Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.

Direct capture and separation of CO_(2) from air

Direct air capture(DAC)has attracted increasing interest and investment over the past few years.There are a fast-growing number of companies that entered the field and demonstrated DAC carbon removal setups and potential.However,current DAC methods are still based on solid absorbents or alkali solutions approaches which have low capture efficiency and low energy efficiency.This highlight proposed a promising CO_(2) capture technology,an electric energy driven closed-loop system for the direct removal of CO_(2) from ambient air which are based on two individual technologies:Polyam-N-Cu hybrid system promoted CO_(2) capture with ocean as anthropogenic CO_(2) sink and a chloride-mediated electrochemical pH swing system to remove CO_(2) from oceanwater.

The influence of resistance exercise training prescription variables on skeletal muscle mass,strength,and physical function in healthy adults:An umbrella review

Purpose:The aim of this umbrella review was to determine the impact of resistance training(RT)and individual RT prescription variables on muscle mass,strength,and physical function in healthy adults.Methods:Following Preferred Reporting Items for Systematic Reviews and Meta-Analyses(PRISMA)guidelines,we systematically searched and screened eligible systematic reviews reporting the effects of differing RT prescription variables on muscle mass(or its proxies),strength,and/or physical function in healthy adults aged>18 years.Results:We identified 44 systematic reviews that met our inclusion criteria.The methodological quality of these reviews was assessed using A Measurement Tool to Assess Systematic Reviews;standardized effectiveness statements were generated.We found that RT was consistently a potent stimulus for increasing skeletal muscle mass(4/4 reviews provide some or sufficient evidence),strength(4/6 reviews provided some or sufficient evidence),and physical function(1/1 review provided some evidence).RT load(6/8 reviews provided some or sufficient evidence),weekly frequency(2/4 reviews provided some or sufficient evidence),volume(3/7 reviews provided some or sufficient evidence),and exercise order(1/1 review provided some evidence)impacted RT-induced increases in muscular strength.We discovered that 2/3 reviews provided some or sufficient evidence that RT volume and contraction velocity influenced skeletal muscle mass,while 4/7 reviews provided insufficient evidence in favor of RT load impacting skeletal muscle mass.There was insufficient evidence to conclude that time of day,periodization,inter-set rest,set configuration,set end point,contraction velocity/time under tension,or exercise order(only pertaining to hypertrophy)influenced skeletal muscle adaptations.A paucity of data limited insights into the impact of RT prescription variables on physical function.Conclusion:Overall,RT increased muscle mass,strength,and physical function compared to no exercise.RT intensity(load)and weekly frequency impacted RT-induced increases in muscular strength but not muscle hypertrophy.RT volume(number of sets)influenced muscular strength and hypertrophy.

The flow behavior of droplet adsorption on a liquid-liquid interface accompanied by cross-linking reaction and phase separation in a microchannel

The adsorption process of droplets on the liquid-liquid interface and phase separation process can regulate the spatial distribution of the fluid system,which are crucial for chemical engineering.However,the cross-linking reaction,which is widely used in the field of polymers,can change the physical properties of the fluids and affect the flow behavior accordingly.A configuration of microchannels is designed to conveniently generate uniform droplets in one phase of the parallel flow.The flow behavior of the adsorption process of sodium alginate droplets on the liquid-liquid interface is investigated,and the subsequent process of phase separation is studied.In the process of droplet adsorption,the crosslinking reaction occurs synchronously,which makes the droplet viscosity and the elasticity modules of the droplet surface increase,thus affecting the dynamics of the adsorption process and the equilibrium shape of the droplet.The variation of the adsorption length with time is divided into three stages,which all conform to power law relationship.The exponents of the second and third stages deviate from the results of the Tanner's law.The flow pattern maps of droplet adsorption and phase separation are drawn,and the operating ranges of complete adsorption and complete separation are provided.This study provides a theoretical basis for further studying the flow behavior of droplets with cross-linking reaction in a microchannel.

