CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS

This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.

Prevalence of Strongyloides stercoralis and other intestinal parasitic infections among mentally retarded residents in central institution of southern Iran

Objective:To determine the prevalence of intestinal parasitic infections among mentally retarded residents of rehabilitation center of Bandar Abbas,Hormozgan province,southern Iran.Methods:A cross-sectional study was carried out in central rehabilitation institute of Hormozgan province in summer 2010.Fecal samples of all 133 residents(72 males,61 females)aged 3-52,were collected in triplicate.Specimens were examined by direct smear,formalin-ether concentration techniques and stained by permanent Trichrome,Ziehl-Neelsen stains.Statistical analysis was conducted by SPSS 13.5.Results:Intestinal parasitic infections were seen in 48.5%(64 out of 133 subjects:53.4%in males and 46.6%in females).Strongyloides stercoralis with17.3%showed the highest incidence followed by Entamoeba coli(9.8%),Blastocystis hominis(7.5%),Giardia lamblia(2.3%),Endolimax nana(2.3%),Hymenolepis nana(0.8%),Oxyuris vermicularis(0.8%),and Chilomasix mesnili(0.8%).Double infections were found to be as:Strongyloides stercoralis+Giardia lamblia(2.3%),Entamoeba coli+Giardia lamblia(1.5%),Entamoeba coli+Blastocystis hominis(1.5%),Oxyuris vermicularis+Entamoeba coli(0.8%),Strongyloides stercoralis+Entamoeba coli(0.8%),respectively.Conclusions:Our findings reveal that strongyloidiasis is a common disease among mentally retarded population in southern Iran.

Viability for a class of semilinear differential equations of retarded type

Let X be a Banach space, A ： D（A） X → X the generator of a compact C0- semigroup S（t） ： X → X, t ≥ 0, D a locally closed subset in X, and f ： （a, b） × X →X a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order to make D a viable domain of the semilinear differential equation of retarded type u＇（t） = Au（t） ＋ f（t, u（t - q））, t ∈ [to, to ＋ T], with initial condition uto = φ ∈C（[-q, 0]; X）, is the tangency condition lim infh10 h^-1d（S（h）v（O）＋hf（t, v（-q））; D） = 0 for almost every t ∈ （a, b） and every v ∈ C（[-q, 0]; X） with v（0）, v（-q）∈ D.

Comparison of Digestive Enzyme Activities in Normal and Growth Retarded Japanese Eels(Anguilla japonics)

[ Objective] This experiment was conducted to compare the activity difference of digestive enzymes in Japanese eels Anguilla japonics and growth retarded eels under different reaction temperature. [Method] Both 20 normal Japanese eels （Weight from 126.4 to 140.2 g per eel） and 20 growth retarded eels （Weight from 3.5 to 8.6 g per eel） were selected, then, the protease, amylase, lipase activities in hepatopancreas, intestine and stomach under the reaction temperature 5, 10, 15, 25, 30, 35, 40, 45 and 55℃ were measured. [ Result] The protease activities in hepatopancreas, intestine and stomach all reached the highest value for both normal eels and growth retarded eels, and the order of protease activities was intestine 〉 stomach 〉 hepatopancreas except the protease activities of growth retarded eels at the temperature of 5, 15, 55℃ The protease activities in hepatopancreas, intestine and stomach of growth retarded eels were 29.5%, 15.7% and 25.2% of those of normal eels（ P 〈0. 05）. The amylase activities of both normal and growth retarded eels reached the highest value at the temperature of 30 ~C. The amylase activity or- der of normal eels was hepatopancreas 〉 intestine 〉 stomach expect the amylase activity at the temperature of 5 ~C, while the amylase activity order of growth retarded eels is intestine 〉 hepatopancreas 〉 stomach. The amylase activities in hepatopancreas, intestine and stomach of growth retarded eels were 42.4%, 73.7% and 43.8% of those of normal eels （ P 〈 0.05）. The lipase activities of both normal and growth retarded eels reached the highest value at the temperature of 35 ~C. The lipase activity order of normal eels was hepatopancreas 〉 stomach 〉 intestine, while the lipase activity order of growth retarded eels was hepatopancreas 〉 intestine 〉 stomach expect the lipase activity at the temperature of 35 ~C. The lipase activities in hepatopancreas, intestine and stomach of growth retarded eels were 41.5%, 45.6% and 23.2% of those of normal eels（ P 〈0.05）. [ Conclusion] The protease, amylase, lipase activities in hepatopancreas, intestine and stomach of growth retarded Japanese eels were significantly lower than those of normal Japanese eels, therefore, its growth was affected directly.

