2T-PERIODIC SOLUTION FOR m ORDER NEUTRAL TYPEDIFFERENTIAL EQUATIONS WITH TIME DELAYS

Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Efficient removal of Al(Ⅲ)and P507 from high concentration MgCl_(2)solution based on in-situ reaction strategy

For a highly efficient recycling of a wastewater containing a high concentration of MgCl_2,Al(Ⅲ)and P507 were scheduled to be removed in advance.In this study,the in-situ removal of Al(Ⅲ)and P507 from a high concentration MgCl_(2)solution at different pH values and Al/P molar ratios was investigated.The results showed that P507 formed organic complexes of Al_x(OH)_y~(Z+)-P507 at pH of 2.0-4.0.At pH of 4.0-5.0,Al(Ⅲ)precipitated and transferred into Al(OH)_(3)with a flocculent amorphous morphology.Active sites on the Al(OH)_(3)surface enhanced the removal efficiency of P507.At pH of 6.0-6.5,Al(Ⅲ)and Mg(Ⅱ)formed layered crystalline Al(OH)_(3)and MgAl_2(OH)_(8with)small pore channels and fewer active sites,resulting in a reduced removal efficiency of P507.When the Al/P molar ratio exceeded 13 and the pH was between 4.0 and 5.0,the removal rates of both Al(Ⅲ)and P507 were higher than98%,while the concentration loss of Mg(Ⅱ)was only 0.2%-0.9%.

Extending the solid solution range of sodium ferric pyrophosphate:Off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)as a novel cathode for sodium‐ion batteries

Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P_(2)O_(7) unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.

CO2 Transformation at Controlled Temperature with Lithium Hydroxide Solution and Metallic Lithium

This paper presents a study on CO2 atmospheric transformation which was reacted directly with lithium hydroxide solution and metallic lithium. This solution was obtained through the reaction between metallic lithium and deionized water where hydrogen is produced and by exposing the metal at ambient conditions. In the transformation process, atmospheric CO2 gas reacts directly with LiOH solution, in both cases, the CO2 transformation kinetics was different. For this purpose, reactions between CO2 and LiOH solution were carried out under controlled temperature and the second process only with metallic lithium, which was exposed at room temperature, however, in these two processes lithium carbonate oxide was formed and identified. According to the results, the efficiency in CO2 transformation is a function of temperature value which was variable until completely obtaining the by-product, its XRD characterization indicated the formation only of Li2CO3 in both procedures. Under laboratory conditions lithium compounds selectively reacted with CO2. In the same way, there is an alternative procedure to obtain LiOH and Li2CO3 for different applications in various areas.

MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE FRACTIONAL SCHR?DINGER-POISSON SYSTEM WITH DOUBLY CRITICAL GROWTH

In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.

Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.

Exact Traveling Wave Solutions to Phi-4 Equation and Joseph-Egri (TRLW) Equation and Calogro-Degasperis (CD) Equation by Modified (G'/G2)-Expansion Method

In this study, we will introduce the modified (G'/G2)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.

Selective recovery of lead from zinc oxide dust with alkaline Na_2EDTA solution

The selective recovery of lead from the zinc oxide dust using an alkaline Na2EDTA solution was investigated. The effects of temperature, leaching time, Na2EDTA concentration and initial NaOH concentration on the leaching rates of lead and zinc were studied. The following optimized leaching conditions were obtained： liquid-to-solid ratio 5：1 mL/g, stirring speed 650 r/min, Na2EDTA concentration 0.12 mol/L, initial NaOH concentration 0.5 mol/L, leaching temperature 70 ℃, leaching time 120 min. Under the optimized conditions, the average leaching rates of lead, zinc, fluoride and chloride are 89.92%, 0.94%, 62.84% and 90.02%, respectively. The filtrate was used to electrowin lead powders. The average current efficiency of electrowinning is about 93% and lead content is higher than 98% under the conditions of temperature of 60 ℃, current density of 200 A/m2, H3PO4 concentration of 1.5 g/L, and lead ion concentration of above 5 g/L. The consumption of Na2EDTA and the direct current are about respectively 0.218 kg and 0.958 kW·h for per kilogram of lead powder.

Removal of S^(2-) ion from sodium aluminate solutions with sodium ferrite

The synthesis of sodium ferrite and its desulfurization performance in S2 -bearing sodium aluminate solutions were investigated. The thermodynamic analysis shows that the lowest temperature is about 810 K for synthesizing sodium ferrite by roasting the mixture of ferric oxide and sodium carbonate. The results indicate that the formation process of sodium ferrite can be completed at 1173 K for 60 min, meanwhile raising temperature and reducing NazCO3 particle size are beneficial to accelerating the formation of sodium ferrite. Sodium ferrite is an efficient desulfurizer to remove the S2- in aluminate solution, and the desulfurization rate can reach approximately 70% at 373 K for 60 min with the molar ratio of iron to sulfur of 1：1-1.5：1. Furthermore, the desulfurization is achieved by NaFeS2·2H2O precipitation through the reaction of Fe（OH）4 and S^2- in aluminate solution, and the desulfurization efficiency relies on the Fe（OH）4^- generated by dissolving sodium ferrite.

