Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Phase space dependence of the multiplicity distribution in π+ andpp collisions at 250 GeV/c

The charged particle multiplicity distribution has been studied for non-single-diffractive π⁺ p andpp collisions at \(\sqrt s = 22\) GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe ⁺ e ^? data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.     

Forward-backward multiplicity correlations in σ+ p,K + p andpp collisions at 250 GeV/c

Forward-backward multiplicity correlations in σ⁺,K ⁺ p andpp collisions at 250 GeV/c ( \(\sqrt s \) =22 GeV) are given for all charges and for the different charge combinations. The correlations are found to be caused predominantly by centrally produced particles. It is demonstrated that this result is an agreement with observations at the ISR and the CERNp \(\bar p\) -Collider. The results are compared to expectations from LUND, DPM and FRITIOF Monte Carlo models and a geometrical picture relating correlations in hadron-hadron collisions toe ⁺ e ^? data in terms of impact parameters is tested.     

Studies on the liquid-liquid extraction and ion and precipitate flotation of Co(II) with decanoic acid

The liquid-liquid extraction, ion and precipitate flotation of Co(II) from chloride media of 1·10^–4M initial Co(II) concentration and =0.1 have been investigated using decanoic acid and the results are compared. Organic solvents used were chloroform in the case of liquid-liquid extraction and ethanol (used as a solvent for the collector and a frother) in the case of flotation. From the results it appears that liquid-liquid extraction takes place through the formation of the complex: (CoR₂)₂(HR)₂ but flotation occurs through the formation of a surface active product which has the empirical formula CoR₂. The effects of pH and of decanoic acid concentration on the three separation processes were also investigated and the results discussed. Good agreement was observed between the experimental precipitate flotation curves and the theoretical curve calculated from the data published for Co(II) hydrolysis.     

聚醚醚酮酮和含联苯聚醚醚酮酮共聚物的熔融热

根据Ｆｌｏｒｙ热力学统计理论和比容－熔融热作国法，由ＤＳＣ结果得到了不同联苯含量的聚醚醚酮酮－含联苯聚醚醚酮酮（ＰＥＥＫＫ－ＰＥＢＥＫＫ）共聚物的熔融热，两种方法获得的结果吻合。在此基础上给出了ＰＥＥＫＫ－ＰＥＢＥＫＫ共聚物不同联苯含量的熔点计算表达式。结果还表明，随着联苯含量ｎＢ，的变化，明显改变；当ｎＢ＝０．３５时，ＰＥＥＫＫＰＥＢＥＫＫ共聚物的值最小。     

Synthesis of Important New Pyrrolo[3,4‐c]Pyrazoles and Pyrazolyl‐Pyrrolines from Heterocyclic β‐Ketonitriles

Treatment of heterocyclic β‐ketonitriles 1a,b with hydrazine hydrate and phenylhydrazine afforded the hydrazine derivatives 2a‐d which cyclized in PPA into pyrrolo[3,4‐c]pyrazoles 3a‐d. Reaction of 1a,b with cyanoacetohydrazide furnished the cyanoacetyl pyrrolo[3,4‐c]pyrazoles 4a,b. The hydrazine 2c reacted with β‐diketone and β‐ketoesters to afford pyrazolyl‐pyrrolines 5‐7. Also the later hydrazine reacted with some D‐aldoses and aceteophenone to give the corresponding hydrazones 10‐12 and hydrazine carboxamide derivatives 15a,b respectively.     

Separation of Co(II) from dilute aqueous solutions by precipitate and adsorbing colloid flotation

Ion, precipitate and adsorbing colloid flotation of cobalt(II) have been investigated at different pH values, using N-dodecylpyridinium chloride (DPCl), A strong cationic surfactant, and sodium lauryl sulfate (NaLS), a strong anionic surfactant, as collectors. In case of adsorbing colloid flotation, hydrous manganese dioxide was used as an adsorbent. The precipitate flotation curves experimentally obtained with the two tested collectors were compared with the corresponding theoretical one calculated from the data published for Co(II) hydrolysis. The effects of the collector concentration, ageing of the water-MnO₂–Co(II) system, bubbling time period, cobalt(II) concentration and foreign salts on the percent removal of Co(II) by adsorbing colloid flotation using DPCl as collector were determined. Removals approaching 100% could be achieved under the optimum conditions.     

REALISIS: a medicinal chemistry-oriented reagent selection, library design, and profiling platform

REALISIS is a software system for reagent selection, library design, and profiling, developed to fit the workflow of bench chemists and medicinal chemists. Designed to be portable, the software offers a comprehensive graphical user interface and rapid, integrated functionalities required for reagent retrieval and filtering, product enumeration, and library profiling. REALISIS is component-based, consisting of four main modules: reagent searching; reagent filtering; library enumeration; and library profiling. Each module allows the chemist to access specific functionalities and diverse filtering and profiling mechanisms. By implementing the entire process of reagent selection, library design, and profiling and by integrating all the necessary functionalities for this process, REALISIS cuts the time required to design combinatorial and noncombinatorial libraries from several days to a few hours.     

带甲基侧基的环氧树脂增容剂对炭黑在丁苯橡胶中分散度的影响

用自制的带甲基侧基的环氧树脂(TMBP)作为界面增容剂, 从拉伸性能、键合胶含量、动态性能、扫描电镜和流变性能等方面, 研究了TMBP对炭黑在丁苯橡胶中分散度的影响, 并与市售通用双酚A型环氧树脂(E-51)和橡胶工业常用软化剂邻苯二甲酸二辛酯(DOP)进行了比较. 结果表明, 带甲基侧基的环氧树脂TMBP在提高炭黑分散性方面的效果远比E-51好， 其作用模式具有典型的增容特性.