Approximate Controllability of Fractional Order Retarded Semilinear Control Systems

In this paper, approximate controllability of fractional order retarded semilinear systems is studied when the nonlinear term satisfies the newly formulated bounded integral contractor-type conditions. We have shown the existence and uniqueness of the mild solution for the fractional order retarded semilinear systems using an iterative procedure approach. Finally, we obtain the approximate controllability results of the system under simple condition.

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).

Synchronization of Stochastic Memristive Neural Networks with Retarded and Advanced Argument

In this paper, we discuss the driving-response synchronization problem for two memristive neural networks with retarded and advanced arguments under the condition of additional noise. The control law is related to the linear time-delay feedback term, and the discontinuous feedback term. Moreover, the random different equation is used to prove the stability of this theory. At the end, the simulation results verify the correctness of the theoretical results.

On the Lawful Rights and Interests of Mentally Retarded Children——A case study of a rehabilitation center in Liaoning Province

Mentally retarded children are the most disadvan- taged among disabled children. Since the reform and opening up, with sup- port from the Communist Party of China, the government and the public, the legitimate rights and interests of mentally retarded children have greatly improved. But problems in this respect remain serious, and vari- ous levels of government, relevant departments and the public should attach much importance to these problems. This paper, taking a reha- bilitation center in Liaoning Province for mentally retarded children as a single case, studies the protection of these children＇s lawful rights and in- terests in a systematic manner.

An Inequality for Second Order Differential Equation with Retarded Argument

Applications of differential equations with retarded argument can be encountered in the theory of automatic control, in the theory of self-oscillatory systems, in the study of problems connected with combustion in rocket engines, in a number of problems in economics, biophysics. The problems in this areas can be solved reducing differential equations with retarded argument. In this work an important inequality for second order differential equation with retarded argument is obtained.

Asymptotic Behavior of Solutions of Retarded Differential Equations

A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.

Effects of dietary Bacillus amyloliquefaciens supplementation on growth performance,intestinal morphology, inflammatory response, and microbiota of intra-uterine growth retarded weanling piglets

Background: The focus of recent research has been directed toward the probiotic potential of Bacillus amyloliquefaciens(BA) on the gut health of animals. However, little is known about BA's effects on piglets with intra-uterine growth retardation(IUGR). Therefore, this study investigated the effects of BA supplementation on the growth performance,intestinal morphology, inflammatory response, and microbiota of IUGR piglets.Methods: Eighteen litters of newborn piglets were selected at birth, with one normal birth weight(NBW) and two IUGR piglets in each litter(i.e., 18 NBW and 36 IUGR piglets in total). At weaning, the NBW piglet and one of the IUGR piglets were assigned to groups fed a control diet(i.e., the NBW-CON and IUGR-CON groups). The other IUGR piglet was assigned to a group fed the control diet supplemented with 2.0 g BA per kg of diet(i.e., IUGR-BA group). The piglets were thus distributed across three groups for a four-week period.Results: IUGR reduced the growth performance of the IUGR-CON piglets compared with the NBW-CON piglets. It was also associated with decreased vil us sizes, increased apoptosis rates, reduced goblet cel numbers, and an imbalance between pro-and anti-inflammatory cytokines in the smal intestine. Supplementation with BA improved the average daily weight gain and the feed efficiency of the IUGR-BA group compared with the IUGR-CON group(P < 0.05). The IUGR-BA group exhibited increases in the ratio of jejunal vil us height to crypt depth, in ileal vil us height, and in ileal goblet cel density. They also exhibited decreases in the numbers of jejunal and ileal apoptotic cel s and ileal proliferative cel s(P < 0.05). Supplementation with BA increased interleukin 10 content, but it decreased tumor necrosis factor alpha level in the smal intestines of the IUGR-BA piglets(P < 0.05). Furthermore, compared with the IUGR-CON piglets, the IUGR-BA piglets had less Escherichia coli in their jejunal digesta, but more Lactobacil us and Bifidobacterium in their ileal digesta(P < 0.05).Conclusions: Dietary supplementation with BA improves morphology, decreases inflammatory response, and regulates microbiota in the smal intestines of IUGR piglets, which may contribute to improved growth performance during early life.

Resveratrol and its derivative pterostilbene ameliorate intestine injury in intrauterine growth-retarded weanling piglets by modulating redox status and gut microbiota

