LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

ON THE CLASS

An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and(υ) ≠￠ then a Hadamard rnatrix of order 4tυ can be constructed.

Nonlinear least square estimation using difference quotient instead of derivative containing different classes of measurements

Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.

A CLASS OF VARIATIONAL DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM

In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element method. Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation. The schemes studied in refs. [1], [3], [4] and [51 belong to the cllass.

On the Presentation of Social Class Difference in The Garden Party in terms of its Narrative Style and Settings Description

Katherine Mansfield was a predominant modernist writer who had written the well-known short story The Garden Party, which explicitly interprets the idea of social class difference between the upper class and the working class. This paper discusses its presentation of social class difference from two aspects, including the narrative style and the settings.

Short-Term Mindfulness Intervention on Adolescents’ Negative Emotion under Global Pandemic

Objective:In this research,we tried to explore how short-term mindfulness(STM)intervention affects adoles-cents’anxiety,depression,and negative and positive emotion during the COVID-19 pandemic.Design:10 classes were divided into experiment groups(5 classes;n=238)and control(5 classes;n=244)randomly.Hospital Anxi-ety and Depression Scale(HADS)and Positive and Negative Affect Schedule(PANAS)were used to measure par-ticipants’dependent variables.In the experiment group,we conducted STM practice interventions every morning in theirfirst class from March to November 2020.No interventions were conducted in the control group.Methods:Paired-sample t-tests were used to identify if a significant difference exists between every time point of the experimental and control groups.Repeated ANOVA and Growth Mixture Model(GMM)were used to analyze the tendency of positive and negative emotions,anxiety,and depression in the experimental group.Results and Conclusions:(1)With the intervention of STM,there was a significant decrease in negative emotions and an increase in positive emotions in the experimental group,whereas there were non-significant differences in the control group.(2)To explore the heterogeneity trajectories of dependent variables,we built a GMM and found there were two latent growth classes in the trajectories.(3)The results of the models showed their trajec-tories were downward,which meant that the levels of anxiety,depression,and negative emotions of participants decreased during the STM training period.Nonetheless,the score of positive affect showed upward in three loops of intervention,which indicated that the level of the participants’positive affect increased through the STM inter-vention.(4)This research indicated that STM should be given increasing consideration to enhance mental health during the worldwide outbreak of COVID-19.

A comparative study of acidic,basic,and reactive dyes adsorption from aqueous solution onto kaolin adsorbent:Effect of operating parameters,isotherms,kinetics,and thermodynamics

Various studies were reported for the evaluation of the adsorption performance of kaolin clay using single dye types.This paper aimed to evaluate the comparative adsorption capacity of prepared adsorbents from Ethiopian kaolin for different dye types(Basic Yellow 28(BY 28),Congo Red(CR),and Reactive Red 120(RR 120)).Because different dye classes may have a significant impact on the removal efficiency by the prepared adsorbent.Moreover,we intended to investigate the interaction effect of adsorbent-sorbate in the adsorption phenomenon for the three different class dyes.The adsorbents from kaolin clay were prepared via mechanical treatment,beneficiation,and calcination(700℃).The effect of operating parameters(pH,adsorbent dose,contact time,dye concentration,and adsorption temperature)was evaluated.before and after adsorption of the adsorbents were characterized using FTIR spectroscopy.Furthermore,adsorption isotherm,kinetic models,and the thermodynamic processes in the adsorption phenomenon were computed.The percentage removal efficiency of dyes was recorded as 92.08%,88.63%,and 73.33%for BY 28,CR,and RR 120 dyes,respectively at the experimental condition:adsorbent dosage=1 g/100 mL,solution pH=9(BY 28),and pH=3(CR,and RR 120),contact time=60 min,initial dyes concentrations=20 mg/L,and temperature=30℃.The adsorption of adsorbates onto kaolin adsorbents was well fitted with pseudo-second-order kinetics and Langmuir isotherm models.The thermodynamic parameters indicate that the adsorption process is spontaneous and exothermic for all dyes.The comparative percentage removal of,with the same operational parameters and kaolin adsorbent,was recorded as BY 28>CR>RR120 resulting from their surface charge and molecular size/structure dyes properties.We confirm that the adsorption at each operational parameter and peak intensity of FTIR spectra,before and after adsorption,revealed that the different dye types have varied removal efficiency onto the prepared kaolin adsorbent.This is due to that being dominantly influenced by the electrostatic interaction and steric effects at the surface of the sorbent and sorbate characteristics.We deduced that the kaolin clay used as an adsorbent is highly dependent on the dye types and their featured characteristics.