Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas

We study two criteria to evaluate quadrature formulas when used in automatic quadrature programs. The former consists of the computation of a quantity depending on both the truncation error behavior and the geometric properties of the nodes of the rule. This measure allows estimating the asymptotical computational cost in various abstract models of automatic quadrature. The latter is a testing technique which can be used to measure the efficiency of the formulas under consideration in a real environment. The relationships between the two criteria are investigated and the two approaches seem in good agreement.Work supported by CNR, Grant No. 93.00570.CT01.     

The capacitated team orienteering problem with incomplete service

In this paper we study the capacitated version of the Team Orienteering Problem (TOP), that is the Capacitated TOP (CTOP) and the impact of relaxing the assumption that a customer, if served, must be completely served. We prove that the profit collected by the CTOP with Incomplete Service (CTOP-IS) may be as large as twice the profit collected by the CTOP. A computational study is also performed to evaluate the average increase of the profit due to allowing incomplete service. The results show that the increase of the profit strongly depends on the specific instance. On the tested instances the profit increase ranges between 0 and 50 %. We complete the computational study with the increase of the profit of the CTOP due to split deliveries, that is multiple visits to the same customer, and to split deliveries combined with incomplete service.     

The second largest prime divisor of an odd perfect number exceeds ten thousand

Let denote the sum of positive divisors of the natural number . Such a number is said to be perfect if . It is well known that a number is even and perfect if and only if it has the form where is prime.

No odd perfect numbers are known, nor has any proof of their nonexistence ever been given. In the meantime, much work has been done in establishing conditions necessary for their existence. One class of necessary conditions would be lower bounds for the distinct prime divisors of an odd perfect number.

For example, Cohen and Hagis have shown that the largest prime divisor of an odd perfect number must exceed , and Hagis showed that the second largest must exceed . In this paper, we improve the latter bound. In particular, we prove the statement in the title of this paper.

     

Calix[8]arene-based glycoconjugates as multivalent carbohydrate-presenting systems

An efficient approach for the introduction of eight mono- or disaccharide sugar moieties (d-glucose, N-acetyl-d-glucosamine, d-galactose, l-fucose, d-maltose and d-cellobiose) at the upper rim of calix[8]arene 1, using thioureido linkers, is reported. The obtained water-soluble, nanosized glycocalix[8]arenes 5b-10b may act as biomimetic carbohydrate systems and as hosts for highly polar organic molecules. Preliminary ¹H NMR complexation experiments of octaglycosyl derivative 7b and 10b with ionic guests are also reported.     

Electron impact induced ortho effects in 2-nitro-substituted aromatic sulphides containing 2-pyridyl, 2-(5-methylthio-1,3,4-thiadiazolyl) and/or 2-(4-methyl-1,3,4-thiadiazolinyl-5-thione) moieties

The most significant mass spectral features of 14 title compounds are discussed with the aid of deuterium labelling experiments. The decomposition patterns of these compounds are strongly affected by several competing ortho effects, due to the interaction of the nitro function(s) with neighbouring electron-poor N-heterocycles. Very intense polycyclic ions are produced via addition-elimination reactions by loss of simple radicals (H˙, OH˙, NO₂˙) from the molecular ion, followed by the ejection of neutral molecules (HNO₂,CH₃SCN or CH₃NCS). In addition, primary or secondary intramolecular oxygen transfers, preceded or not by hydrogen migration, from the nitro group to the imino carbon via spirocyclic intermediates, are generally observed. Minor skeletal rearrangements, triggered by single or multiple intramolecular oxygen transfer to the bridgehead sulphur atom, followed by SO or SO₂ ejection, are also noticed.     

Antioxidant activity and fatty acids quantification in Sicilian purslane germplasm

Abstract

Portulaca oleracea is an annual succulent herb in the family Portulacaceae. It is a nutritious vegetable with high antioxidant properties and, it is among the richest plant source of ω-3 fatty acids, as well as a rich source of ω-6 fatty acids, ascorbic acid, tocopherols and beta-carotene. In the present study, three purslane populations under different Mediterranean environmental conditions for two years, for future valorization as novel food sources of omega-3 fatty acids, were evaluated. In particular, biomorphological characteristics, total phenols and fatty acids content were determined. The antioxidant activities were evaluated using 2,2-diphenyl-1-picrylhydrazyl assay. The population “Cas” appears to have higher antioxidant activity than the other two populations (“Cal” and “S. Ven”).The saturated fatty acid content is influenced only by the year of collection, while the polyunsaturated fatty acid by the populations. The most abundant unsatured fatty acids are linoleic and linolenic acids and “Cas” attained the highest contents.     

