Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations

~~Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations@宋明辉 @刘明珠 @B S SIDIBE~~nal,2000:111. [6]BELLENA ,JACKIEWICZZ ,ZENNAROM .Stabilityanalysisofone stepmethodsforneutraldelaydifferentialequations[J].NumerMath,1988,52:605619. [7]BRAYTONRK ,WILLOUGHBYRA .Onthenumericalintegrationofasymmetricsys temofadifference differentialequation[J].JMathAnalAppl,1967,18:182189. [8]DEKKERK ,VERWERJG .Stability…     

A parallel method for numerical solution of delay differential equations

0　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｉｓｐａｐｅｒｄｅａｌｓｗｉｔｈｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ (ＤＤＥｓ) :ｙ′(ｔ) =ｆ(ｙ(ｔ) ,ｙ(ｔ-τ) ) ｔ≥ｔ0ｙ(ｔ) =φ(ｔ)　　　　　　 ｔ≤ｔ0( 1)　　Ｗｅａｓｓｕｍｅｔｈａｔ ( 1)ｉｓａｓｃａｌａｒｅｑｕａｔｉｏｎ ,ｔｈｉｓｈａｓａｎａｄｖａｎｔａｇｅｔｈａｔｗｅｃａｎａｖｏｉｄｔｅｎｓｏｒｐｒｏｄｕｃｔｓｉｎｏｕｒｆｏｒｍｕ ｌａｔｉｏｎ .ｆ ,φｄｅｎｏｔｅｇｉｖｅｎｆｕｎｃｔｉｏｎｓａｎｄ…     

Geometric representation for numerical stability region of linear multistep methods

0　ＩＮＴＲＯＤＵＣＴＩＯＮＣｏｎｓｉｄｅｒｔｈｅｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ(ＤＤＥ)ｏｆｔｈｅｆｏｒｍ :ｙ′(ｔ) =ａｙ(ｔ) +ｂｙ(ｔ- 1) ,ｔ>0 ,ｙ(ｔ) =ｇ(ｔ) ,　 - 1≤ｔ≤ 0 ,ａ ,ｂ∈Ｒ .(1)ＵｓｉｎｇＬａｐｌａｃｅｔｒａｎｓｆｏｒｍａｔｉｏｎ ,ｗｅａｒｅｌｅｄｔｏｔｈｅｑｕａｓｉ ｐｏｌｙｎｏｍｉａｌｃｈａｒａｃｔｅｒｉｓｔｉｃｅｑｕａｔｉｏｎａｓｓｏｃｉａｔｅｄｗｉｔｈ (1)ａｓ ,λ=ａ+ｂｅｘｐ(-λ) . (2 )Ｓｔａｂｉｌｉｔｙｃｒｉｔｅｒｉａｆｏｒｓｙｓｔｅｍｓｗ…     

Stability analysis of linear multistep methods for neutral delay differential equations

0　INTRODUCTIONWeconsidertheDDEsoftheformy′(t) =f(t,y(t) ,y(t-τ) ,y′(t-τ) )　t≥ 0 ,y(t) =g(t)　t≤t0 ,(1)whichiscalledneutraldelaydifferentialequation .ThedifferencebetweenDDEsandNDDEsisthepresenceoftheneutraltermy′(t-τ)inthelattercase .Inthispa perweconsiderthestabilityanalysisoflineartestequationy′(t) =ay(t) +by(t -τ) +cy′(t-τ) ,t≥ 0 ,y(t) =g(t) ,t∈ [-τ ,0 ],(2 )wherea ,b ,c∈witha≠-bandg(t) ,y(t) ∈ .Fortheaboveneutraldelaydifferentialequations (ND DEs) ,onecanf…     

Treatment Methods for the Quality Improvement of Recycled Concrete Aggregate (RCA)–A Review

For the purpose of providing references for further research and practical application about the quality improvement of RCA,in this paper,various treatment methods were firstly classified into four categories:removing old mortar (OM),strengthening OM,multi-stage mixing methods,and combination methods.Thereafter,the improvement mechanisms and important conclusions of various treatment methods were elucidated and summarised respectively.In the section of discussion,the improved effects as well as advantages and disadvantages of various treatment methods were compared and discussed respectively,and recommendations for the selection of treatment methods were proposed.Finally,the further research directions were pointed out,and an integrative programme on the quality improvement of RCA was recommended.     

Synthesis and adsorption properties for Au（Ⅲ） of alkoxycarbonyl thiourea resin

A novel alkoxycarbonyl thiourea resin（ATR） was synthesized by monomer polymerization of oxydiethane-2,1-diyl dicarbonisothiocyanatidate and polyethylene polyamine, and characterized by FT-IR. The adsorption properties of ATR were investigated by batch test. The adsorption capacities for Au（Ⅲ）, Ag（Ⅰ）, Cu（Ⅱ）, Zn（Ⅱ, Fe（Ⅲ）, Ca（ Ⅱ ） and Mg（ Ⅱ ） are 4.65, 4.40, 0.40, 0.90, 0.86, 0.0080 and 0.016 mmol/g, respectively, when the adsorption condition is as follows： contact time 24 h, temperature 30 ℃, initial concentration of Au（Ⅲ） 5.08 mmol/L and that of other metals 0.10 mol/L, and concentration of acid 1.0 mol/L. The adsorption capacity for Au（Ⅲ） increases with the increase of contact time, temperature and initial concentration of Au（Ⅲ）. The capacity after five adsorption-desorption cycles remains 90% that of the first time, and the separation factors of ATR for binary metal ion solutions are larger than 995, indicating that ATR is of good regeneration property and selectivity. XPS results show that the functional atoms of ATR supply electrons for Au and coordinate with Au during the adsorption.     