Environmental,economic and exergy analysis of separation of ternary azeotrope by variable pressure extractive distillation based on multi-objective optimization

In this work,the ternary azeotrope of tert-butyl alcohol/ethyl acetate/water is separated by extractive distillation(ED)to recover the available constituents and protect the environment.Based on the conductor like shielding model and relative volatility method,ethylene glycol was selected as the extractant in the separation process.In addition,in view of the characteristic that the relative volatility between components changes with pressure,the multi-objective optimization method based on nondominated sorting genetic algorithm II optimizes the pressure and the amount of solvent cooperatively to avoid falling into the optimal local solution.Based on the optimal process parameters,the proposed heat-integrated process can reduce the gas emissions by 29.30%.The heat-integrated ED,further coupled with the pervaporation process,can reduce gas emission by 42.36%and has the highest exergy efficiency of 47.56%.In addition,based on the heat-integrated process,the proposed two heat pump assisted heat-integrated ED processes show good economic and environmental performance.The double heat pump assisted heat-integrated ED can reduce the total annual cost by 28.78%and the gas emissions by 55.83%compared with the basis process,which has a good application prospect.This work provides a feasible approach for the separation of ternary azeotropes.

Flotation separation of scheelite from calcite using luteolin as a novel depressant

This paper proposes luteolin(LUT)as a novel depressant for the flotation-based separation of scheelite and calcite in a sodium oleate(NaOL)system.The suitability of LUT as a calcite depressant is confirmed through micro-flotation testing.At pH=9,with LUT concentration of 50 mg·L^(-1) and NaOL concentration of 50 mg·L^(-1),scheelite recovery reaches 80.3%.Calcite,on the other hand,exhibits a recovery rate of 17.6%,indicating a significant difference in floatability between the two minerals.Subsequently,the surface modifica-tions of scheelite and calcite following LUT treatment are characterized using adsorption capacity testing,Zeta potential analysis,Fourier transform infrared spectroscopy(FT-IR),X-ray photoelectron spectroscopy(XPS),and atomic force microscopy(AFM).The study in-vestigates the selective depressant mechanism of LUT on calcite.Adsorption capacity testing and Zeta potential analysis demonstrate sub-stantial absorption of LUT on the surface of calcite,impeding the further adsorption of sodium oleate,while its impact on scheelite is min-imal.FT-IR and XPS analyses reveal the selective adsorption of LUT onto the surface of calcite,forming strong chemisorption bonds between the hydroxyl group and calcium ions present.AFM directly illustrates the distinct adsorption densities of LUT on the two miner-al types.Consequently,LUT can effectively serve as a depressant for calcite,enabling the successful separation of scheelite and calcite.

Mid-infrared Period-Luminosity Relations of Gaia DR3 Long Period Variables

Long period variable(LPV)stars are very promising distance indicators in the infrared bands.We selected asymptotic giant branch(AGB)stars in the Large and Small Magellanic Cloud(LMC and SMC)from the Gaia Data Release 3 LPV catalog,and classified them into oxygen-rich(O-rich)and carbon-rich(C-rich)AGB stars.Using the Wide-field Infrared Survey Explorer database,we determined the W1-and W2-band period-luminosity relations(PLRs)for each pulsation-mode sequence of AGB stars.The dispersion of the PLRs of O-rich AGB stars in sequences C'and C is relatively small,around 0.14 mag.The PLRs of LMC and SMC are consistent in each sequence.In the W2 band,the PLR of large-amplitude C-rich AGB stars is steeper than that of small-amplitude C-rich AGB stars,due to their more circumstellar dust.By two methods,we find that some PLR sequences of O-rich AGB stars in the LMC are dependent on metallicity.The coefficients of the metallicity effect areβ=-0.533±0.213 mag dex~1andβ=-0.767±0.158 mag dex~1for sequence C in W1 and W2 bands,respectively.The significance of the metallicity effect in W1 band for the four sequences is 2.2-3.5σ.Both of these imply that distance measurements using O-rich Mira may need to take the metallicity effect into account.

Comment on:Recurrence after spontaneous separation of epiretinal membrane in a young woman:a case report

Dear Editor,Herein,we provide a commentary on the recently published article by Zeng QZ and Yu WZ[1].This case report provides interesting novel insights into the recurrence of epiretinal membrane(ERM)following self-separation in a young patient.In addition to the study,we have been investigating spontaneous ERM release for many years and have recently published a related paper[2].

