Cyclic actions on some Klein bottle bundles over S1

Leth be a cyclic action of periodn onM, whereM is eitherS ¹×K, K is the Klein bottle or on , the twisted Klein bottle bundle overS ¹, such that there is a fiberingq:MS ¹ with fiber a Klein bottleK or a torusT with respect to which the action is fiber preserving. We classify all such actions and show that they might be distinguished by their fixed points or by their orbit spaces.     

On depth first search strees inm-out digraphs

We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let _i be thei ^th vertex encountered by DFS andL(i, m, n) be the height of _i in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.     

Quantitative weight of evidence method for combining predictions of quantitative structure-activity relationship models

ABSTRACT

A method for combining statistical-based QSAR predictions of two or more binary classification models is presented. It was assumed that all models were independent. This facilitated the combination of positive and negative predictions using a quantitative weight of evidence (qWoE) procedure based on Bayesian statistics and the additivity of the logarithms of the likelihood ratios. Previous studies combined more than one prediction but used arbitrary strengths for positive and negative predictions. In our approach, the combined models were validated by determining the sensitivity and specificity values, which are performance metrics that are a point of departure for obtaining values that measure the weight of evidence of positive and negative predictions. The developed method was experimentally applied in the prediction of Ames mutagenicity. The method achieved a similar accuracy to that of the experimental Ames test for this endpoint when the overall prediction was determined using a combination of the individual predictions of more than one model. Calculating the qWoE value would reduce the requirement for expert knowledge and decrease the subjectivity of the prediction. This method could be applied to other endpoints such as developmental toxicity and skin sensitisation with binary classification models.     

The convergence of spline collocation for strongly elliptic equations on curves

Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk     

Low Pass metallic mesh interference filters for operation in the 165 GHz to 880 GHz region

Low Pass metallic mesh interference filters have been designed and constructed for operation in the region 340 m (880 GHz) to 1.8 mm (165 GHz). These filters have been shown to have excellent edge characteristics and good rejection regions. The results show that the mesh filter can be effectively used in both millimetre and submillimetre regions.Part of this work was performed while this author was at Heriot-Watt University, Edinburgh, U.K.     

Potentiometric studies of dithiooxamide with a sulphide-selective membrane electrode

The sulphide-selective electrode is applicable to the determination of dithiooxamide by titration with silver nitrate. The effect of the alkali content of the solutions on the reaction has been studied. The reaction products are silver sulphide, oxalic acid, and nitric acid. If the alkali concentration of the solution is lower than that equivalent to the acid formed during the titration, the amount of sulphide produced by hydrolysis decreases and the equilibrium potential is established more slowly.The determination is rapid and accurate in the presence of 1 M sodium hydroxide.     

Spectrophotometric assay of cephalosporins in pharmaceutical products,using chromotrope 2B and chromotrope 2R

A simple, rapid and sensitive Spectrophotometric method is proposed for the determination of cephadroxil (I), cephalexin (II) and cephradine (III). The method is based on ion-pair complex formation between these derivatives and Chromotrope 2B (C2B) or Chromotrope 2R (C2R), to give a highly coloured radical anion. The coloured products are quantified spectrophotometrically at 542 and 564 nm for C2B and C2R, respectively. The optimization of the experimental conditions is described. The method has been used for the determination of 0.4–15, 0.4–14 and 0.4–18 g/ml of drugs I, II and III, respectively. The accuracy of the method is indicated by the excellent recovery (100.0±1.7%) and the precision is supported by the low relative standard deviations 1.5%. The sensitivity of the method is discussed and the results are compared with the official method. The interference from common degradation products and excipients was also studied. The proposed method was applied successfully to the determination of the different cephalosporins in dosage forms, with good precision and accuracy. The results were compared with those given by the official B.P. 1993 method.     

The effectiveness of solvents as hydrogen bond donors

Taft and Kamlet's -scale of solvent hydrogen bond donation ability is reexamined with regard to its correlations with three widely used polarity scales: Dimroth and Reichardt's E _T (30), Kosower's Z and Mayer's A _N , as well as with the _m values of the solvents when present as monomeric solutes. The correlation with E _T serves to extend the solvent -scale according to the expression:

Solubility Measurements of Surfactants and Dissolution of Cytochrome c in 1,1,1,2‐Tetrafluoroethane Modified with Organic Solvents

The solubilities of four surfactants, sodium bis‐2‐ethylhexyl sulfosuccinate (AOT), cetyltrimethylammonium chloride, didodecyldimethylammonium bromide, and n‐dodecyltrimethylammonium chloride in liquid refrigerant 1,1,1,2‐tetrafluoroethane (R134a) modified with methanol, ethanol, and 2‐propanol were measured. The measurements were performed under 25 and 50 bar at 25 °C. The solubility of AOT was as high as 92 mM in R134a with addition of 2% ethanol. Cytochrome c molecules were then verified to be soluble in the AOT‐containing and ethanol‐modified R134a solution. Accordingly, liquid R134a is suggested as a potential extraction solvent for hydrophilic compounds.     

Tunable CW laser oscillation of NdP5O14 at 1.3 μm

Low-threshold tunable cw laser oscillation is achieved at the⁴ F _3/2⁴ I _13/2 transition of NdP₅O₁₄. Continuous tunign over 1.8% of the central wavelenght is possible with 55 mW of absorbed pump power. At gain line maximum near 1.32 , the output power exceeded 1 mW. Pump threshold as low as 8 mW was observed. Reliable cw operation of the 1.3 m NdP₅O₁₄ laser pumped by a 15 mW AlGaAs laser diode is demonstrated.