On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Study on the Relationship between Emulsion Properties and Interfacial Rheology of Sugar Beet Pectin Modified by Different Enzymes

The contribution of rheological properties and viscoelasticity of the interfacial adsorbed layer to the emulsification mechanism of enzymatic modified sugar beet pectin (SBP) was studied. The component content of each enzymatic modified pectin was lower than that of untreated SBP. Protein and ferulic acid decreased from 5.52% and 1.08% to 0.54% and 0.13%, respectively, resulting in a decrease in thermal stability, apparent viscosity, and molecular weight (Mw). The dynamic interfacial rheological properties showed that the interfacial pressure and modulus (E) decreased significantly with the decrease of functional groups (especially proteins), which also led to the bimodal distribution of particle size. These results indicated that the superior emulsification property of SBP is mainly determined by proteins, followed by ferulic acid, and the existence of other functional groups also promotes the emulsification property of SBP.     

Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property

A graph is concave-round if its vertices can be circularly enumerated so that the closed neighborhood of each vertex is an interval in the enumeration. In this study, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J. Discrete Math., 13 (2000), pp. 179–193]. In addition, we show that it is possible to find one such forbidden induced subgraph in linear time in any given graph that is not concave-round. As part of the analysis, we obtain characterizations by minimal forbidden submatrices for the circular-ones property for rows and for the circular-ones property for rows and columns and show that, also for both variants of the property, one of the corresponding forbidden submatrices can be found (if present) in any given matrix in linear time. We make some final remarks regarding connections to some classes of circular-arc graphs.     

Effect of high intensity ultrasound on gelation properties of silver carp surimi with different salt contents

Surimi from silver carp with different salt contents (0–5%) was obtained treated by high intensity ultrasound (HIU, 100 kHz 91 W·cm⁻²). The gelation properties of samples were evaluated by puncture properties, microstructures, water-holding capacity, dynamic rheological properties and intermolecular interactions. As the salt content increased from 0 to 5%, gel properties of surimi without HIU significantly improved. For samples with low-salt (0–2% NaCl) content, HIU induced obvious enhancement in breaking force and deformation. HIU promoted the protein aggregation linked by SS bonds, hydrophobic interactions and non-disulfide covalent bonds in surimi gels with low-salt content. Moreover, microstructures of HIU surimi gels with low-salt content were more compact than those of the corresponding control samples. HIU also improved the gelation properties of surimi with 3% NaCl to an extent. However, for high-salt (4–5% NaCl) samples, HIU decreased the breaking force and deformation of surimi gels due to the degradation of proteins suggested by increased TCA-soluble peptides. In conclusion, HIU effectively improved the gelation properties of surimi with low-salt content (0–2% NaCl), but was harmful for high-salt (4–5% NaCl) surimi. This might provide the theoretical basis for the production of low-salt surimi gels.     

Investigation of mononuclear,dinuclear, and trinuclear transition metal (II) complexes derived from an asymmetric Salamo‐based ligand possessing three different coordination modes

A new asymmetric Salamo‐based ligand H₂L was synthesized using 3‐tert‐butyl‐salicylaldehyde and 6‐methoxy‐2‐[O‐(1‐ethyloxyamide)]‐oxime‐1‐phenol. By adjusting the ratio of the ligand H₂L and Cu (II), Co (II), and Ni (II) ions, mononuclear, dinuclear, and trinuclear transition metal (II) complexes, [Cu(L)], [{Co(L)}₂], and [{Ni(L)(CH₃COO)(CH₃CH₂OH)}₂Ni] with the ligand H₂L possessing completely different coordination modes were obtained, respectively. The optical spectra of ligand H₂L and its Cu (II), Co (II) and Ni (II) complexes were investigated. The Cu (II) complex is a mononuclear structure, and the Cu (II) atom is tetracoordinated to form a planar quadrilateral structure. The Co (II) complex is dinuclear, and the two Co (II) atoms are pentacoordinated and have coordination geometries of distorted triangular bipyramid. The Ni (II) complex is a trinuclear structure, and the terminal and central Ni (II) atoms are all hexacoordinated, forming distorted octahedral geometries. Furthermore, optical properties including UV–Vis, IR, and fluorescence of the Cu (II), Co (II), and Ni (II) complexes were investigated. Finally, the antibacterial activities of the Cu (II), Co (II), and Ni (II) complexes were explored. According to the experimental results, the inhibitory effect was found to be enhanced with increasing concentrations of the Cu (II), Co (II), and Ni (II) complexes.     

Characterization of new Pt(IV)–thiazole complexes: Analytical,spectral, molecular modeling and molecular docking studies and applications in two opposing pathways

New thiazole derivatives were synthesized and fully characterized, then coordinated with PtCl₄ salt. Also, the newly synthesized Pt(IV) complexes were investigated analytically (elemental and thermogravimetric analyses), spectrally (infrared, UV–visible, mass, ¹H NMR, ¹³C NMR, X‐ray diffraction) as well as theoretically (kinetics, modeling and docking). The data extracted led to the establishment of the best chemical and structural forms. Octahedral geometry was the only formula proposed for all complexes, which is favorable for d⁶ systems. The molecular ion peaks from mass spectral analysis coincide with all analytical data, confirming the molecular formula proposed. X‐ray diffraction (XRD) and scanning electron microscopy (SEM) allowed discrimination of features between crystalline particles and other amorphous morphology. By applying Gaussian09 as well as HyperChem 8.2 programs, the best structural forms were obtained, as well as computed significant parameters. Computed parameters such as softness, hardness, surface area and reactivity led us towards application in two opposing pathways: tumor inhibition and oxidation activation. The catalytic oxidation for CO was conducted over PtO₂, which was yielded from calcination of the most reactive complex. The success of catalytic role for synthesized PtO₂ was due to its particulate size and surface morphology, which were estimated from XRD patterns and SEM images, respectively. The antitumor activity was tested versus HCT‐116 and HepG‐2 cell lines. Mild toxicity was recorded for two of the derivatives and their corresponding complexes. This degree of toxicity is more favorable in most cases, due to exclusion of serious side effects, which is coherently attached with known antitumor drugs.     

Nb(iPrNPMe2)3Fe–PMe3: A potential high reactivity heterobimetallic catalyst for acetylene cycloadditions

Alkynes cycloaddition reactions are powerful tools for constructing cyclic molecules with optimal atom efficiency, but these reactions cannot proceed at ambient temperature without transition-metal catalysts. In this work, a heterobimetallic complex featuring an Nb–Fe triple bond, Nb(ⁱPrNPMe₂)₃Fe–PMe₃, has been evaluated as the potential catalyst for acetylene cycloaddition, using density functional theory. The calculated results show that the singlet-state (i.e. ground-state) Nb(ⁱPrNPMe₂)₃Fe–PMe₃ can be applied to benzene synthesis, but is not suitable for cyclobutadiene. Benzene can be obtained easily at room temperature and is the unique product on the singlet potential surface. The irradiation of infrared-red light can drive the excitation of singlet Nb(ⁱPrNPMe₂)₃Fe–PMe₃ to its triplet state. Both benzene and cyclobutadiene can be formed on the triplet reaction potential surface due to their low energy barriers. Therefore, Nb(ⁱPrNPMe₂)₃Fe–PMe₃ is a potential high reactivity heterobimetallic catalyst for the cyclotrimerization of alkynes. In the reaction process, the catalytic active site of Nb(ⁱPrNPMe₂)₃Fe–PMe₃ moves from niobium to iron.     

FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

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Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.