Influence of solution treatment on microstructure and properties of in-situ Mg_2Si/AZ91D composites

The influence of solution treatment on the microstructure and properties of Mg2Si/AZ91D composites fabricated from Mg-SiO2 system via in-situ processing method was investigated.The results show that coarse Chinese script shape Mg2Si phases can be formed by adding SiO2 into AZ91D magnesium alloy with Si content up to 1.5% of the alloy melt.During solution treatment,the morphology and distribution of the coarse Chinese script shape Mg2Si phases are modified.Meanwhile,the β-Mg17Al12 phase is dissolved into the magnesium matrix.With increasing holding time,the coarse Mg2Si phases tend to dissolve,break and spheroidize.After solution treatment at 420 ℃ for 16 h,Mg2Si phases become the finest and relatively well-distributed phase.The tensile strength and elongation are increased by 14.9% and 38.9%,respectively.It is believed that the Mg2Si phases continuously dissolve and break,and finally the spheroidized Mg2Si particles are obtained due to the interface tension of Mg2Si/Mg interface.

Measurements of zinc oxide solubility in sodium hydroxide solution from 25 to 100 °C

The solubility of zinc oxide in sodium hydroxide solution was measured in a closed polytetrafluoroethylene vessel from 25 to 100 ℃. The ZnO solubility was determined by employing the method of isothermal solution saturation. The results show that only ZnO solid exists in the equilibrium state in the low concentration alkali regions, and the solubility of zinc oxide is almost invariable with temperature. With the increase of alkali concentration, equilibrium solid turns from ZnO to NaZn（OH）3 suddenly, this mutation is called invariant point. The alkali concentration of the invariant points increases with increasing temperature, but the solubility of NaZn（OH）3 decreases with increasing alkali concentration at the same temperature. At the same Na2O concentration, the higher the temperature is, the higher the solubility of NaZn（OH）3 is.

Fabrication of Cu_2O@Cu_2O core-shell nanoparticles and conversion to Cu_2O@Cu core-shell nanoparticles in solution

Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive ascorbic acid (AA) in air at room temperature, which was an interesting phenomenon. The features of the two kinds of NPs were characterized by XRD, TEM and extinction spectra. Cu2O@Cu NPs with different shell thicknesses showed wide tunable optical properties for the localized surface plasmon (LSP) in metallic Cu. But Cu2O@Cu2O NPs did not indicate this feature. FTIR results reveal that Cu+ ions on the surface of Cu2O shell coordinate with N and O atoms in PVP and are further reduced to metallic Cu by excessive AA and then form a nucleation site on the surface of Cu2O nanocrystalline. PVP binds onto different sites to proceed with the reduction utill all the Cu sources in Cu2O shell are completely assumed.

Synthesis of nanostructured Li_2FeSiO_4/C cathode for lithium-ion battery by solution method

Nanosphere-like Li2FeSiO4/C was synthesized via a solution method using sucrose as carbon sources under a mild condition of time-saving and energy-saving, followed by sintering at high temperatures for crystallization. The amount of carbon in the composite is less than 10% （mass fraction）, and the X-ray diffraction result confirms that the sample is of pure single phase indexed with the orthorhombic Pmn21 space group. The particle size of the Li2FeSiO4/C synthesized at 700 °C for 9 h is very fine and spherical-like with a size of 200 nm. The electrochemical performance of this material, including reversible capacity, cycle number, and charge-discharge characteristics, were tested. The cell of this sample can deliver a discharge capacity of 166 mA-h/g at C/20 rate in the first three cycles. After 30 cycles, the capacity decreases to 158 mA-h/g, and the capacity retention is up to 95%. The results show that this method can prepare nanosphere-like Li2FeSiO4/C composite with good electrochemical performance.

Solution广泛多孔钛涂层长柄假体结合钢丝环扎固定治疗股骨头置换术后VancouverB2型假体周围骨折的中期随访

背景：股骨头置换术后Vancouver B2型假体周围骨折多伴有假体松动，患者年龄大，并存疾病多，骨质条件差，围手术期处理及手术技术难度大，并发症发生率高。 目的：评价Solution广泛多孔钛涂层长柄假体结合钢丝环扎固定治疗股骨头置换术后Vancouver B2型假体周围骨折的中期疗效。 方法：回顾分析2008年1月至2010年12月我科收治的14例股骨头置换术后Vancouver B2型假体周围骨折患者的临床资料，其中男6例，女8例，年龄66-80岁，平均70.3岁。所有患者均采用骨折切开复位钢丝环扎固定结合Solution股骨柄进行翻修手术。末次随访时进行Harris髋关节评分（术前由于骨折未能进行Harris髋关节评分）；术前，术后3、6、12个月及末次随访时摄X线片，用于评价骨折复位及愈合，假体初始固定及中期生存情况。 结果：共16例患者，1例术后3年死于肺癌，1例失访，14例获得随访，随访时间3-5年，平均4.2年。末次随访时Harris评分88.7分。X线显示骨折复位，股骨柄超过骨折远端的固定长度超过5 cm，与股骨压配良好。骨折愈合时间3-6个月，平均（3.8＆#177;1.3）个月。末次随访时未见股骨柄松动、下沉。无感染、深静脉血栓形成和肺栓塞。 结论：Solution股骨柄结合钢丝环扎固定治疗股骨头置换术后Vancouver B2型假体周围骨折中期疗效好，其远期结果有待于进一步的随访。

