Mean convergence of an extended Lagrange interpolation process on [0,+∞)

We study some extended Lagrange interpolation processes based on the zeros of the generalized Laguerre polynomials. We give necessary and sufficient conditions such that the convergence of these processes, in suitable L _p weighted spaces on the real semiaxis, is assured for 1<p<+∞.     

Evaluation of forces in magnetic materials by means of energy and co-energy methods

The evaluation of the total force of magnetic origin acting upon a body in a stationary magnetic field is often carried out using the so-called magnetic energy (or co-energy) method, which is based on the derivation of the magnetic energy (or co-energy) with respect to a virtual rigid displacement of the considered body. The application of this method is usually justified by resorting to the energy conservation principle, written in terms both of electrical and of mechanical quantities. In this paper we shall re-examine the whole matter in the context of classical thermodynamics, in order to obtain a more comprehensive and general proof of the validity of the energy (or co-energy) approach and to point out its limitations. Two typical configurations will be discussed; in the first one, the field sources are represented by conducting bodies carrying free currents, whereas in the second one a permanent magnet creates the driving field. All magnetic materials are assumed to be non-hysteretic and permanent magnets are represented by means of the well-known linear model in the second quadrant of the (B,H) plane. Received 25 July 2001 and Received in final form 5 November 2001     

Riemann-Type Definition of the Improper Integrals

Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane's definition of the Lebesgue integral by imposing a Kurzweil-Henstock's condition on McShane's partitions.     

Unilateral NMR, 13C CPMAS NMR spectroscopy and micro-analytical techniques for studying the materials and state of conservation of an ancient Egyptian wooden sarcophagus

A multi-technique approach was employed to study a decorated Egyptian wooden sarcophagus (XXV–XXVI dynasty, Third Intermediate Period), belonging to the Museo del Vicino Oriente of the Sapienza University of Rome. Portable non-invasive unilateral NMR was applied to evaluate the conservation state of the sarcophagus. Moreover, using unilateral NMR, a non-invasive analytical protocol was established to detect the presence of organic substances on the surface and/or embedded in the wooden matrix. This protocol allowed for an educated sampling campaign aimed at further investigating the state of degradation of the wood and the presence of organic substances by ¹³C cross polarization magic angle spinning (CPMAS) NMR spectroscopy. The composition of the painted layer was analysed by optical microscopy (OM), scanning electron microscopy–energy dispersive spectroscopy (SEM–EDS), Raman and surface enhanced (resonance) Raman spectroscopy (SERS/SERRS), infrared and GC–MS techniques, evidencing original components such as clay minerals, Egyptian green, indigo, natural gums, and also highlighting restoration pigments and alteration compounds. The identification of the wood, of great value for the reconstruction of the history of the artwork, was achieved by means of optical microscopy.     

NMR depth profiles as a non-invasive analytical tool to probe the penetration depth of hydrophobic treatments and inhomogeneities in treated porous stones

Hydrophobic treatment is one of the most important interventions usually carried out in the conservation of stone artifacts and monuments. The analytical study reported in this paper was aimed at answering general questions such as the penetration depth of a hydrophobic treatment into a porous material, its capability to impair the water absorption, how the presence of a treatment may change the open porosity available to the water, and how a treatment may affect the diffusion of water inside a porous structure. Also, inhomogeneities in treated stones due to sharp variations of the amount of the absorbed product in the porous material were evidenced and scaled. The results of this fully non-invasive analytical study were rationalized in terms of new parameters obtained by a suitable process of nuclear magnetic resonance data. These analytical parameters reported here for the first time, namely the hydrophobic efficiency, the penetration depth, and angles describing changes in slope in depth profiles, gave important information in assessing the performance of a treatment.     

Synthesis, crystal structures and magnetic properties of cyanide- and phenolate-bridged [M(III)NiII]2 tetranuclear complexes (M=Fe and Cr)

The binuclear complex NiII2L(H2O)2(ClO4)2(1) and the neutral tetranuclear bimetallic compounds [{M(III)(phen)(CN)4}2{NiII2L(H2O)2}].2CH3CN with M=Fe (2) and Cr (3)[H2L=11,23-dimethyl-3,7,15,19-tetraazatricyclo[19.3.1.1(9,13)]hexacosa-2,7,9,11,13(26),14,19,21(25),22,24-decaene-25,26-diol] have been synthesized and the structures of and determined by single crystal X-ray diffraction. and are isostructural compounds whose structure is made up of centrosymmetric binuclear cations [Ni2(L)(H2O)2]2+ and two peripheral [M(phen)(CN)4]- anions [M=Fe (2) and Cr (3)] acting as monodentate ligands towards the nickel atoms through one of their four cyanide nitrogen atoms. The environment of the metal atoms in 2 and 3 is six-coordinated: two phen-nitrogen and four cyanide-carbon atoms at the iron and chromium atoms and a water molecule, one cyanide-nitrogen and two phenolate-oxygens and two imine-nitrogens from the binucleating ligand L2- at the nickel atom build distorted octahedral surroundings. The values of the FeNi and CrNi separations through the single cyanide bridge are 5.058(1) and 5.174(2)A respectively, whereas the Ni-Ni distances across the double phenolate bridge are 3.098(2)(2) and 3.101(1) A (3). The magnetic properties of have been investigated in the temperature range 1.9-290 K. The magnetic behaviour of corresponds to that of an antiferromagnetically coupled nickel(II) dimer with J=-61.0(1) cm-1, the Hamiltonian being defined as H=-J S(A).S(B). An overall antiferromagnetic behaviour is observed for and with a low-lying singlet spin state. The values of the intramolecular magnetic couplings are J(Fe-Ni)=+17.4(1) cm-1 and J(Ni-Ni(a))=-44.4(1) cm-1 for and J(Cr-Ni)=+11.8(1) cm-1 and J(Ni-Ni(a))=-44.6(1) cm-1 for [H=-J(M-Ni)(S(M).S(Ni)+S(Ma).S(Nia))-J(Ni-Nia)S(Ni)S(Nia)]. Theoretical calculations using methods based on density functional theory (DFT) have been employed on in order to analyze the efficiency of the exchange pathways involved and also to substantiate the exchange coupling parameters.     

