Packing of linearly arranged benzene molecules inside single walled carbon nanotubes: The high pressure study

The high pressure behaviors and electronic properties of (C₆H₆)_n@SWCNT peapod structure with the different encapsulation densities are studied by the DFT calculation. The weak van der Waals interaction and electronic orbital hybridization interaction between the host and guest molecules are exhibited in the pressure lower and higher than 3 GPa, respectively. The encapsulation density of C₆H₆ molecules plays an important role in the structural deformation, the bonding behaviors, and the electronic orbital hybridization interaction of the considered four hybrid systems under the pressures.     

Regioselective Synthesis of Aurone Derivatives via PBu3‐Catalyzed Cyclization of 2‐Alkynoylphenols

Aurone derivatives were synthesized in good to high yields by PBu₃‐catalyzed intramolecular 5‐exo cyclization of 2‐alkynoylphenols. The reaction proceeds in high regioselectivity without forming 6‐endo cyclization products.     

Magnetization tunneling in an enneanuclear manganese cage

The enneanuclear mixed-valent manganese cage [Mn₉O₇(OAc)₁₁(thme)(py)₃(H₂O)₂] 1 {Mn₉} possesses an S=17/2 ground state as a result of an antiferromagnetic interaction between three ferromagnetically coupled Mn^IV ions and a wheel of four Mn^III and two Mn^II ions. AC magnetization measurements show a frequency-dependent out-of-phase signal at 3.4 K and 997 Hz, indicative of single-molecule magnetism behaviour. Data obtained from varying the frequency of oscillation of the AC field gives an effective energy barrier (U_eff) for the reversal of magnetization of 27 K. Magnetic measurements of single crystals of 1 at low temperature show time- and temperature-dependent hysteresis loops which contain steps at regular intervals of field. DC and AC relaxation measurements show both the temperature-dependent and temperature-independent regions, the latter being definitive evidence of magnetization tunneling in the lowest energy zero-field split component of the ground state.     

On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods

Recent results in the study of quantum manifestations in classical chaos raise the problem of computing a very large number of eigenvalues of selfadjoint elliptic operators. The standard numerical methods for large eigenvalue problems cover the range of applications where a few of the leading eigenvalues are needed. They are not appropriate and generally fail to solve problems involving a number of eigenvalues exceeding a few hundreds. Further, the accurate computation of a large number of eigenvalues leads to much larger problem dimension in comparison with the usual case dealing with only a few eigenvalues. A new method is presented which combines multigrid techniques with the Lanczos process. The resulting scheme requires O(mn) arithmetic operations and O(n) storage requirement, where n is the number of unknowns and m, the number of needed eigenvalues. The discretization of the considered differential operators is realized by means of p-finite elements and is applicable on general geometries. Numerical experiments validate the proposed approach and demonstrate that it allows to tackle problems considered to be beyond the range of standard iterative methods, at least on current workstations. The ability to compute more than 9000 eigenvalues of an operator of dimension exceeding 8 million on a PC shows the potential of this method. Practical applications are found, e.g. in the numerical simulation of quantum billiards.     

Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices

In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.     

A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques

In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433–446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.     

Periodic solutions to a delayed predator–prey model with Hassell–Varley type functional response

In this paper, a delayed predator–prey model with Hassell–Varley type functional responses is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions to it by applying the coincidence degree theorem. It is interesting that the result is based on the delay, which is different from the previous work (the results are delay-independent). Furthermore, the simulation shows that some conditions are sharp.     

Fe2O3/ZnO/ZnFe2O4 composites for the efficient photocatalytic degradation of organic dyes under visible light

In this study, novel ternary Fe₂O₃/ZnO/ZnFe₂O₄ (ZFO) composites were successfully prepared through a simple hydrothermal reaction with subsequent thermal treatment. The as-prepared products were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), Brunauer-Emmett-Teller (BET) analysis, Barrett-Joyner-Halenda (BJH) measurement, and UV–vis diffuse reflectance spectroscopy (UV–vis DRS). The photocatalytic degradation of rhodamine B (Rh B) under visible light irradiation indicated that the ZFO composites calcined at 500 °C has the best photocatalytic activity (the photocatalytic degradation efficiency can reach up to 95.7% within 60 min) and can maintain a stable photocatalytic degradation efficiency for at least three cycles. In addition, the photocatalytic activity of ZFO composites toward dye decomposition follows the order cationic Rh B > anionic methyl orange. Finally, using different scavengers, superoxide and hydroxyl radicals were identified as the primary active species during the degradation reaction of Rh B.     

The estimated number of irreducible binomials

Let ${\mathbb{F}}_q$ be the finite field with q elements, and T a positive integer. In this article, we find an asymptotic formula for the total number of monic irreducible binomials in ${\mathbb{F}}_q[x]$ of degree less or equal to T, when T is large enough. We also show explicit lower and upper bounds for the number of binomials in the case when T is small.