Flotation separation of brucite and calcite in dodecylamine system enhanced by regulator potassium dihydrogen phosphate

To achieve efficient flotation separation of brucite and calcite,flotation separation experiments were conducted on two minerals using dodecylamine(DDA)as the collector and potassium dihydrogen phosphate(PDP)as the regulator.The action mechanism of DDA and PDP was explored through contact angle measurement,zeta potential detection,solution chemistry calculation,FTIR analysis,and XPS detection.The flotation results showed that when DDA dosage was 35 mg/L and PDP dosage was 40 mg/L,the maximum floating difference between brucite and calcite was 79.81%,and the selectivity separation index was 6.46.The detection analysis showed that the main dissolved component HPO_(4)^(2−)of PDP is selectively strongly adsorbed on the Ca site on the surface of calcite,promoting the adsorption of the main dissolved component RNH_(3)^(+)of DDA on calcite surface,while brucite is basically not affected by PDP.Therefore,PDP is an effective regulator for the reverse flotation separation of brucite and calcite in DDA system.

Preparation of a zeolite-palladium composite membrane for hydrogen separation:Influence of zeolite film on membrane stability

With the development of hydrogen energy,palladium-based membranes have been widely used in hydrogen separation and purification.However,the poor chemical stability of palladium composite membranes limits their commercial applications.In this study,a zeolite-palladium composite membrane with a sandwich-like structure was obtained by using a TS-1 zeolite film grown on the surface of palladium membrane.The membrane microstructure was characterized by SEM and EDX.The effects of the TS-1 film on the hydrogen permeability and stability of palladium composite membrane were investigated in details.Benefited from the protection of the TS-1 zeolite film,the stability of palladium composite membrane was enhanced.The results indicate that the TS-1-Pd composite membrane was stable after eight cycles of the temperature exchange cycles between 773 K and 623 K.Especially,the loss of hydrogen permeance for TS-1-Pd composite membrane was much smaller than that of the pure palladium membrane when the membrane was tested in the presence of C3H6atmosphere.It indicated that the TS-1-Pd composite membrane had better chemical stability in comparison with pure palladium membrane,owing to its sandwich-like structure.This work provides an efficient way for the deposition of zeolite film on palladium membrane to enhance the membrane stability.

Role of tannin pretreatment in flotation separation of magnesite and dolomite

Flotation separation of magnesite and its calcium-containing carbonate minerals is a difficult problem.Recently,new regulat-ors have been proposed for magnesite flotation decalcification,although traditional regulators such as tannin,water glass,sodium carbon-ate,and sodium hexametaphosphate are more widely used in industry.However,they are rarely used as the main regulators in research because they perform poorly in magnesite and dolomite single-mineral flotation tests.Inspired by the limonite presedimentation method and the addition of a regulator to magnesite slurry mixing,we used a tannin pretreatment method for separating magnesite and dolomite.Microflotation experiments confirmed that the tannin pretreatment method selectively and largely reduces the flotation recovery rate of dolomite without affecting the flotation recovery rate of magnesite.Moreover,the contact angles of the tannin-pretreated magnesite and dolomite increased and decreased,respectively,in the presence of NaOl.Zeta potential and Fourier transform infrared analyses showed that the tannin pretreatment method efficiently hinders NaOl adsorption on the dolomite surface but does not affect NaOl adsorption on the magnesite surface.X-ray photoelectron spectroscopy and density functional theory calculations confirmed that tannin interacts more strongly with dolomite than with magnesite.

Ferric ion-triggered surface oxidation of galena for efficient chalcopyrite-galena separation

The efficient separation of chalcopyrite(CuFeS2)and galena(PbS)is essential for optimal resource utilization.However,find-ing a selective depressant that is environmentally friendly and cost effective remains a challenge.Through various techniques,such as mi-croflotation tests,Fourier transform infrared spectroscopy,scanning electron microscopy(SEM)observation,X-ray photoelectron spec-troscopy(XPS),and Raman spectroscopy measurements,this study explored the use of ferric ions(Fe^(3+))as a selective depressant for ga-lena.The results of flotation tests revealed the impressive selective inhibition capabilities of Fe^(3+)when used alone.Surface analysis showed that Fe^(3+)significantly reduced the adsorption of isopropyl ethyl thionocarbamate(IPETC)on the galena surface while having a minimal impact on chalcopyrite.Further analysis using SEM,XPS,and Raman spectra revealed that Fe^(3+)can oxidize lead sulfide to form compact lead sulfate nanoparticles on the galena surface,effectively depressing IPETC adsorption and increasing surface hydrophilicity.These findings provide a promising solution for the efficient and environmentally responsible separation of chalcopyrite and galena.