CeO_(2)-Ps-LaCoO_(3)/Al_(2)O_(3)的制备及其对高浓度有机废水的臭氧催化降解研究

为有效降解高浓度造纸废水有机物,通过电化学沉积法分别在磷酸盐中性缓冲溶液和纯水中制得CeO_(2)-Ps-LaCoO_(3)/Al_(2)O_(3)和CeO_(2)-LaCoO_(3)/Al_(2)O_(3)。通过对CeO_(2)-Ps-LaCoO_(3)/Al_(2)O_(3)、CeO_(2)-LaCoO_(3)/Al_(2)O_(3)以及LaCoO_(3)/Al_(2)O_(3)进行XRD、SEM、析氧过电位和电阻抗等物性表征发现,CeO_(2)-Ps-LaCoO_(3)/Al_(2)O_(3)具有更强催化氧化性及稳定性。对高浓度造纸废水臭氧催化氧化降解3 h后,CeO_(2)-Ps-LaCoO_(3)/Al_(2)O_(3)对废水COD的降解率为76.5%,而相同条件下CeO_(2)-LaCoO_(3)/Al_(2)O_(3)和LaCoO_(3)/Al2O_(3)的化学需氧量(COD)降解率分别为68.5%和63.5%。

CaCl_(2)和MgCl_(2)及其复合溶液制备α-半水石膏

为提高磷石膏的利用率和附加值,采用常压水热合成法以磷石膏为主要原材料制备α-半水石膏材料,主要研究不同质量分数的CaCl_(2)、MgCl_(2)及其复合溶液对磷石膏常压水热制备α-半水石膏脱水速率、物相组成和微晶形貌的影响。研究发现,磷石膏在95℃的CaCl_(2)溶液、MgCl_(2)溶液及CaCl_(2)-MgCl_(2)复合溶液中均可脱水转晶生成α-半水石膏。在CaCl_(2)溶液和MgCl_(2)溶液中,随着盐溶液浓度的增加,α-半水石膏的生成速率加快,其中经质量分数为35%的CaCl_(2)溶液反应4 h后或质量分数为25%的MgCl_(2)溶液反应1 h后,磷石膏可完全反应成α-半水石膏。在CaCl_(2)-MgCl_(2)复合溶液中,随着MgCl_(2)溶液浓度的增加,磷石膏的脱水转化速率逐渐加快,当CaCl_(2)质量分数≤19%和MgCl_(2)质量分数≥11%时,磷石膏水热反应1 h即可形成颗粒分布较为完整的α-半水石膏。

时效处理对Cu-Y_(2)O_(3)-Ti复合材料组织及性能的影响

以Cu、Y、Ti和CuO粉末为原料,采用机械合金化(MA)和热还原的方法制备了Cu-Y_(2)O_(3)-Ti复合粉末。然后经放电等离子烧结(SPS)技术制备了Cu-Y_(2)O_(3)-Ti复合材料,并对材料进行了900℃固溶1 h和不同温度时效2 h的处理。采用光学显微镜(OM)、扫描电镜(SEM)、X射线衍射仪(XRD)、能谱仪(EDS)、拉伸试验和导电率测量仪等研究了不同温度时效处理对Cu-Y_(2)O_(3)-Ti复合材料组织及性能的影响。结果表明:随着时效温度的升高,Cu-Y_(2)O_(3)-Ti复合材料的晶粒和第二相尺寸增大,导电率降低,最大应变和抗拉强度先增大后减小。Cu-Y_(2)O_(3)-Ti复合材料经900℃固溶1 h+400℃时效2 h后,综合性能最优,其具有良好塑性的同时,抗拉强度和导电率分别达到326.4 MPa和73.0%IACS。

新标09CrCuSb耐酸钢的耐50%H_(2)SO_(4)腐蚀性能

通过电化学测试和全浸腐蚀试验,研究了不同温度(25,50,60,70℃)条件下新标09CrCuSb耐酸钢在50%H_(2)SO_(4)溶液中的腐蚀行为。结果表明:随着温度从25℃升至70℃,新标09CrCuSb钢的腐蚀速率整体呈现增大趋势,在70℃时,腐蚀速率达到最高,为2.70 g/(m^(2)·h),这与随温度升高,腐蚀产物中具有保护性作用的Fe_(3)O_(4)含量减少,无保护作用的FeSO_(4)·H_(2)O含量增加以及锈层中微孔变化有关。另外,由于新标调整了09CrCuSb钢中Cu、Mo、Sn、Sb、W等元素的含量,与旧标09CrCuSb钢相比,阳极维钝电流密度J维钝降低,同等温度条件下,新标09CrCuSb钢的耐蚀性得到较大改善。