A note on commutators of Hardy operators

Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.     

Poisson’s equation for discrete-time single-birth processes

We consider Poisson’s equation for discrete-time single-birth processes, and we derive its solutions by solving a linear system of infinitely many equations. We apply the solution of Poisson’s equation to obtain the asymptotic variance. The results are further applied to birth–death processes and the scalar-valued GI/M/1-type Markov chains.     

Effective and selective aerobic oxidation of primary and secondary alcohols using CoFe2O4@HT@Imine‐CuII and TEMPO in the air atmosphere

In this study, we present a versatile and easy procedure for modifying a cobalt ferrite nanoparticle step by step. A new nanocatalyst was prepared via Cu^II immobilized onto CoFe₂O₄@HT@Imine. The catalyst was fully characterized by Fourier‐transform infrared (FT‐IR), energy‐dispersive X‐ray spectroscopy (EDX), field emission scanning electron microscopy (FE‐SEM), X‐ray diffraction (XRD), and vibrating sample magnetometer (VSM) analyses. The current procedure as a green protocol offers benefits including a simple operational method, an excellent yield of products, mild reaction conditions, minimum chemical wastes, and short reaction times. Without any significant reduction in the catalytic performance, up to five recyclability cycles of the catalyst were obtained. The optimization results suggest that the best condition in the oxidation of benzyl alcohol derivatives is 0.003 g of the CoFe₂O₄@HT@Imine‐Cu^II catalyst, TEMPO, at 70°C under solvent‐free condition and air.     

The Determination Of Sub Part-Per-Billion Levels Of Volatile Organic Compounds In Air By Pre-Concentration From Small Sample Volumes

Abstract

Trace level Volatile Organic Compounds (VOCs) in ambient air are normally determined according to EPA Method TO-14. This method describes the analysis in ambient air of 41 VOCs, ranging in boiling point from -29 to 215°C. It covers a concentration range from 0.2 to 20 parts per billion, volume/volume (ppb), and specifies sample enrichment of a 400 mL air sample on glass beads at -160°C. While this sample volume provides sub-ppb levels of VOC detection for target analytes when using a quadrupole mass spectrometer detector in SIM mode or when using GC detectors, the identification of non-target analytes may only be done in full scan mode for higher concentrations. Also with this sample volume a Nafion dryer is needed for water removal thereby lowering the recovery of polar VOCs.

Because of the very high sensitivity of the ion trap MS, relatively small air volumes (60 mL) are adequate to obtain the required or lower detection levels. An integrated air analysis system based on a GC-ion-trap MS has been investigated and is described. This system has a built-in cryogenic trap and necessary valving, internal standard gas sampling loop, and is controlled from the GC-MS workstation. The linearity, precision, and method detection levels obtainable with this system when using small volumes are reported. In addition, examples of the quantitative and qualitative analysis of ambient air samples are shown.     

Impacts of air pressure on the evolution of nanosecond pulse discharge products

Based on the nonequilibrium plasma dynamics of air discharge, a dynamic model of zero-dimensional plasma is established by combining the component density equation, the Boltzmann equation, and the energy transfer equation. The evolution properties of nanosecond pulse discharge (NPD) plasma under different air pressures are calculated. The results show that the air pressure has significant impacts on the NPD products and the peak values of particle number density for particles such as O atoms, O3 molecules, N2(A3) molecules in excited states, and NO molecules. It increases at first and then decreases with the increase of air pressure. On the other hand, the peak values of particle number density for N2(B3) and N2(C3) molecules in excited states are only slightly affected by the air pressure.     

搪瓷承压水箱在空气源热泵中实际运用研究

随着经济的快速发展，人们的生活水平得到了显著的提升，由此，人们对生活的质量就有了更高的要求，尤其是对热水的要求，更是出现了显著的提升。当前，国内的空气源热水器行业发展的十分迅速，能够充分地满足人们对热水的需求，这使得空气源热泵在人们的生活中应用的越来越广泛。在本文中，介绍了空气源热泵的工作原理以及优点，并介绍了搪瓷承压水箱在空气源热泵中的实际应用。     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Synthesis of guar gum-based hydrogel for sugarcane field solid conditioning

The water crisis is increased everywhere in recent years, which has affected the water demand in different sectors like industries, agriculture, residential, etc. The present research aims to the development of superabsorbent polymer (SAP) using bio-material. The hydrogel is synthesized by grafting Guar gum (GG) with methyl methacrylate (MMA) and crosslinking with polyethylene glycol (PEG). The developed GG-based hydrogelwas characterized by various analytical instruments. The Scanning Electron Microscopy (SEM) demonstrated hydrogels havepores of size 50 ​μm–10 ​μm. The Transmission Electron Microscopy (TEM) analysis has shownthat thematerial consists of spherical shapesand particles of size 141.11nm–182.19 ​nm.The Fourier-Transform Infrared Spectroscopy (FTIR) and Thermogravimetric analysis (TGA) study have confirmedthepresence of functional groups of material, and thermal resistivity. The absorption capacity of developed hydrogelwas found to be 110 ​ml per gram (110% of its dry weight). The hydrogelwasapplied in the field of sugarcane crop and measured soil moisture content after 20 days of application. A better resultwas found of moisture content in the area of hydrogel application (28%) compared to the area without hydrogel application (10%). Moreover, the comparison of different hydrogels is also shown in a study, and the developed hydrogel proves good moisture retention capacity. This technology could be promising in terms of improving perennial crop productivity and combating moisture stress in agriculture. As a soil conditioning material for agricultural applications, the synthesized hydrogel showed tremendous potential.