scanning calorimetry indicated that conjugate whey protein–pectin aggregates had greater thermal stabilities than their parent individual biopolymers. The occurrence of crosslinkages was confirmed by the results of Fourier transform infrared spectroscopy.     

Comparison of optical and structural properties of nanostructure TiO2 thin film doped by Sn and Nb

The thin films of TiO₂ doped by Sn or Nb were prepared by sol–gel method under process control. The effects of Sn and Nb doping on the structural, optical and photo-catalytic properties of applied thin films have been studied by X-ray diffraction (XRD) high resolution transmission electron microscopy and UV–Vis absorption spectroscopy. Surface chemical state of thin films was examined by atomic X-ray photoelectron spectroscopy. XRD results suggest that adding impurities has a great effect on the crystallinity and particle size of TiO₂. Titania rutile phase formation in thin film was promoted by Sn⁴⁺ addition but was inhibited by Nb⁵⁺ doping. The activity of the photocatalyst was evaluated by photocatalytic degradation kinetics of aqueous methylene blue under UV and Visible radiation. The results show that the photocatalytic activity of the Sn-doped TiO₂ thin film have a larger degradation efficiency than Nb-doped TiO₂ under visible light, but under UV light photocatalytic activity of the Nb-doped TiO₂ thin film is better.     

A Practical and Eco-Friendly Method for Conversion of Epoxides to Thiiranes with Immobilized Thiourea on CaCO3

Abstract

Solvent-free conversion of various epoxides to the corresponding thiiranes was carried out efficiently with immobilized thiourea on CaCO₃. The reactions were completed within 1–12 min under oil bath (60 °C–70 °C) conditions to afford thiiranes in 88%–98% yields.

[Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: Figures S1–S3.]

GRAPHICAL ABSTRACT      

An inorganic–organic hybrid material based on ZnO nanoparticles anchored to a composite made from polythiophene and hexagonally ordered silica for use in solid-phase fiber microextraction of PAHs

We report on an inorganic–organic hybrid nanocomposite that represents a novel kind of fiber coating for solid-phase microextraction (SPME) of polycyclic aromatic hydrocarbons (PAHs). The material is composed of ZnO nanoparticles, polythiophene and hexagonally ordered silica, and displays good extraction capability due to its nanostructure. The nanocomposite was synthesized by an in-situ polymerization technique, and the ZnO nanoparticles were anchored to the pores in the walls. The ZnO/polythiophene/hexagonally ordered silica (ZnO/PT/SBA-15) nanocomposite was then deposited on a stainless steel wire to obtain the fiber for SPME of PAHs. Optimum conditions include an extraction temperature of 85 °C (for 30 min only), a desorption temperature of 260 °C (for 2 min), and a salt concentration (NaCl) of 20 % (w/v). The detection limits are between 8.2 and 20 pg mL^?1, and the linear responses extend from 0.1 to 10 ng mL^?1. The repeatability for one fiber (for n?=?5), expressed as relative standard deviation, is between 4.3 and 9.1 %. The method offers the advantage of being simple to use, rapid, and low-cost (in terms of equipment). The thermal stability of the fiber and high relative recovery (compared to conventional methods) represent additional attractive features.

Experimental and Modelling Study of Gravity Drainage in a Three-Block System

Transport in Porous Media - Gravity drainage is known as the controlling mechanism of oil recovery in naturally fractured reservoirs. The efficiency of this mechanism is controlled by...     

Effects of an electric field on the electronic and optical properties of zigzag boron nitride nanotubes

We have investigated the electro-optical properties of zigzag BNNTs, under an external electric field, using the tight binding approximation. It is found that an electric field modifies the band structure and splits the band degeneracy. Also the large electric strength leads to coupling the neighbor subbands which these effects reflect in the DOS and JDOS spectrum. It has been shown that, unlike CNTs, the band gap of BNNTs can be reduced linearly by applying a transverse external electric field. Also we show that the larger diameter tubes are more sensitive than small ones. The semiconducting metallic transition can be achieved through increasing the applied fields. The number and position of peaks in the JDOS spectrum are dependent on electric field strength. It is found that at a high electric field, the two lowest subbands are oscillatory with multiple nodes at the Fermi level.