Optimizing constrained subtrees of trees

Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the rooted subtree problem, is to find a maximum weight subtree, with a specified root, from a given set of subtrees.The second problem, called the subtree packing problem, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root.We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by pasting together the convex hulls of the rooted subtree problems.We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk 4.Research supported in part by Nato Collaborative Research Grant CRG 900281, Science Program SC1-CT91-620 of the EEC, and contract No 26 of the programme Pôle d'attraction interuniversitaire of the Belgian government.     

Potential reduction method for harmonically convex programming

In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and them constraint functions are allk-harmonically convex in the feasible set, then the number of iterations needed to find an -optimal solution is bounded by a polynomial inm, k, and log(1/). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constantk as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.The authors like to thank Dr. Hans Nieuwenhuis for carefully reading this paper and the anonymous referees for the worthy suggestions.     

Investigation of superconductivity effects in single-phase and multiphase Bi2Sr2CaCu2O8 single-crystals at 2-MM wavelengths

Experimental investigations of superconductivity effects in single-phase and multiphase Bi₂Sr₂CaCu₂O₈ single-crystals have been carried out at 142 GHz frequency by means of the standing wave profile method [1]. Josephson harmonic generation has been observed to be responsible for the appearence of additional peaks on the standing wave profile of the open dielectric resonator loaded with a properly orientated multiphase high-T_c superconductor specimen. This leads to the conclusion that most of the Josephson junctions in multiphase crystals are located in certain crystallographic planes. The investigations of temperature dependencies showed that sharp resonant peaks of conductivity observed earlier [2] at 60 GHz could also be observed at 142 GHz.     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

An alternative interface for CE-ICP-MS cadmium speciation in metallothioneins based on volatile species generation

An alternative CE-ICP-MS interface based on volatile species generation (VSG) is here developed, evaluated and compared to the conventional sample introduction systems via nebulisation. For this purpose, the speciation of Cd-metallothioneins (MTs) in rabbit liver is taken as a model. Cd, bound to the different MT isoforms previously separated by CE, is transformed into volatile species at the exit of the capillary and on-line detected by ICP-MS. Optimum conditions for Cd VSG have been investigated in a flow injection device, using NaBH₄ as hydrogenation reagent in a HCl medium containing cobalt and thiourea as catalysts. Sample volume injected, CE separation voltage and reagents flows have been optimised. Analytical performance characteristics of the CE-VSG-ICP-(Q)MS coupling developed were evaluated, in terms of repeatability and linearity of response, using standard rabbit liver metallothionein isoforms (MT1 and MT2). Detection limits for Cd-MTs turned out to be almost one order of magnitude better than those derived from using a conventional Babington nebuliser-based interface. Compared to a MicroMist-based interface detection limits resulted to be similar, but the observed peak height was eight times higher using the VSG interface, indicating the enhanced analyte transport efficiency derived from VSG sample introduction systems.     

Metal furnace heated by flame as a hydride atomizer for atomic absorption spectrometry: Sb determination in environmental and pharmaceutical samples

The present work describes a metallic hydride atomizer for atomic absorption spectrometry, by evaluating the performance of the Inconel 600^® tube. For this purpose, stibine was used as the model volatile compound and antimony determination in river and lake sediments and in pharmaceutical samples was carried out to assess the metal furnace performance. Some parameters are evaluated such as those referring to the generation and transport of the hydride (such as KBH₄ and acid concentrations, carrier gas flow rate, injected volume, etc.), as well as those referring to the metal furnace (such as tube hole area, flame composition, long-term stability, etc.). The method presents linear Sb concentration from 2 to 80 μg L⁻¹ range (r > 0.998; n = 3) and the analytical frequency of ca. 140 h⁻¹. The limit of detection (LOD) is 0.23 μg L⁻¹ and the precision, expressed as R.S.D., is less than 5% (40 μg L⁻¹; n = 10). The accuracy is evaluated through the reference materials, and the results are similar at 95% confidence level according to the t-test.     

Green method for ultrasensitive determination of Hg in natural waters by electrothermal-atomic absorption spectrometry following sono-induced cold vapor generation and ‘in-atomizer trapping’

Sono-induced cold vapor generation (SI-CVG) has been used for the first time in combination with a graphite furnace atomizer for determination of Hg in natural waters by electrothermal-atomic absorption spectrometry after in situ trapping onto a noble metal-pretreated platform (Pd, Pt or Rh) inserted into a graphite tube. The system allows ‘in-atomizer trapping’ of Hg without the use of conventional reduction reactions based on sodium borohydride or tin chloride in acid medium for cold vapor generation. The sono-induced reaction is accomplished by applying ultrasound irradiation to the sample solution containing Hg(II) in the presence of an organic compound such as formic acid. As this organic acid is partly degraded upon ultrasound irradiation to yield CO, CO₂, H₂ and H₂O, the amount of lab wastes is minimized and a green methodology is achieved.     

Crystal structure and luminescence property of ternary terbium p-aminobenzoic acid complexes with different second ligands

Ternary terbium complexes with p-aminobenzoic acid (HL), [TbL₃(DMSO)(H₂O)]₂ (1), [TbL₃(DMF)(H₂O)]₂ (2) and [TbL₃(Bpy)(H₂O)]₂·2H₂O (3) (DMSO=dimethyl sulfoxide, DMF=N, N- dimethylformamide, Bpy=2, 2′- bipyridyl) have been synthesized, and their crystal structures determined. The luminescence properties of these complexes, including both the emission quantum yield and the fluorescence lifetime, have been investigated. The effect of a second ligand on the crystal structure and luminescence property of the ternary terbium p-aminobenzoic acid complexes, and the relationship between luminescence properties and crystal structure, including coordination mode of the L⁻ ligand and the characteristics of a second ligand, are discussed.     

氢化物原子荧光法测定中草药中痕量铅

提出了以重铬酸钾为氧化剂、碱性铁氰化钾为络合剂 ,在柠檬酸介质中进行铅的氢化物发生反应。采用断续流动氢化物发生器 ,对原子荧光法测定痕量铅的条件进行了系统研究 ,并考察了共存元素的干扰情况。在最佳测试条件下 ,测得铅的检出限 (3σ)为 0 .19μg·L- 1,相对标准偏差为 0 .92 %。应用于中草药中痕量铅的测定 ,回收率为 95 .1%～ 10 9.5 % ,结果满意     

微波消解-氢化物发生原子荧光法测定塑料原料及其制品中的砷、汞

采用微波消解进行样品前处理，以硫脲为预还原剂，用氢化物发生原子荧光法测定塑料原料及其制品中的砷、汞。测定砷和汞的线性范围均为0～8μg／L，砷、汞的检出限分别为0．005、0．076μg／L，测定结果的相对标准偏差分别为4.96％～7．38％、2．94％～7．20％(n=6)，回收率分别为92．0％～103．2％、92．0％～98.0％。