A novel molybdenite depressant for efficient selective flotation separation of chalcopyrite and molybdenite

A novel small molecule depressant(M-DEP)was used to separate chalcopyrite and molybdenite via flotation.The results showed that M-DEP had an excellent selective depression on molybdenite,while had little effect on the flotation of chalcopyrite.The adsorption capacity of M-DEP on the surface of molybdenite was greater than that on chalcopyrite surface.The adsorption of M-DEP reduced the floatability of molybdenite and had less effect on the floatability of chalcopyrite,which was due to its different adsorption modes on the surface of the two minerals.Furthermore,the interaction between chalcopyrite and M-DEP was mainly chemical interaction,and almost all of the adsorbed M-DEP molecules were removed and replaced by sodium butyl xanthate(SBX).By contrast,hydrophobic interaction was the main way in which M-DEP was adsorbed on the molybdenite surface with little chemical interaction,which was less interfered by SBX addition.Therefore,M-DEP had a super selective depression on molybdenite.The study provided a novel depressant and approach for the deep separation of chalcopyrite and molybdenite via flotation.

Influences of fractional separation on the structure and reactivity of wheat straw cellulose for producing 5-hydroxymethylfurfural

High-efficient production of 5-hydroxymethylfurfural(HMF),a“sleeping giant”in sustainable chemistry,from cellulose depends significantly on the effective separation of cellulose from lignocellulosic biomass.Herein,we report the fractional separation of wheat straw cellulose(WSC)from wheat straw under solvothermal conditions using a mixed solvent of γ-valerolactone(GVL)and H_(2)O as the separating solvent,wherein the impacts of fractional separation parameters(solvent composition,temperature,and time)on removals of lignin and hemicellulose as well as purity and recovery of cellulose were studied by a Box-Behnken Design of response surface method.The optimization of the solvothermal parameters enabled an optimal fractional separation condition(V_(GVL):~60.0%,T:205℃,t:~1.7 h)that led to a higher purity(89.4%)and recovery(86.7%)of cellulose in WSC.A further correlation of the removals of lignin and hemicellulose as well as purity and recovery of cellulose with the yield of HMF excluded an independent influence of the above factors.Instead,a comprehensive contribution of high fractional separation efficiency(defined as the product of cellulose purity and recovery)and low crystallinity of WSC was found to improve the HMF yield.However,the heat-and freeze-dryings of WSC after the solvothermal separation were found to lower the HMF molar yield because it re-improved the crystallinity of WSC.A high HMF molar yield of 58.6%was achieved after reacting wet-WSC in a mixed solvent of 1,4-dioxane and H_(2)O at 180℃for 20 min,which was 1.5 fold higher than that from microcrystalline cellulose.This work highlights the importance of enhancing the fractional separation efficiency of cellulose from lignocellulosic biomass while avoiding the drying process for future HMF biorefinery.

Responses of Annual Variability of Vegetation NPP to Climate Variables Using Satellite Techniques in Gadarif State, Sudan

Plants play an essential role in matter and energy transformations and are key messengers in the carbon and energy cycle. Net primary productivity (NPP) reflects the capability of plants to transform solar energy into photosynthesis. It is very sensible for factors affecting on vegetation variability such as climate, soils, plant characteristics and human activities. So, it can be used as an indicator of actual and potential trend of vegetation. In this study we used the actual NPP which was derived from MODIS to assess the response of NPP to climate variables in Gadarif State, from 2000 to 2010. The correlations between NPP and climate variables (temperature and precipitation) are calculated using Pearson’s Correlation Coefficient and ordinary least squares regression. The main results show the following 1) the correlation Coefficient between NPP and mean annual temperature is Somewhat negative for Feshaga, Rahd, Gadarif and Galabat areas and weakly negative in Faw area;2) the correlation Coefficient between NPP and annual total precipitation is weakly negative in Faw, Rahd and Galabat areas and somewhat negative in Galabat and Rahd areas. This study demonstrated that the correlation analysis between NPP and climate variables (precipitation and temperature) gives reliably result of NPP responses to climate variables that is clearly in a very large scale of study area.