Background:Intestinal disorder is an important factor contributing to growth lag and high rates of morbidity and mortality of piglets with intrauterine growth retardation(IUGR).Resveratrol(RSV)and its derivative pterostilbene(PT)are natural stilbenes possessing various bioactivities,such as antioxidative and anti-inflammatory effects.This study compared the protective potential of RSV and PT on the intestinal redox status and gut microbiota in weanling piglets with IUGR.Methods:Eighteen male piglets of normal body weight(NBW)and 54 same-sex IUGR piglets were chosen according to their birth and weaning weights.The NBW piglets accepted a basal diet,while the IUGR piglets were allotted to one of three groups according to their body weight at weaning and received a basal diet,an RSV-supplemented diet(300 mg/kg),or a PT-supplemented diet(300 mg/kg),respectively.Results:Compared with IUGR piglets,both RSV and PT improved the IUGR-associated decrease in jejunal villus height and increases in plasma diamine oxidase activity and D-lactate level and jejunal apoptosis of piglets(P<0.05).Administering RSV and PT also enhanced jejunal superoxide dismutase activity and the mRNA and protein expression of superoxide dismutase 2 of IUGR piglets by promoting nuclear factor erythroid 2-related factor 2(Nrf2)nuclear translocation(P<0.05).Comparatively,PT was more effective than RSV in elevating the villus height/crypt depth ratio and occludin mRNA and protein levels in the jejunum of IUGR piglets(P<0.05).PT was also superior to RSV in increasing Nrf2 nuclear translocation and inhibiting malondialdehyde accumulation in the jejunum of IUGR piglets(P<0.05).Additionally,RSV modulated the composition of cecal microbiota of IUGR piglets,as evidenced by increasing the prevalence of the phylum Bacteroidetes and the genera Prevotella,Faecalibacterium,and Parabacteroides and inhibiting the growth of the phylum Proteobacteria and its genera Escherichia and Actinobacillus(P<0.05).Moreover,RSV significantly increased the butyrate concentration in the cecum of IUGR piglets(P<0.05).Conclusion:PT is more potent than RSV to prevent intestinal oxidative stress,while RSV has a stronger capacity to regulate gut microbiota compared to PT.

Halogen-Free Flame Retarded Poly(Lactic Acid)with an Isosorbide-Derived Polyphosphonate

Fabrication of flame retardants from renewable biomass has aroused extensive interest over the past decade.This work reported a synthesis of isosorbide-derived polyphosphonate(PICPP)as an anti-flammable agent for poly(lactic acid)(PLA).The presence of PICPP notably declined the storage modulus of PLA/PICPP owing to the declined molecular weight of PLA catalyzed by the presence of PICPP.PLA and PLA/PICPP thermally degraded in one stage under either air or nitrogen atmosphere.With increasing the amount of PICPP,the onset thermal decomposition temperature of PLA/PICPP was decreased gradually,owing to the earlier decomposition of PICPP.With only 10 wt%of PICPP,PLA/PICPP-10 achieved a high limiting oxygen index of 30.0%and UL-94 V-0 classification,manifesting that PICPP was an efficient anti-flammable agent for PLA.The inclusion of 15 wt%PICPP also caused 33%and 16%decline in PHRR and THR of PLA,respectively.TG-IR results clarified that PLA/PICPP produced the less typical pyrolysis products especially flammable carbonyls than PLA,which may account for the suppressed PHRR and THR values of PLA/PICPP.

Synergistic effects of zeolitic imidazolate frameworks(ZIFs)with different transition metals on intumescent flame-retarded polypropylene composites:A comparative study

The use of intumescent flame retardants(IFRs)is considered an environmentally friendly and cost-effective strategy to suppress potential fire hazards from synthetic polymers.However,some conventional IFRs are neither efficient in developing a thermally stable char layer nor reducing the release of toxic byproducts during polymer combustion.In this work,we aim to discuss the effects of zeolitic imidazolate frameworks(ZIFs)on synergistically improving the flame retardancy behaviors in polypropylene(PP)composites,including thermal degradation(evolved gas analysis),free radical reactions in the gaseous phase(in-situ chemiluminescent image analysis),and carbonaceous structure in the condensed phase(micro-morphology and composition analysis).It is found that the transition metals in ZIFs can catalytically accelerate the crosslinking reaction at a lower initial temperature and decrease the amount of hydrocarbon volatiles in the gaseous phase.Once ignited,the embedded ZIFs can firstly bridge adjacent phosphorus chains in the polymer matrix to expand crosslinking degrees and then they are anchored in the developed N-doped phospho-carbonaceous networks after pyrolysis.As a result,more compact char residue structures are observed in the condensed phase for ZIF-reinforced composites.For example,by replacing 2 wt%of IFR with ZIF-67,the peak heat release rate,peak smoke production rate,and peak CO production rate are reduced by 69%,80%,and 72%,respectively,when compared to the conventional composite.These results indicate an excellent solution to resolve inherent fire hazards associated with IFRs in polymers and achieve necessary efficiency for industrial applications.It also provides a new strategy for determining flammability characteristics and combustion mechanisms of polymer composites using in-situ chemiluminescence analysis.

