On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies

In this Letter, we study the constrained KP hierarchies by employing Segal-Wilson's theory on the -functions of the KP hierarchy. We first describe the elements of the Grassmannian which correspond to solutions of the constrained KP hierarchy, and then we show how to construct its rational and soliton solutions from these elements of the Grassmannian.     

Variable step size destabilizes the Störmer/leapfrog/verlet method

For fixed step-sizeh the Störmer method is stable for the standard test equationÿ= ² y,>0, if and only ifh<2. We show that for variable step sizeh _n there does not exist a (positive) limit onh which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratioh _n/h _n–1.This work was supported in part by National Science Foundation Grant DMS 90 15533.     

Perturbed unstable variational inequalities with unbounded operators on approximately given sets

The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science.     

The erdös-dushnik-miller theorem for topological graphs and orders

A topological graph is a graph G=(V, E) on a topological space V such that the edge set E is a closed subset of the product space V x V. If the graph contains no infinite independent set then, by a well-known theorem of Erdös, Dushnik and Miller, for any infinite set LV, there is a subset LL of the same oardinality |L| = |L| such that the restriction G L is a complete graph. We investigate the question of whether the same conclusion holds if we weaken the hypothesis and assume only that some dense subset AV does not contain an infinite independent set. If the cofinality cf (|L|)>|A|, then there is an L as before, but if cf (|L|)<-|A|, then some additional hypothesis seems to be required. We prove that, if the graph GA is a comparability graph and A is a dense subset, then for any set LV such that cf (|L|)>, there is a subset LL of size |L|=|L| such that GL is complete. The condition cf (|L|)> is needed.Research supported by NSERC grant #A5198.     

5－（4－乙酰氧基苯基），10，15，20－三苯基卟啉金属配合物修饰的铂支撑双层脂膜的IV性质

合成并表征了５－（４－乙酰氧基苯基），１０，１５，２０－三苯基卟啉及其金属配合物，将它们作为修饰物，制得铂支撑的双层脂膜，用循环伏安法研究了抗坏血酸的氧化还原反应，并对其机理作了探讨。     

Miniature electrophoresis for speed and productivity

Attempts to miniaturize electrophoresis (EP) to save time or enhance productivity and efficiency remains a challenge for science and industry. Other advantages of miniaturization include: increased sensitivity, saving of reagents, greater yield of data, and enabling studies where only small samples are available. Since electrophoresis that takes hours may be reduced to a matter of minutes, the limitations of miniaturization in clinical, industrial, and research applications are evaluated. Clinical electrophoresis (EP) on cellulose acetate media can be performed in 3.5 min instead of 20–45 min and on SDS polyacrylamide gels in 15–30 min compared with conventional 3–8 h.     

Biological generation of tritiated vitamin D3 metabolites and their purification by high-performance liquid chromatography

Summary A simple, reproducible method for the biological synthesis of tritiated 24,25-dihydroxycholecalciferol, 25,26-dihydroxycholecalciferol and 1,25-dihydroxycholecalciferol is described. Kidney homogenates from both vitamin D deficient and replete chicks were usedin vitro to generate these dihydroxylated metabolites using 25 (23,24-³H) hydroxycholecalciferol as the substrate. Tritiated products were purified by Sephadex LH 20 chromatography followed by high-performance liquid chromatography; the identity of each metabolite was established by chromatography with authentic crystalline preparations.Presented at the Symposium organised by the Chromatography Discussion Group, held at Hatfield Lodge on 29 November 1979.     

Cellulose hydrolysis using zinc chloride as a solvent and catalyst

Cellulose gel with < 10% of crystallinity was prepared by treatment of microcrystalline cellulose, Avicel, with zinc chloride solution at a ratio of zinc chloride to cellulose from 1.5 to 18 (w/w). The presence of zinc ions in the cellulose gels enhanced the rate of hydrolysis and glucose yield. The evidence obtained from X-ray diffraction, iodine absorption experiments; and Nuclear Magnetic Resonance spectra analysis suggested the presence of zinc-cellulose complex after Avicel was treated with zinc chloride. Zinc-cellulose complex was more susceptible to hydrolysis than amorphous cellulose. Under the experimental condition, cellulose gels with zinc ions were hyrolyzed to glucose with 95% theoretical yield and a concentration of 14% (w/v) by cellulases within 20 h. The same gel was hydrolyzed by acid to glucose with 91.5% yield and a concentration of 13.4% (w/v).     

Linear combination of concomitants of order statistics with application to testing and estimation

Summary Let (X ₁,Y ₁), (X ₂,Y ₂),…, (X _n,Y _n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX _rn is denoted byY _rn and terms the concomitant of therth order statistic. Statistics of the form are considered. The asymptotic normality ofT _n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity ofX andY, and to estimate regression coefficient based on complete and censored samples.     

Methane production from synthesis gas using a mixed culture ofR. rubrum M. barkeri,and M. formicicum

The components of synthesis gas, CO, H₂, and CO₂, may be converted into CH₄ biologically through either acetate or H₂/CO₂ as intermediates. Of these two routes, conversion through H₂/CO₂ is preferred. This paper presents results of mixed-culture studies employing the photosynthetic bacteriumR. rubrum for converting CO to CO₂ and H₂ by the water gas shift reaction and two methanogens,M. formicicum andM. barkeri, for converting CO₂ and H₂ into CH₄. Results are presented for triculture operation in two types of reactors, the packed bubble column and the trickle-bed reactor.