Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

Far-Red Dibenzo[a,j]Perylene-8,16-Dione Dyes as Fluorescent Enzyme Substrates and Tags for Biomolecules

The synthesis of fluorescent 2,10-derivatives of the title chromophore are described. The substituents contain amino-reactive N-hydroxysuccinimde ester and thiol-reactive iodoacetamide groups for attachment to biomolecules. A phosphate derivative was also prepared as an enzyme substrate.     

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.     

Silica gel-mediated hydrohalogenation of unactivated alkenes using hydrohalogenic acids under organic solvent-free conditions

Silica gel-mediated hydrochlorination of unactivated alkenes using 35% hydrochloric acid under organic solvent-free conditions proceeded to give the corresponding chlorides in good yields. Hydrobromination or hydriodination using 47% hydrobromic acid or 55% hydriodic acid afforded the corresponding halides, respectively. Silica gel could be recycled five times without any significant loss of activities.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

真空冷却过程中实验条件对真空冷却速率的影响

以熟肉为实验材料,对实验条件对真空冷却速率的影响进行了理论分析和实验研究。实验结果表明:真空室有效容积越小、真空泵抽速越高,则真空冷却时间就会越短;冷阱温度对真空冷却速率有着明显的影响;当真空室内的最终压力在0.4～0.61kPa变化时,熟肉的表面温度一直在0℃以上,其真空冷却的时间随着真空室内压力的升高而增加。而真空室内的最终压力在0.3kPa左右时,熟肉的表面温度在真空冷却过程会低于0℃。     

Coupled Navier–Stokes/molecular dynamics simulations in nonperiodic domains based on particle forcing

This paper focuses on coupling methods for hybrid Navier–Stokes/molecular dynamics (MD) simulations. The computational domain is split in a continuum flow region, where a finite‐volume discretisation of the Navier–Stokes equations is used, and one or more particle domains, where molecular level modelling of the flow is employed. The domains are defined with a partial overlap, in which the flow states are coupled through an exchange of the velocity components. For the steady flows considered, an under‐relaxed Newton iteration method is used to drive the coupled system to convergence. The main focus of the present work is on methods to impose nonperiodic boundary conditions on the particle domain(s). A particle forcing is applied in the direction normal to the particle domain boundary to impose the boundary normal velocity component. A novel aspect of the present work is the extension of this method to more general nonplanar particle domain boundaries. The main contribution of the paper is the development of a particle forcing method in the direction tangential to the domain boundary, which is based on the equivalent continuum‐flow boundary shear stresses along with an iterative forcing strength adjustment based on the extrapolated particle boundary velocity. Furthermore, an adaptation scheme is presented, which uses the finite‐volume flux residuals of the particle bin averaged velocity field as a truncation criterion for the iterative force‐update scheme. It is demonstrated that by comparing the residual reduction for the momentum equation in the nonhomogeneous directions during the molecular dynamics simulations with that for a homogeneous direction, the forcing iteration at which the statistical noise in the velocity field dominates the uncertainty in the forcing strength can be determined. At this point the iteration can be truncated. It is shown that with adaptive schemes of this type, the total number of MD evaluations required in a coupled Navier–Stokes/MD simulation can be reduced relative to a hybrid scheme with a fixed number of forcing‐strength updates. Copyright © 2011 John Wiley & Sons, Ltd.     

A new approach in modeling of constant temperature boundary condition in thermal lattice‐Boltzmann method

The lattice‐Boltzmann method is being applied to a diversity of fluid flow and heat transfer problems nowadays. Because of its microscale nature, strict attention should be paid when introducing macroscopic inputs to the model. One of the challenging issues dealing with macroscale and microscale treatment is the implementation of boundary conditions. In this regard constant‐temperature boundaries are frequently used in energy transfer problems. Such boundaries are simply modeled in Navier–Stokes based solvers, but they are not so harnessed in lattice‐Boltzmann models. One of the problems is that the calculated tangential heat flux is not zero along such boundaries in most of the previous models. In the present paper, a model has been developed, which has the capability of controlling tangential heat flux along the constant‐temperature boundaries. It aims to set the heat flux nearly zero along the boundary in midplane grid schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Surface modified SPIONs‐Cr(VI) ions‐immobilized organic‐inorganic hybrid as a magnetically recyclable nanocatalyst for rapid synthesis of polyhydroquinolines under solvent‐free conditions at room temperature

In this work, a magnetic hybrid dichromate nanocomposite with triphenylphosphine surface modified superparamagnetic iron oxide nanoparticles (SPIONs) as a recyclable nanocatalyst was designed, prepared and characterized by Fourier transform infrared spectroscopy (FT‐IR) spectra, X‐ray diffraction (XRD) pattern analysis, vibrating sample magnetometer (VSM) curves, X‐ray fluorescence (XRF) analysis, thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images and dynamic light scattering (DLS) analysis. Then, it was used in a green and efficient procedure for one‐pot multicomponent synthesis of polyhydroquinoline derivatives by the condensation of aldehydes, dimedone or 1,3‐cyclohexadione, ethyl acetoacetate and ammonium acetate. This protocol includes some new and exceptional advantages such as short reaction times, low catalyst loading, high yields, solvent‐free and room temperature conditions, easy separation and reusability of the catalyst.     

An approach for solving a fuzzy multiobjective programming problem

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.