A note on 3‐partite graphs without 4‐cycles

Let $C_4$ be a cycle of order 4. Write $ex\left(n,n,n,C_4\right)$ for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has $n$ vertices that have no subgraph isomorphic to $C_4$. In this paper, we show that $ex\left(n,n,n,C_4\right)\ge \frac{3}{2}n\left(p+1\right)$, where $n=\frac{p\left(p?1\right)}{2}$ and $p$ is a prime number. Note that $ex\left(n,n,n,C_4\right)\le \left(\frac{3\sqrt{2}}{2}+o\left(1\right)\right)n^{\frac{3}{2}}$ from Tait and Timmons's works. Since for every integer $m$, one can find a prime $p$ such that $m\le p\le \left(1+o\left(1\right)\right)m$, we obtain that $\underset{n\to \infty }{\lim }\frac{ex\left(n,n,n,C_4\right)}{\frac{3\sqrt{2}}{2}{n}^{\frac{3}{2}}}=1$.     

Magnetite nanoparticles−based hydroxyl radical scavenging activity assay of antioxidants using N,N-dimethyl-p-phenylenediamine probe

Excessive amounts of reactive oxygen species (ROS), unless counterbalanced by antioxidants, can cause cellular damage under oxidative stress conditions; therefore, antioxidative defenses against ROS must be measured. With the development of nanotechnology, nanoparticles have found numerous applications in science, health, and industries. Magnetite nanoparticles (Fe ₃ O ₄ :MNPs) have attracted attention because of their peroxidase-like activity. In this study, hydroxyl radicals (•OH) generated by MNPs-catalyzed degradation of H ₂ O ₂ converted the N,N-dimethyl-p-phenylenediamine (DMPD) probe into its colored DMPD•+ radical cation, which gave an absorbance maximum at λ = 553 nm. In the presence of antioxidants, •OH was partly scavenged by antioxidants and produced less DMPD• ⁺ , causing a decrease in the 553 nm-absorbance. Antioxidant concentrations were calculated with the aid of absorbance differences between the reference and sample solutions. The linear working ranges and trolox equivalent antioxidant capacity coefficients of different classes of antioxidants were determined by applying the developed method. In addition, binary and ternary mixtures of antioxidants were tested to observe the additivity of absorbances of mixture constituents. The method was applied to real samples such as orange juice and green tea. Student t-test, F tests, and the Spearman’s rank correlation coefficient were used for statistical comparisons.     

Sensitive and selective determination of 4-nitrophenol in water and food using modified polyethyleneimine-capped carbon dots

Hazardous 4-nitrophenol (4-NP) has created serious threats to humans and the environment; therefore, it is highly desirable to develop a facile and practical method for the monitoring of 4-NP in environment and food. Here, a fluorescence method based on modified polyethyleneimine-capped carbon dots (mPEI-CDs) was developed for sensitive and selective determination of 4-NP in water, fruit, and vegetable samples. First, highly fluorescent mPEI-CDs (quantum yield about 40.3%) were easily synthesized via a one-step hydrothermal method by using novel acetic anhydride modified polyethyleneimine (mPEI) and citric acid as precursors. Compared to the unmodified PEI-CDs, the acetic anhydride mPEI-CDs exhibited excellent fluorescent stability in a wider pH range of 4.0–9.0. Under pH 8.0, a selective determination of 4-NP was achieved based on the inner filter effect (IFE) mechanism. After optimization, good linear relationships between fluorescence intensity function (F₀-F)/F₀ and the concentration of 4-NP were obtained in ranges of 0.5–10 and 10–100 μM, respectively, while efficiently avoiding the interferences from two other nitrophenol isomers, possible coexisting metal cations and anions in samples. Finally, the proposed approach was successfully applied for the determination of 4-NP in water, honey, strawberry, and tomato samples.     

Synthesis and characterization of VO–vanillin complex immobilized on MCM-41 and its facile catalytic application in the sulfoxidation reaction,and synthesis of 2,3-dihydroquinazolin-4(1H)-ones and disulfides in green media

In this work, a vanillin complex is immobilized onto MCM-41 and characterized by FT-IR, X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetric analysis, and BET techniques. This supported Schiff base complex was found to be an efficient and recoverable catalyst for the chemoselective oxidation of sulfides into sulfoxides and thiols into their corresponding disulfides (using hydrogen peroxide as a green oxidant) and also a suitable catalyst for the preparation of 2,3-dihydroquinazolin-4(1H)-one derivatives in water at 90°C. Using this protocol, we show that a variety of disulfides, sulfoxides, and 2,3-dihydroquinazolin-4(1H)-one derivatives can be synthesized in green conditions. The catalyst can be recovered and recycled for further reactions without appreciable loss of catalytic performance.     