Enhancement of magnetic properties and thermal stability of nanocrystalline （NdDyTb）12.3（FeZrNbCu）81.7B6.0 alloy with Co substitution

The major drawbacks of Nd-Fe-B magnets are relatively low Curie temperature and poor thermal stability. Ribbons with the near stoichiometric 2:14:1 composition of Nd_(10.8)Dy_(0.75)Tb_(0.75)Fe_(79.7-x)Co_xZr_(0.8)Nb_(0.8)Cu_(0.4)B_(6.0)(x=0, 3, 6, 9, 12, 15) were prepared by rapid quenching and subsequent heat treatment. The effect of Co element on the magnetic properties, thermal stability, and microstructure of the ribbons was systematically studied by vibrating sample magnetometer(VSM), thermal magnetic analysis, atomic force microscopy (AFM), and transmission electron microscopy (TEM).It was found that Co substitution was significantly effective in improving the magnetic properties and the thermal stability of nanocrystalline ribbons. Although the intrinsic coercivity decreased from 1308.7 kA/m for x=0 to 817.4 kA/m for x=15, the remanence polarization and maximum energy product increased from 0.839 T and 116.5 kJ/m~3 for the Co-free samples to 1.041 T and 155.1 kJ/m~3 for the 12at% Co-substituted samples,respectively.About 10 K increase in Curie temperature was observed for the 2:14:1 phase with lat% Co substitution. The absolute values of temperature coefficients of induction and coercivity were significantly decreased with Co substitution, which may be attractive for high operational temperature applications. The microstructure of nanocrystalline ribbons was slightly refined with Co substitution.     

Synthesis of modified D401 chelating resin and its adsorption properties for Pb^2＋

A novel chelating resin with sulfonic group was synthesized by chemical modification of D401 resin with sulphonation reaction and characterized by FT-IR spectrometry. The adsorption properties of the novel chelating resin for Pb²⁺ were studied by batch adsorption, and the adsorption process was analyzed from thermodynamics and kinetics aspects. The adsorption mechanism of Pb²⁺ on the modified D401 chelating resin was discussed by FT-IR spectrometry. Experimental results show that in the Pb²⁺ concentration range of 200–400 mg/L, the adsorption capacities of the modified D401 chelating resin for Pb²⁺ increase by 77%–129%, and Langmuir isothermal adsorption model is more suitable for the equilibrium adsorption data. Adsorption is an endothermic process that runs spontaneously. Kinetic analysis shows that the adsorption rate is mainly governed by liquid film diffusion. The best pH value under adsorption condition is 4–5. The saturated resin can be regenerated by 3 mol/L nitric acid, and the adsorption capacity remains stable after five consecutive adsorption-desorption cycles. The maximal static saturated adsorption capacity of the resin is 206 mg/g at 333 K in the Pb²⁺ concentration range of 200–400 mg/L. The modified D401 chelating resin is an efficient adsorbent for the removal of Pb²⁺ from its single-metal ion solution. Foundation item: Project(708049) supported by the Important Item Cultivation Foundation of Scientific Innovation Project of Colleges and Universities of China     

Synthesis and properties of the modification of micro-crystal LiMn2−x Al x O4 cathode material for Li-Ion batteries

The micro-single crystal material spinel LiMn2-xAlxO4 was prepared by a sol-gel procedure and modified by alumina; the electrochemical measurements show that the performances and characteristics of modified LiMn2-xAlxO4 electrode material are better than those of LiMn2O4. Hence, the modified LiMn2-xAlxO4 is a good cathode material for lithium batteries. This can be explained that the size of the modified particle is larger than that of unmodified material, so electrons can be easily transported between the particles.     

Preparation and properties of composite membrane of bisphenol A-based sulfonated poly（arylene ether sulfone）and phosphotungstic acid for proton exchange membranes

A series of bi A-SPAES(Ds=0.4)/phosphotungstic acid(PWA/bi A-SPAES)composite membranes with various contents of PWA were prepared and characterized by FT-IR.Scanning electron microscopy(SEM)images indicated the PWA were well dispersed within polymer matrix.These composite membranes were evaluated for proton exchange membranes(PEM)in direct methanol fuel cell(DMFC).These membranes showed good thermal stability.It was found that the water uptake of these membranes increased with the increase of the PWA content in the hybrid membranes.Meanwhile,the introduction of inorganic particles increased both the proton conductivity and the methanol permeability.The proton conductivities of composite membranes were increased from 0.017 S/cm to 0.045 S/cm at 20 ℃ and from 0.054 S/cm to 0.093 S/cm at 100 ℃ with the increase of PWA content from 0 to 50 %.Especially,all the methanol diffusion coefficients(4.20×10-8-1.05×10-7cm2/s)of bi A-SPAES/PWA hybrid membranes are much lower than that of Nafion 117 membrane(2.1×10-6 cm2/s).Bi A-SPAES/PWA hybrid membranes were therefore proposed as candidates of material for PEM in DMFC.