Osservazioni sulle caratteristiche dei grafi o singrammi

Riassunto Si introducono certi gruppi di numeri associati ad un grafo o singrammaG che vengono chiamati caratteristiche diG. Si studiano alcune proprietà delle caratteristiche e se ne fanno applicazioni a vari problemi sui grafi.

---

Résumé On introduit certains groupes de nombres qui sont associés à un grapheG et qu’on appelle caractéristiques deG. Ou étudie quelques proprietés des caractéristiques et on en fait des applications a divers problèmes sur les graphes.

---

---

Lavoro eseguito nell’ambito del Gruppo N. 26 del Comitato Naz. per la Mat. del C.N.R.     

Optimale Bestelltermine bei zufallsveränderlichen Lieferfristen

Zusammenfassung Ermittlung des günstigsten Bestellzeitpunktes, wenn die Zeitspanne zwischen der Bestellung und der Lieferung eine Zufallsveränderliche mit bekannter Verteilung ist.

---

Summary Determination of the optimal time for placing orders in those cases where the time interval between order and supply is a random variable with known distribution.

     

N,N′-dialkylsubstituted Imidazolidine-2-thionecopper(I) complexes. X-ray analysis of chloro-bis(N,N′-dimethylimidazolidine-2-thione)copper(I)

Summary New complexes of copper(I) withN,N-dialkylsubstituted imidazolidine-2-thione ligands were prepared by reduction of CuX₂ (X = Cl or Br). The i.r. spectra show that in all the complexes the ligand coordinates through the sulphur atom. The crystal structure of chloro-bis(N,N-dimethylimidazolidine-2-thione)copper(I) has been determined from x-ray diffraction data. Crystals are monoclinic. space groupC ₂, with unit cell dimensions:a = 16.022(15),b = 9.942(10),c = 15.112(15) A, = 139.84(10)², Z = 4. The final R index is 5.2%. The copper coordination is trigonal, involving sulphur atoms of the two ligands and One chlorine atom. The steric effect of the two methyls imposes a rotation of the imidazolidine rings with respect to the coordination plane. The dihedral angle between the mean plane of thiourea moieties. parallel one with the other. and the coordination plane is 119.3°.This work was supported by the National Research Council (C.N.R.) of Rome.     

Gunshot residues on paraffin drops

In an attempt to facilitate the removal of gunpowder residues from the skin, a simplified method has been tested as compared to the commonly used one of brushing with liquid paraffin. The removing material is still paraffin, but it is dropped from a lighted paraffin candle onto the first interdigital space of the hand. Maps were constructed for gunpowder residues on hands after pistol firing and the first interdigital space was found to be the most significant. Analysis of paraffin “blanks” from candles showed them to be free from antimony, barium and copper. Many samples were examined from the left and the right hands of individuals who had or had not fired a pistol. The results clearly show that from the content of Sb, primarily, and also of Ba, it is possible to identify the person who fired the pistol. Due to the random distribution of copper coming from the skin, this element appears not to be meaningful for the identification of pistol firers. Some practical cases of suicides and shootings are reported.     

A new tricyclic triketone from tandem condensation reactions

Perhydrophenanthrene-1,5,10-trione (6) was isolated from the reaction of methyl 3-(carboxymethyl)cyclohexanone and cyclohexenone in a tandem Michael-Claisen reaction. NMR and X-ray analysis confirmed the structure of the product.     

Atomic force microscopy study of early morphological changes during apoptosis

Apoptosis is defined by a distinct set of morphological changes observed during cell death including loss of focal adhesions, the formation of cell membrane buds or blebs, and a decrease in total cell volume. Recent studies suggest that these dramatic morphological changes, particularly apoptotic volume decrease (AVD), are an early prerequisite to apoptosis and precede key biochemical time-points. Here we use atomic force microscopy to observe early stage AVD of KB cells undergoing staurosporine-induced apoptosis. After a 3-h exposure to 1 microM staurosporine, a 32% decrease in total cell height and a 50% loss of total cell volume is observed accompanied by only a 15% change in cell diameter. The observed AVD precedes key biochemical hallmarks of apoptosis such as loss of mitochondrial membrane potential, phosphatidyl serine translocation, nuclear fragmentation, and measurable caspase-3 activity. This suggests that morphological volume changes occur very early in the induction of apoptosis.     

