Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

高纯金属镨中痕量稀土杂质的电感耦合等离子体原子发射光谱分析及光谱干扰的校正

本文提出了PGS-2型平面光栅光谱仪(色散率0.18纳米,二级光谱)与PlasmaTherm ICP-5000D射频发生器联用,乙醇预去溶方式进样,同时直接测定高纯金属镨中5个痕量稀土杂质元素的方法。并讨论了基体浓度对检出限的影响以及光谱干扰及其校正方法。当样品溶液中镨的浓度为5毫克/毫升时,测定下限分别为镧、钕和钐0.002%,铈0.003%和钇0.0005%。获得了良好的实验结果,其相对标准偏差为1.2-6.2%。     

Crystal structure of m-nitrobenzoic anhydride

The title compound (C₁₄H₈N₂O₇,M _r =306.2) crystallizes in the orthorhombic space group Pbca witha=6.962(1).b=24.688(1), andc=15.890(1)Å,V=2731.0 ų,D _x =1.489 g·cm^–3 forZ=8,=0.98 mm^–1,F(000)=1296,T=293 K. FinalR=0.053 for 1873 observed reflections. The structure was solved by direct methods. Approximately planar molecules lie perpendicular to the [100] direction and show partial stacking. The structure is the first example of a symmetric anhydride which does not retain the symmetry in the crystal state. The two independent nitro groups twist out of the ring planes by 10.5 and 14.8°, respectively.     

On two mean value properties and functional equations associated with them

Summary Motivated by different mean value properties, the functional equationsf(x) – f(y)/x–y=[(x, y)], (i)xf(y) – yf(x)/x–y=[(x, y)] (ii) (x y) are completely solved when, are arithmetic, geometric or harmonic means andx, y elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).)     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.     

Ozone production in oxygen by means of F2-laser irradiation at λ=157.6 nm

Ozone is generated in pure oxygen (p5 kPa), synthetic air (p7 kPa) and oxygen-argon mixtures (p3 kPa) by irradiation of these gases with the VUV light of a repetitively pulsed (f _L15 Hz) F₂-laser at =157.6 nm with maximum about 4 mJ/pulse. An absorption photometer measurement operating at 253.7 nm (Hg line) determines the ozone concentration as a function of oxygen and/or additive gas pressure, the repetition frequency of the laser and the wall temperature of the reaction chamber. The temporal development of the ozone concentration as a function of these parameters is calculated by means of rate equations for the species O(³ P), O₂(X ³ _g ^– ), O₃(¹ A ₁), O(¹ D), O₂(a ¹_g), O₂(b ¹ _g ⁺ ) and vibrationally excited O ₃ ^* (¹ A ₁) and the photon distribution. The maximum concentration of O₃ in the sealed-off chamber reaches 1.6% in pure O₂, 4.1% in air and 1.2% in a 1:5 O₂-Ar mixture at 3 kPa. The annihilation of O₃ by the wall and temperature dependent volume processes (300 KT395 K) is studied and the experimental and theoretical results are compared.     

Maskierung mit Kaliumjodid bei direkten Titrationen von Kupfer(II) mit Äthylendiamintetraessigsäure

Zusammenfassung Die Jodidoxydation durch Cu(II) wird in Anwesenheit von Ammoniak, Natriumtartrat, citrat oder -oxalat infolge Komplexbildung verhindert. Daher kann man z. B. Quecksüber(II) in Anwesenheit der genannten Komplexbildner mit Kaliumjodid maskieren und Kupfer(II) durch direkte Titration mit ÄDTA gegen Murexid, Brenzcatechinviolett, Chromazurol S, PAN oder PAR als Indikator bestimmen.

---

Masking with potassium iodide in direct titrations of copper(II) with ethylenediamine tetraacetic acid

Summary The formation of a complex prevents the iodide oxidation by Cu(II) in the presence of ammonia, sodium tartrate, citrate, or oxalate. Hence mercury(II) for instance, can be masked against potassium iodide in the presence of these complex formers, and Cu(II) can be determined by direct titration with EDTA in the presence of murexide, pyrocatechol violet, chromazurol, PAN or PAR as indicator.