General theoretical results on rectilinear embedability of graphs

In the design of certain kinds of electronic circuits the following question arises: given a non-negative integerk, what graphs admit of a plane embedding such that every edge is a broken line formed by horizontal and vertical segments and having at mostk bends? Any such graph is said to bek-rectilinear. No matter whatk is, an obvious necessary condition fork-rectilinearity is that the degree of each vertex does not exceed four. Our main result is that every planar graphH satisfying this condition is 3-rectilinear: in fact, it is 2-rectilinear with the only exception of the octahedron. We also outline a polynomial-time algorithm which actually constructs a plane embedding ofH with at most 2 bends (3 bends ifH is the octahedron) on each edge. The resulting embedding has the property that the total number of bends does not exceed 2n, wheren is the number of vertices ofH.     

From Levulinic Acid to Biheterocycles: Synthesis of 1-[(5-Hydroxy-5-trifluoromethyl-3-substituted-4,5-dihydro-1H-pyrazol-1-yl)-3-(5-trifluoromethyl-1H-pyrazol-3-yl)propan-1-ones

We develop an efficient method to synthesize novel propionyl-spaced bisheterocyclic compounds. It entails cyclocondensation of 3-(5-trifluoromethyl-1H-pyrazol-3-yl)propanoyl hydrazide obtained from levulinic acid, with 1,1,1-trifluoro-4-methoxy-3-alken-2-ones proceeding regiospecifically to 1-[(5-trifluoromethyl-5-hydroxy-3-substituted-4,5-dihydro-1H-pyrazol-1-yl)-3-(5-trifluoromethyl-1H-pyrazol-3-yl)propan-1-one derivatives.     

Pflanzenchemie

Analytical and Bioanalytical Chemistry -     

Comparison of direct sampling and emulsion analysis using a filter furnace for the determination of lead in crude oil by graphite furnace atomic absorption spectrometry

The determination of trace elements in crude oil is difficult due to the complex nature of the sample and the various different chemical forms in which the metals can occur. The advantage of graphite furnace atomic absorption spectrometry is that only a minimum of sample pretreatment is required. In this work two techniques have been compared to establish a fast and reliable method for lead determination in crude oil. In the first one the crude oil samples were weighed directly onto solid sampling (SS) platforms and introduced into the graphite tube for analysis. In the second one the samples were prepared as oil-in-water emulsions and analyzed in a filter furnace (FF). Twenty μL of a mixture of 0.5 mg L^− 1 Pd + 0.3 mg L^− 1 Mg + Triton X-100 has been used as the modifier, and calibration against aqueous solutions has been used for both methods. The sensitivity obtained with the FF was more than a factor of two better than that with SS; however, as a larger sample mass could be introduced in the latter case, so that the limits of detection for both techniques were 0.004 mg kg^− 1. Seven crude oil samples were analyzed using the two procedures, and all results were in agreement at a 95% confidence level using a paired Student's t-test. For validation purposes, three crude oil samples have been mineralized using an open-vessel acid digestion, and the results were in agreement with those found with direct sampling and with emulsion sampling using FF according to ANOVA test. Both methods are simple, fast and reliable, being appropriated for routine analysis; however, the direct method using SS technology should be preferred because of its simplicity, speed and commercial availability.     

Direct determination of arsenic in petroleum derivatives by graphite furnace atomic absorption spectrometry: A comparison between filter and platform atomizers