Metabolic profile of lettuce leaves by high-field NMR spectra

A detailed analysis of the proton high-field NMR spectra of aqueous and organic extracts of lettuce leaves is reported for the first time. A combination of COSY, TOCSY, (1)H-(13)C HSQC, (1)H-(13)C HMBC bidimensional sequences and DOSY was used to assign each spin system and to separate the components of the complex patterns. A large number of water-soluble metabolites belonging to different classes such as carbohydrates, polyols, organic acids and amino acids were fully assigned. Moreover, the complex spectra of metabolites extracted in organic solvents belonging to sterols, fatty acids, diacylglycerophospholipids, galactosyldiacylglycerols, sulpholipids, pheophytins, carotenoids and hydrocarbons were also assigned.     

Measurement of coupling constants in symmetrical spin systems using a full multiple-step cross-polarization-driven NMR pulse scheme

New NMR pulse schemes completely driven under homonuclear and heteronuclear cross-polarization conditions are proposed for the study and the measurement of coupling constants in symmetrical molecules in solution. The appropriate superimposition of independent magnetization components can afford several spin-selective multiplet patterns that are suitable for the determination of the magnitude and the sign of proton-proton and proton-carbon coupling constants with optimum sensitivity levels. A detailed product operator formalism analysis for the proposed doubly selective 1D and nonselective 2D HCP-TOCSY versions is provided and experimental verification for the configurational analysis of symmetric olefinic systems having chemical equivalence is demonstrated.     

Tuning of redox properties for the design of ruthenium anticancer drugs: part 2. Syntheses, crystal structures, and electrochemistry of potentially antitumor [Ru III/II Cl6-n(Azole)n]z(n = 3, 4, 6) complexes

A series of mixed chloro-azole ruthenium complexes with potential antitumor activity, viz., mer-[RuIIICl3(azole)3] (B), trans-[RuIIICl2(azole)4]Cl (C), trans-[RuIICl2(azole)4] (D), and [RuII(azole)6](SO3CF3)2 (E), where azole = 1-butylimidazole (1), imidazole (2), benzimidazole (3), 1-methyl-1,2,4-triazole (4), 4-methylpyrazole (5), 1,2,4-triazole (6), pyrazole (7), and indazole (8), have been prepared as a further development of anticancer drugs with the general formula [RuCl4(azole)2]- (A). These compounds were characterized by elemental analysis, IR spectroscopy, electronic spectra, electrospray mass spectrometry, and X-ray crystallography. The electrochemical behavior has been studied in detail in DMF, DMSO, and aqueous media using cyclic voltammetry, square wave voltammetry, and controlled potential electrolysis. Compounds B and a number of C complexes exhibit one RuIII/RuII reduction, followed, at a sufficiently long time scale, by metal dechlorination on solvolysis. The redox potential values in organic media agree with those predicted by Lever's parametrization method, and the yet unknown EL parameters were estimated for 1 (EL = 0.06 V), 3 (EL = 0.10 V), 4 (EL = 0.17 V), and 5 (EL = 0.18 V). The EL values for the azole ligands 1-8 correlate linearly with their basicity (pK(a) value of the corresponding azolium acid H2L+). In addition, a logarithmic dependence between the homogeneous rate constants for the reductively induced stepwise replacement of chloro ligands by solvent molecules and the RuIII/RuII redox potentials was observed. Lower E(1/2) values (higher net electron donor character of the ligands) result in enhanced kinetic rate constants of solvolysis upon reduction. The effect of the net charge on the RuIII/RuII redox potentials in water is tentatively explained by the application of the Born equation. In addition, the pH-dependent electrochemical behavior of trans-[RuCl2(1,2,4-triazole)4]Cl is discussed.