Structure-Property Relationships in the Basicity and Lipophilicity of Arylalkylamine Oxides

Homologous N,N-dimethyl-phenylalkylamine oxides and N,N-dimethyl-diphenylalkylamine oxides were prepared. Their basicity and lipophilicity (octan-1-ol/H₂O) were compared to those of the parent amines. In contrast to the amines, the basicity of all N,N-dimethyl-arylalkylamine oxides showed very limited pK_a variations (range 4.65 – 5.01) with increasing chain length and number of Ph groups. The N-oxides in their neutral form had a log P^N value lower by 2.77±0.34 (n=9) units than that of the parent amine. The log P^C of the cationic N,N-dimethyl-diphenylalkylamines was lower than that of their neutral form, with a decrement diff(log P^N−C) that increased from 3.25 to 4.21 in the homologous series. Unexpectedly, the decrement diff(log P^N−C) for the N-oxides was much smaller than for the tertiary amines, being 0.23 for the aliphatic N,N-dimethyl-pentylamine oxide, 0.47±0.13 for the phenylalkylamine oxides, and 0.80±0.07 for the diphenylalkylamine oxides. In fact, the protonated N-oxides had log P^C values that were quite comparable to those of the protonated parent amines. Because of the differences in basicity, the difference in distribution coefficients at physiological pH (log D^7.4) between a tertiary arylalkylamine and its N-oxide was 0.82±0.66 (n=9). The pharmacokinetic implication is that N-oxygenation may have a smaller effect on the urinary excretion of tertiary amines than usually assumed.     

Ligand effects on the structures and magnetic properties of tricyanomethanide-containing copper(II) complexes

The preparation, crystal structure and magnetic properties of four heteroleptic copper(II) complexes with the tricyanomethanide (tcm(-)) and the heterocyclic nitrogen donors 3,6-bis(2-pyridyl)pyridazine (dppn), 2,5-bis(2-pyridyl)pyrazine (2,5-dpp), 2,3-bis(2-pyridyl)pyrazine (2,3-dpp) and 2,3-bis(2-pyridyl)quinoxaline (2,3-dpq) are reported, {[Cu(2)(dppn)(OH)(tcm)(2)] x tcm}(n) (1), {[Cu(2,5-dpp)(tcm)] x tcm}(n) (2), {[Cu(2)(2,3-dpp)(2)(tcm)(3)(H(2)O)(0.5)] x tcm x 0.5H(2)O}(n) (3) and [Cu(2,3-dpq)(tcm)(2)](n) (4). 1 has a ladder-like structure with single mu-1,5-tcm ligands forming the sides and a bis-bidentate dppn and a single mu-hydroxo providing the rung. Each copper atom in 1 exhibits a distorted square pyramidal CuN(4)O surrounding: the basal plane is built by the hydroxo-oxygen, a nitrile-nitrogen atom from a tcm group and one pyrazine and a pyridyl nitrogen atoms from the dppn whereas the apical position is filled by a nitrile-nitrogen atom from a symmetry-related tcm ligand. The structures of 2-4 consists of zig-zag (2 and 3)/linear (4) chains of copper(II) ions which are bridged by either bis-bidentate 2,5-dpp (2) and 2,3-dpp (3) molecules or single mu-1,5-tcm (4) groups. The copper atoms in 2 and 4 are five coordinated with distorted trigonal bipyramidal (2) and square pyramidal (4) CuN(5) surroundings. The axial positions in 2 are occupied by two pyridyl-nitrogen atoms from two 2,5-dpp ligands whereas the trigonal plane is built by a nitrile-nitrogen from a terminally bound tcm group and two pyrazine nitrogen atoms from two 2,5-dpp molecules. The basal plane in 4 is defined by a pyridyl and a pyrazine nitrogen atoms from the bidentate 2,3-dpq ligand and two nitrile nitrogen atoms from two tcm groups (one terminal and the other bridging) whereas the apical position is filled by a nitrile nitrogen from another tcm ligand. The crystallographically independent copper atoms in 3 [Cu(1) and Cu(2)] exhibit elongated octahedral geometries being defined by four nitrogen atoms from two 2,3-dpp groups [Cu(1) and Cu(2)] either two terminally bound tcm ligands [Cu(1)] or a water molecule and a monodentate tcm ligand [Cu(2)] in cis positions. Magnetic susceptibility measurements for 1-4 in the temperature range 1.9-295 K reveal the occurrence of strong [J ca.-1000 cm(-1) (1); H = -JS(A) x S(B)] and weak [J = -0.13 (2), -0.67 (3) and -0.18 cm(-1) (4); H = -J Sigma(I)S(i) x S(i+1)] antiferromagnetic interactions in agreement with the different nature of the exchange pathways involved, diazine and single mu-hydroxo (1) and the extended 2,5-dpp (2), 2,3-dpp (3) and single mu-1,5-tcm (4) bridges with copper-copper separations of 3.363(8) (1), 7.111(1) (2), 6.823(1) and 7.056(1) (3) and 7.446(1) A (4).