Synthesis of Bio-based Epoxy Containing Phosphine Oxide as a Reactive Additive Toward Highly Toughened and Fire-retarded Epoxy Resins

The integration of high mechanical toughness,impact strength as well as excellent flame-retardant properties toward epoxy resins(EPs)have always been a dilemma.The inadequate overall performance of EPs severely restricts their sustainable utilization in engineering aspects over long-term.Herein,a new bio-based agent(diglycidyl ether of magnolol phosphine oxide,referred as DGEMP)derived from magnolol(classified as lignan),extracted from natural plants Magnolia officinalis,was successfully synthesized and further employed as a flameretardant reactive additive to diglycidyl ether of bisphenol A(DGEBA).As demonstration,the composite resin,DGEBA/15DGEMP(15 wt%DGEMP),achieved an Underwriters Laboratories-94 V-0 rating with a high limiting oxygen index(LOI)value(41.5%).In cone calorimeter tests,it showed that heat release and smoke production were effectively inhibited during combustion,wherein the peak heat release rate(PHRR)value of DGEBA/15DGEMP was reduced by 50%compared to neat DGEBA.Additionally,it exhibited a superior tensile strength(82.8 MPa),toughness(5.11MJ/m^(3))and impact strength(36.5 k J/m^(2)),much higher than that of neat DGEBA(49.7 MPa,2.05 MJ/m^(3)and 20.9 k J/m^(2)).Thus,it is highly anticipated that DGEMP imparts significantly improved mechanical and fire-retarded properties to conventional EPs,which holds a great potential to address the pressing challenges in EP thermosets industry.

Electromagnetic retarded interaction and symmetry violation of time reversal in high order stimulated radiation and absorption processes of light

It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account,the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated,though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field,there is no such kind of symmetry violation of time reversal. In this way,the current formula on the parameters of stimulated radiation and absorption of light with time reversal sym-metry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are in-volved.

Asymptotic Behavior of Solutions for a Class of Retarded Difference Equations

Consider the retarded difference equation xn-xn-1=F（-f（xn）+g（xn-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）】0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.

A GENERALIZATION OF A RETARDED INEQUALITY AND ITS APPLICATIONS

We prove some new retarded nonlinear integral inequality and present its applications to the global existence of differential equations with delay.

OSCILLATORY AND ASYMPTOTIC BEHAVIOUR OF FIRST ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH RETARDED ARGUMENT[t]

B. G Zhang introduced an oscillatory and asymptotic behaviour of the equation X′(t)+p(t)X(t-[t])=0, t≥0, (1) where [t] denotes the greatest integer function.Now, we consider in a broad sense the first order nonlinear

Preparation of Polyurea Elastomer with Flame Retardant, Insulation and Thermal Conductivity Properties

By using 6,6-((sulfonylbis(4,1-phenylene)bis(azanediyl))bis(thiophen-2-ylm-ethylene))bis6H-di-benzo[c,e][1,2]oxaphosphinine 6-oxide(DOPO-N)as phosphorus-nitrogen flame retardant,the polyurea(PUA)with flame retardant properties(PUA/DOPO-N)was prepared.In addition,organically modified montmorillonite(OMMT)and magnesium hydroxide(MH)were used as co-effectors respectively,and the flame retardant PUA(PUA/DOPO-N/OMMT and PUA/DOPO-N/MH)were also prepared.Thermal properties,flame retardant properties,flame retardant mechanism and mechanical properties of PUA/DOPO-N,PUA/DOPO-N/OMMT and PUA/DOPO-N/MH were investigated by thermogravimetric(TG)analysis,limiting oxygen index(LOI),UL 94,cone calorimeter test,scanning electron microscopy(SEM),and tensile test.The results show that the LOI value of PUA/20%DOPO-N,PUA/18%DOPO-N/2%OMMT and PUA/15%DOPO-N/5%MH are 27.1%,27.7%,and 28.3%,respectively,and UL 94 V-0 rating is attained.Compared with PUA,the peak heat release rate(pk-HRR),total heat release(THR)and average effective heat combustion(av-EHC)of PUA/20%DOPO-N,PUA/18%DOPO-N/2%OMMT and PUA/15%DOPO-N/5%MH decrease significantly.SEM results indicate that the residual chars of PUA/20%DOPO-N,PUA/18%DOPO-N/2%OMMT and PUA/15%DOPO-N/5%MH are completer and more compact.The complex of DOPO-N/OMMT and DOPO-N/MH have synergistic flame retardancy.The mechanical properties of PUA can be improved by the addition of DOPO-N,DOPO-N/OMMT and DOPO-N/MH,respectively.The insulation performance test shows that the volume resistivity of PUA/20%DOPO-N is 6.25×10^(16)Ω.cm.Furthermore,by using modified boron nitride(MBN)as heat dissipating material,the complex of PUA/MBN was prepared,and the thermal conductivity of PUA/MBN was investigated.The thermal conductivity of PUA/8%MBN complex coating at room temperature is 0.166 W/(M·K),which is a 163%improvement over pure PUA.