In the present work a direct method for the determination of arsenic in petroleum derivatives has been developed, comparing the performance of a commercial transversely heated platform atomizer (THPA) with that of a transversely heated filter atomizer (THFA). The THFA results in a reduction of background absorption and an improved sensitivity as has been reported earlier for this atomizer. The mixture of 0.1% (m/v) Pd + 0.03% (m/v) Mg + 0.05% (v/v) Triton X-100 was used as the chemical modifier for both atomizers. The samples (naphtha, gasoline and petroleum condensate) were stabilized in the form of a three-component solution (detergentless microemulsion) with the sample, propan-1-ol and 0.1% (v/v) HNO₃ in a ratio of 3.0:6.4:0.6. The characteristic mass of 13 pg found in the THFA was about a factor of two better than that of 28 pg obtained with the THPA; however, the limits of detection (LOD) and quantification (LOQ) were essentially the same for both atomizers (1.9 and 6.2 μg L⁻¹, respectively, for THPA, and 1.8 and 5.9 μg L⁻¹, respectively, for THFA) due to the increased noise observed with the THFA. A possible explanation for that is a partial blockage of the radiation from the hollow cathode lamp by the narrow inner diameter of this tube and the associated loss of radiation energy. Due to the lack of an appropriate certified reference material, recovery tests were carried out with inorganic and organic arsenic standards and the results were between 89% and 111%. The only advantage of the THFA found in this work was a reduction of the total analysis time by about 20% due to the ‘hot injection’ that could be realized with this furnace. The arsenic concentrations varied from < LOQ to 43.3 μg L⁻¹ in the samples analyzed in this work.     

Studies on Immobilization and Partial Characterization of Lipases from Wheat Seeds (<Emphasis Type="Italic">Triticum aestivum</Emphasis>)

The objective of this study was to provide some features on immobilization and partial characterization of lipases from wheat seeds. The optimum pH and temperature were found to be 5.5 and 32–37 °C, respectively. The stability of the concentrated enzymatic extract to high temperatures (25, 35, 45, and 55 °C) showed that the incubation of the extract at 55 °C led to its complete inactivation. The concentrated enzymatic extract kept 90% of its hydrolytic and esterification activities until 70 and 40 days of storage at 4 °C, respectively. The extract presented higher hydrolytic specificity to substrates of medium and long chains and higher esterification affinity to fatty acids of short and medium chains and alcohols with two and three carbon atoms. After the immobilization process using activated coal and sodium alginate as supports, an enhancement of about threefold in lipase activity was observed. The development of the present work permitted us to point out some characteristics of lipases from wheat seeds necessary for the proposition of new future industrial applications for this important biocatalyst.     

A graph partition problem

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Polynomial algorithms that prove an NP-Hard hypothesis implies an NP-hard conclusion

A number of results in hamiltonian graph theory are of the form “ implies ”, where is a property of graphs that is NP-hard and is a cycle structure property of graphs that is also NP-hard. An example of such a theorem is the well-known Chvátal–Erd s Theorem, which states that every graph G with κ is hamiltonian. Here κ is the vertex connectivity of G and is the cardinality of a largest set of independent vertices of G. In another paper Chvátal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than κ independent vertices. In this note we point out that other theorems in hamiltonian graph theory have a similar character. In particular, we present a constructive proof of a well-known theorem of Jung (Ann. Discrete Math. 3 (1978) 129) for graphs on 16 or more vertices.     

Investigation of artifacts caused by deuterium background correction in the determination of phosphorus by electrothermal atomization using high-resolution continuum source atomic absorption spectrometry

The artifacts created in the measurement of phosphorus at the 213.6-nm non-resonance line by electrothermal atomic absorption spectrometry using line source atomic absorption spectrometry (LS AAS) and deuterium lamp background correction (D₂ BC) have been investigated using high-resolution continuum source atomic absorption spectrometry (HR-CS AAS). The absorbance signals and the analytical curves obtained by LS AAS without and with D₂ BC, and with HR-CS AAS without and with automatic correction for continuous background absorption, and also with least-squares background correction for molecular absorption with rotational fine structure were compared. The molecular absorption due to the suboxide PO that exhibits pronounced fine structure could not be corrected by the D₂ BC system, causing significant overcorrection. Among the investigated chemical modifiers, NaF, La, Pd and Pd + Ca, the Pd modifier resulted in the best agreement of the results obtained with LS AAS and HR-CS AAS. However, a 15% to 100% higher sensitivity, expressed as slope of the analytical curve, was obtained for LS AAS compared to HR-CS AAS, depending on the modifier. Although no final proof could be found, the most likely explanation is that this artifact is caused by a yet unidentified phosphorus species that causes a spectrally continuous absorption, which is corrected without problems by HR-CS AAS, but which is not recognized and corrected by the D₂ BC system of LS AAS.