Hydrogen bonding and structure of Ba2Ru2Cl10O·10H2O

Dibarium μ‐oxido‐bis[pentachloridoruthenate(IV)] decahydrate, Ba₂Ru₂Cl₁₀O·10H₂O, has been prepared from ruthenium(III) chloride and barium chloride in hydrochloric acid. It crystallizes in the monoclinic system (space group C2/c). The structure consists of alternating layers of [Ru₂Cl₁₀O]⁴⁻ and [Ba(H₂O)₇]²⁺ complex ions along the a direction. The O atom bonded to ruthenium occupies the 4e site, with symmetry, while the other atoms occupy general 8f sites. The overall structure is held together by O—H...O hydrogen bonds and O—H...Cl dipole–dipole interactions.     

Polycyclic aromatic hydrocarbons in the atmosphere: monitoring, sources, sinks and fate. I: Monitoring and sources

This is the first of a series of two papers intended to review the state-of-the-art knowledge on atmospheric PAHs, concerning their monitoring, sources and transformation processes in the atmosphere. The monitoring section briefly introduces this class of compounds, mainly focusing on the 16 PAHs indicated by the US-EPA as priority pollutants. These compounds undergo partitioning between the gas phase and particulate, which has to be considered in the choice of the sampling methodology. Furthermore, sampling artifacts may arise from further phase transfers inside the sampling device. After sampling, extraction, clean up and detection/quantification procedures will follow. They are closely related since the choice of the extraction technique will heavily condition the clean-up step, and both procedures will place demands on the performance of the detection technique (usually GC-MS or HPLC). This is particularly true in the case of complex samples such as those arising from atmospheric sampling. The sources of atmospheric PAHs are then discussed with a particular focus on receptor models, which can allow the apportionment of PAH sources based on concentration data that can be routinely obtained by pollution control networks.     

Time-domain theoretical analysis of the noncoincidence effect, diagonal frequency shift, and the extent of delocalization of the C=O stretching mode of acetone/dimethyl sulfoxide binary liquid mixtures

A time-domain method for simulating vibrational band profiles that simultaneously takes into account both the diagonal and off-diagonal effects is developed and applied to the C=O stretching bands of neat liquid acetone and the acetone/dimethyl sulfoxide (DMSO) binary liquid mixtures. By using this method, it is possible to examine the influence of liquid dynamics on the noncoincidence effect (NCE), which arises from the off-diagonal vibrational interactions, as well as the frequency shifts and band broadening, which are related to both the diagonal and off-diagonal effects. It is shown that the simulations for the C=O stretching bands of acetone in acetone/DMSO binary liquid mixtures on the basis of this method can reproduce the experimentally observed concave curvature of the concentration dependence of the NCE and the unusually large frequency shift of the anisotropic Raman band. The widths of the infrared, isotropic Raman, and anisotropic Raman bands calculated for neat liquid acetone are also in good agreement with those observed. Based on these calculations, the extent of delocalization of the C=O stretching vibrational motions is examined by referring to two quantitative measures of this property, one calculated in the frequency domain and the other in the time domain. It is shown that the extent of delocalization gets larger as the mole fraction of acetone increases, the C=O stretching vibrations being delocalized over a few tens of molecules in neat liquid acetone. It is also shown that the extent of delocalization is related to the quantity called NCE detectability, which is the ratio between the magnitude of NCE and the bandwidth. It is therefore suggested that the extent of delocalization of vibrational motions may be estimated from observable features of Raman band profiles.     

Core-shell photoabsorption and photoelectron spectra of gas-phase pentacene: experiment and theory

The C K-edge photoabsorption and 1s core-level photoemission of pentacene (C22H14) free molecules are experimentally measured, and calculated by self-consistent-field and static-exchange approximation ab initio methods. Six nonequivalent C atoms present in the molecule contribute to the C 1s photoemission spectrum. The complex near-edge structures of the carbon K-edge absorption spectrum present two main groups of discrete transitions between 283 and 288 eV photon energy, due to absorption to pi* virtual orbitals, and broader structures at higher energy, involving sigma* virtual orbitals. The sharp absorption structures to the pi* empty orbitals lay well below the thresholds for the C 1s ionizations, caused by strong excitonic and localization effects. We can definitely explain the C K-edge absorption spectrum as due to both final (virtual) and initial (core) orbital effects, mainly involving excitations to the two lowest-unoccupied molecular orbitals of pi* symmetry, from the six chemically shifted C 1s core orbitals.