On the equality of two-variable general functional means

Aequationes mathematicae - Given two functions $$f,g:I\rightarrow \mathbb {R}$$ and a probability measure $$\mu $$ on the Borel subsets of [0, 1], the two-variable mean $$M_{f,g;\mu...     

Spectroscopic studies of structural changes in irradiated LDPE and its blends

The low temperature glass transition occurring at low temperature in polyethylene samples was studied using Fourier transform infrared, FT‐Raman spectroscopic techniques, which are known to be sensitive to any structural changes in the investigated samples. Anomalous behavior was obtained in the temperature range (98 K → 383 K) indicating the existence of phase transition occurring at about 98 K and disappearing at about 323 K while heating for unirradiated virgin low density polyethylene (VPE) sample with or without crosslinking agent (trimethylol propane triacrylate, TMPTA). Addition of TMPTA monomer caused severe changes in the temperature dependence of both unirradiated and irradiated polyethylene samples. The results given indicated the occurrence of abnormal temperature dependence, which is thought to be related with low temperature structural change resulting from local crosslinking in scrapped polyethylene (SPE) sample already suffering from high degree of crosslinking. Differential scanning calorimetry (DSC) thermograms confirmed the observed new phase transition observed in both unirradiated and irradiated TMPTA loaded VPE/SPE (50/50 wt %) blend. Irradiation, addition of TMPTA as a crosslinking agent, and blending VPE with SPE were found to affect remarkably the variation of the vibration spectrum of LDPE and consequently the resulting structural changes. The experimental results obtained were discussed and correlated with reorientational disorders of the molecular segments (local crosslinking). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 850–859, 2007     

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

The effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed using linear and non-linear stability analysis in the long wave limit. The principle aim of this study is to illustrate the influence of electric field on the non-linear stability of a thin liquid layer flow down incline substrate when the plane is porous. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the dividing interface. The coupled non-linear evolution equations for the local film thickness and the interfacial charge for two-dimensional disturbances are derived to analyze the effect of long-wave instabilities. The method of multiple scales is applied to obtain approximate solutions and analyze the stability criteria. Numerical simulations of this system of non-linear evolution equations are performed. It is found that the permeability parameter as well as the inclination of the plane plays a destabilizing role in the stability criteria, while the damping influence is observed for increasing of the electrical conductivity in both linear and non-linear behavior.     

Crystal structure of 1,2,4,6-tetraphenylpyridinium tetrabromoferrate(III)

The title structure, which belongs to the triclinicP¯1 space group witha=13.901(4),b=10.732(1),c=10.570(8)Å=109.14(4),=96.17(4), =90.34(2)°, is refined toR=0.052 for 2985I3(I) reflections. The structure consists of a non-interacting 1,2,4,6-tetraphenylpyridinium and tetrahedral tetrabromoferrate (III) ions.     

Crystal structure of N-benzylmethylammonium dihydrogen-monophosphate monohydrate, [C6H5CH2NH2CH3]H2PO4·H2O

The salt N-benzylmethylammonium dihydrogenmonophosphate monohydrate is monoclinic with the following unit cell dimensions: a = 6.356(1)Å, b = 8.385(7)Å, c = 11.472(5)Å, = 104.32(1)°, space group P2₁ with Z = 2. The structure consists of infinite parallel two-dimensional [110] planes built of mutually connected ions and water molecules by strong O–H···O and N–H···O hydrogen bonding. There are no contacts other than normal van der Waals interactions between the layers.     

Reduction in the Resonance Error in Numerical Homogenization II: Correctors and Extrapolation

This paper is the follow-up of Gloria (Math Models Methods Appl Sci 21(8):1601–1630, 2011). One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio \(\frac{\varepsilon }{\rho }\), where \(\rho \) is a typical macroscopic lengthscale and \(\varepsilon \) is the typical size of the heterogeneities. In the present work, we make a systematic use of regularization and extrapolation to reduce this resonance error at the level of the approximation of homogenized coefficients and correctors for general non-necessarily symmetric stationary ergodic coefficients. We quantify this reduction for the class of periodic coefficients, for the Kozlov subclass of almost-periodic coefficients, and for the subclass of random coefficients that satisfy a spectral gap estimate (e.g., Poisson random inclusions). We also report on a systematic numerical study in dimension 2, which demonstrates the efficiency of the method and the sharpness of the analysis. Last, we combine this approach to numerical homogenization methods, prove the asymptotic consistency in the case of locally stationary ergodic coefficients, and give quantitative estimates in the case of periodic coefficients.     

Crystal Structure,Thermal Analysis and IR Spectroscopic Investigation of Bis Benzyl Ammonium Monohydrogentetraoxoarsenate(V) Monohydrate

Abstract  

The salt bis benzyl ammonium monohydrogentetraoxoarsenate(V) monohydrate [C₆H₅CH₂NH₃ ⁺]₂HAsO₄ ²⁻·H₂O, M = 373.92, Triclinic, P−1. a = 6.514(1), b = 8.910(2), c = 15.061(3) ?, α = 99.26(2), β = 93.93(1), γ = 97.64(1)°, V = 851.5(3), Z = 2, D _x  = 1.460, λ (MoKα) = 0.71073 ?, μ = 0.99 mm⁻¹, F(000) = 126, T = 20(2)  °C, final R = 0.673 for 5488 unique reflections. Planes of HAsO₄ ²⁻ alternate with planes of C₆H₅CH₂NH₃ ⁺ groups. The structure consists of infinite parallel two-dimensional planes built of mutually connected ions and water molecules by strong O–H···O and N–H···O hydrogen bonding. There are no contacts other than van der Waals interactions between the layers. Differential scanning calorimetry study on bis benzyl ammonium monohydrogentetraoxoarsenate(V) monohydrate was carried out. The infrared of polycrystalline samples of this compound have been recorded at room temperature.     

Tualang Honey: A Decade of Neurological Research

Tualang honey has been shown to protect against neurodegeneration, leading to improved memory/learning as well as mood. In addition, studies have also demonstrated its anti-inflammatory and antioxidant properties. However, a substantial part of this research lacks systematization, and there seems to be a tendency to start anew with every study. This review presents a decade of research on Tualang honey with a particular interest in the underlying mechanisms related to its effects on the central nervous system. A total of 28 original articles published between 2011 and 2020 addressing the central nervous system (CNS) effects of Tualang honey were analysed. We identified five main categories, namely nootropic, antinociceptive, stress-relieving, antidepressant, and anxiolytic effects of Tualang honey, and proposed the underlying mechanisms. The findings from this review may potentially be beneficial towards developing new therapeutic roles for Tualang honey and help in determining how best to benefit from this brain supplement.