Boosting kinetic separation of ethylene and ethane on microporous materials via crystal size control

The adsorptive separation of C_(2)H_(4)and C_(2)H_(6),as an alternative to distillation units consuming high energy,is a promising yet challenging research.The great similarity in the molecular size of C_(2)H_(4)and C_(2)H_(6)brings challenges to the regulation of adsorbents to realize efficient dynamic separation.Herein,we reported the enhancement of the kinetic separation of C_(2)H_(4)/C_(2)H_(6)by controlling the crystal size of ZnAtzPO_(4)(Atz=3-amino-1,2,4-triazole)to amplify the diffusion difference of C_(2)H_(4)and C_(2)H_(6).Through adjusting the synthesis temperature,reactant concentration,and ligands/metal ions molar ratio,ZnAtzPO4 crystals with different sizes were obtained.Both single-component kinetic adsorption tests and binary-component dynamic breakthrough experiments confirmed the enhancement of the dynamic separation of C_(2)H_(4)/C_(2)H_(6)with the increase in the crystal size of ZnAtzPO_(4).The separation selectivity of C_(2)H_(4)/C_(2)H_(6)increased from 1.3 to 98.5 with the increase in the crystal size of ZnAtzPO_(4).This work demonstrated the role of morphology and size control of adsorbent crystals in the improvement of the C_(2)H_(4)/C_(2)H_(6)kinetic separation performance.

A novel surfactant N-hydroxy-9,10-epoxy group-octadecanamide:Part II.Its synthesis and application in flotation separation of spodumene and albite

A novel hydroxamic acid,N-hydroxy-9,10-epoxy group-octadecanamide(N-OH-9,10-O-ODA),was synthesised by modifying the structure of oleic acid.The carboxyl group of oleic acid was converted into an N-hydroxy amide group,and an epoxy group was introduced into its structure.N-OH-9,10-O-ODA was used as a novel collector in the flotation separation of spodumene from one of its associated gangue minerals,specifically albite.N-OH-9,10-O-ODA exhibits remarkable selectivity,with a stronger affinity for collecting spodumene particles compared to albite particles.Zeta potential measurements and X-ray photoelectron spectroscopic analysis reveal that the adsorption quantity of N-OH-9,10-O-ODA on spodumene surface is comparable to that on albite surface.First-principles calculations demonstrate the diverse adsorption configurations of N-OH-9,10-O-ODA on surfaces of spodumene and albite,leading to its distinct collecting abilities for spodumene and albite particles.

Numerical Simulation Study of Oil-Water Emulsion Separation in an Ultrasonic Field:Effect of Coupling between Acoustic and Flow Field Parameters

In this study,the separation and coalescence of oil-in-water emulsions are explored in an ultrasonic field using the lattice Boltzmann method.By simulating the propagation of ultrasonic waves,this study focuses on examining the effects of acoustic wave frequency,the ratio of oil to water components,and the aspect ratio of the boundary on the emulsification and separation processes of oil-water mixtures.The following conclusions are drawn.①Frequency affects the speed of oil droplet separation,leading to an increase in droplet size over time.Larger droplets are found near the source,while smaller droplets are distributed throughout the wave web.②As the boundary aspect ratio increases,the emulsification efficiency of the droplets weakens,and the system takes longer to stabilize.③Emulsions with a higher component of oil can better resist acoustic waves.④At the same acoustic frequency,longer wavelength ultrasonic fields promote the formation of uniformly distributed,smaller oil droplets,which is beneficial to the storage of emulsions.These numerical simulation results offer insights for optimizing conditions for oil-in-water separation and serve as a numerical reference for the study of oil-in-water emulsion separation in ultrasonic environments.

Optimizing extractants selection for efficient separation of phenols and nitrogen-containing heteroaromatics using hydrogen bond interaction strategies

Focusing on the use of imidazolium ionic liquids and quaternary ammonium salts-based deep eutectic solvents for the separation of phenols and nitrogen-containing heteroaromatics,the role of heteroaromatics as specific sites for hydrogen bond-based separation has been investigated.These environmentally friendly solvents are known for their ability to form hydrogen bonds with heteroatoms,a key aspect in separation processes.We quantified the hydrogen bond interaction energy to reach the threshold energy for efficient O-and N-heteroaromatics separation.This article provides an in-depth study of the structural nuances of different hydrogen bonding sites and their affinity properties while conducting a comparative evaluation of the separation efficiency of ionic liquids and deep eutectic solvents from a thermodynamic perspective.Results showed that phenols with dual hydrogen bonding recognition sites were easier to separate than nitrogen-containing heteroaromatics.Imidazolium ionic liquids were more suitable for the extraction of nonbasic nitrogen-containing heteroaromatics,and quaternary ammonium salts-based deep eutectic solvents are more effective for phenols and basic nitrogen-containing heteroaromatics,which was confirmed by Fourier transform infrared spectroscopy and empirical tests.Therefore,this study provides a theoretical basis for the strategy design and selection of extractants for the efficient separation of O-and N-containing aromatic compounds.

A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM

By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.