New oxacalix[4]arene carboxylate detects viologen in protic media

ABSTRACT

We demonstrate that Ullman fragment-coupling can be used to synthesise an oxacalix[4]arene monocarboxylic acid, which provides easy access to its water-soluble carboxylato derivatives. Crystallographic and computational data suggest that the new carboxyl-substituted oxacalix[4]arene adopts a 1,3-alternate conformation both in the solid-state and in methanol solution. Its water-soluble tetrabutylammonium derivate can detect the herbicide paraquat at neutral pH in aqueous media (K _a = 111 ± 3 M^–1) and in methanol (K _a = 2020 ± 70 M^–1).     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Electrical and Thermal Transport Properties of n-type Bi6Cu2Se4O6 (2BiCuSeO + 2Bi2O2Se)

New thermoelectric materials, n-type Bi₆Cu₂Se₄O₆ oxyselenides, composed of well-known BiCuSeO and Bi₂O₂Se oxyselenides, are synthesized with a simple solid-state reaction. Electrical transport properties, microstructures, and elastic properties are investigated with an emphasis on thermal transport properties. Similar to Bi₂O₂Se, it is found that the halogen-doped Bi₆Cu₂Se₄O₆ possesses n-type conducting transports, which can be improved via Br/Cl doping. Compared with BiCuSeO and Bi₂O₂Se, an extremely low thermal conductivity can be observed in Bi₆Cu₂Se₄O₆. To reveal the origin of low thermal conductivity, elastic properties, sound velocity, Grüneisen parameter, and Debye temperature are evaluated. Importantly, the calculated phonon mean free path of Bi₆Cu₂Se₄O₆ is comparable to the interlayer distance for BiO─CuSe and BiO─Se layers, which is ascribed to the strong interlayer phonon scattering. Contributing from the outstanding low thermal conductivity and improved electrical transport properties, the maximum ZT ≈0.15 at 823 K and ≈0.11 at 873K are realized in n-type Bi₆Cu₂Se_3.2Br_0.8O₆ and Bi₆Cu₂Se_3.6Cl_0.4O₆, respectively, indicating the promising thermoelectric performance in n-type Bi₆Cu₂Se₄O₆ oxyselenides.     

Sonication-Assisted Synthesis of Bimetallic Hg/Pd Alloy Nanoparticles for Catalytic Reduction of Nitrophenol and its Derivatives

In this article, we report a facile approach for the synthesis of an inexpensive catalyst of bimetallic Hg/Pd alloys comprising nanoparticles with various structures using a unique ultrasonic reaction that is conducted without the use of any reducing agent. The nanoparticles of Hg/Pd alloys (HgPd and Hg₂Pd₅) were achieved for the first time by sonicating an aqueous solution of Palladium (II) nitrate with metallic liquid mercury, as evidenced by XRD. EDS further confirmed the presence of Pd and Hg elements in the alloy. The surface morphology and structure of the nanoparticles have been systematically investigated by HRSEM, HRTEM and SAED pattern. In order to explore the catalytic activity of the as-synthesized nanoalloys, the catalytic reduction of 4-nitrophenol and a few other nitrophenol derivatives were investigated. Excellent catalytic activity was obtained for Hg/Pd (1:1) alloy, and the rate constant for the reduction of 4-NP with Hg/Pd at room temperature was found to be 58.4 × 10⁻³ s⁻¹, which is possibly the highest ever reported. The catalyst exhibited superior stability and reusability when compared with those reported in the literature for other catalysts based on noble metals.     

Nanostructured BiVO4 Derived from Bi-MOF for Enhanced Visible-light Photodegradation

BiVO4,a promising visible-light responding photocatalyst,has aroused extensive research interest because of inexpensiveness and excellent chemical stability.However,its main drawback is the poor photoinduced charge-transfer dynamics.Building nanostructures is an effective way to tackle this problem.Herein,we put forward a new method to prepare nanostructured BiVO4 from Bi-based metal-organic frameworks[Bi-MOF(CAU-17)]precursor.The as-prepared material has a rod-like morphology inherited from the Bi-MOF sacrificial template and consists of small nanoparticle as building blocks.Compared with its counterparts prepared by conventional methods,MOF-derived nanostructured BiVO4 shows better light absorption ability,narrower bandgap,and improved electrical conductivity as well as reduced recombination.Consequently,BiVO4 nanostructure demonstrates high photocatalytic activity under visible light towards the degradation of methylene blue.Methylene blue can be degraded up to 90%within 30 min with a reaction rate constant of 0.058 min-1.Moreover,the cycling stability of the catalyst is excellent to withstand unchanged degradation efficiency for at least 5 cycles.