On the extreme spectral properties of Toeplitz matrices generated byL 1 functions with several minima/maxima

In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue ₁ ⁽ⁿ⁾ of symmetric (Hermitian)n ×n Toeplitz matricesT _n (f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that ₁ ⁽ⁿ⁾ tends to essinff =m _f in the following way: ₁ ⁽ⁿ⁾ –m _f 1/n ^2k . These authors use three assumptions:A1)f –m _f has a zero inx =x ₀ of order 2k.A2)f is continuous and at leastC ^2k in a neighborhood ofx ₀.A3)x =x ₀ is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L ¹[–, ]. In this paper we further extend this theory to the case of a functionf L ¹[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m _f is the only parameter which characterizes the rate of convergence of ₁ ⁽ⁿ⁾ tom _f .     

Minimum blocking configurations

Some results on configurations realizing minimum blocking sets of a finite projective plane are obtained by introducing a suitable attraction property.Dedicated to Professor M. Scafati Tallini on the occasion of her 65th birthday     

Formation and stability of pyrophosphate complexes with aliphatic amines in aqueous solution

The complex formation between pyrophosphate (P(2)O(7)(4-)) and protonated methylamine, ethylenediamine, diethylenetriamine, triethylenetetramine, tetraethylenepentamine and pentaethylenehexamine, has been studied potentiometrically, in aqueous solution, at 25 degrees C. It was found that the species ALH(q)(A = amine, L = P(2)O(7)(4-)) are formed with q = 1 ... n(n = 3, 5, 6, 7, 7 and 8 for the above amines respectively). Mono- and di-amines form species A(p)LH(q) too. The stability of these species is quite high [e.g. H(4)A(4+) + HL(3-)ALH(5)(+): log K = 8.1 (A = pentaethylenehexamine)] and depends strictly on the charges involved in the formation reaction. Charges of reactants being equal, the stability trend is penten > tetren > trien > dien > en > meta and cationic mixed species are more stable than anionic ones. These results are discussed in relation to speciation problems in natural and biological fluids.     

Solid-state supramolecular organization, established directly from powder diffraction data, and photoluminescence efficiency of rigid-core oligothiophene-S,S-dioxides

The "rigid-core" material 3,5-dimethyl-2,3'-bis(3-methylthiophene)-dithieno[3,2-b:',3'-d]thiophene-4,4-dioxide (DTTOMe4) has the highest photoluminescence ever reported for thiophene-based molecules in the solid state. We report the structure of this material, determined directly from powder X-ray diffraction data using the Genetic Algorithm method for structure solution, followed by Rietveld refinement, and the structural properties are discussed in relation to the structures of the corresponding subsystems DTTO and DTTOMe. While the crystal structures of the latter compounds contain cofacial dimers, the crystal structure of DTTOMe4 comprises layers of molecules aligned in an antiparallel fashion. Intermediate neglect of differential overlap with single configuration interaction (INDO/SCI) calculations on the intermolecular interactions in the three crystal structures show that the different solid-state photoluminescence efficiencies of DTTOMe4, DTTOMe, and DTTO cannot be correlated with the different types of dipole-dipole alignment in the solid state. Instead, photoluminescence efficiencies correlate well with the rate of formation of nonradiatively decaying charge-transfer pairs upon photoexcitation. Because of larger intermolecular distances in DTTOMe4, the photoluminescence is less effectively quenched by charge-transfer processes than in DTTOMe and DTTO.     

Dramatic changes in geometry after ionization: experimental and theoretical studies on the electronic properties of fluorocarbonyl (mono-, di-, and tri-) sulfur compounds

In this work, we present a complete study on He I photoelectron spectroscopy (PES) for the fluorocarbonyl mono-, di-, and trisulfur compounds FC(O)SCl, FC(O)SSCH(3), and FC(O)SSSC(O)F. After optimizations of the structure for stable conformers at different levels of theory, a complete theoretical study involving the calculation of the ionization energies using orbital valence Green's functional (OVGF) was performed. Calculations of radical-cationic forms were carried out in order to compare their properties with those of the neutral molecules. The first IP values are 10.7, 9.0, and 10.5 eV for FC(O)SCl, FC(O)SSCH(3), and FC(O)SSSC(O)F, respectively. The groups bonded to the S atom mainly influence the ionizations originating from the sulfur lone pairs. A wide electronic delocalization in the FC(O)S moiety can be deduced from experimental and theoretical results, which leads to a strong energetic stabilization of the n' '(S) (sulfur lone pair pi orbital). Other conclusions relate to effects on the substituents attached to the S atom and the importance of the molecular planarity in the orbital stabilization of the FC(O)S moiety for the neutral molecules. It is worthwhile mentioning that FC(O)SCl retains its planar structure after ionization, but drastic changes occur in the geometry of both FC(O)SSCH(3) and FC(O)SSSC(O)F. The FC(O)SSCH(3) molecule adopts a heavy atom planar structure after ionization. The FC(O)SSS moiety becomes a planar form after the ionization of the FC(O)SSSC(O)F molecule, whereas the second C(O)F group maintains its original conformation with respect to the SSS group.     

Copper(II) complexes of N-(phosphonomethyl)glycine in aqueous solution: a thermodynamic and spectrophotometric study

Copper(II) complexes with the herbicide N-(phosphonomethyl)glycine (glyphosate) have been investigated in aqueous solution by means of pH-metric measurements at different temperatures, 5 相似文献   

The effects of oxygenation on the optical properties of dimethyl-dithienothiophenes: comparison between experiments and first-principles calculations

Modifications of the optical properties of dimethyl-dithienothiophenes due to the oxygen functionalization of the central sulfur atom are investigated. We have measured the absorption, photoluminescence (PL) and PL excitation spectra, the PL quantum efficiencies, and the PL decay times. These experimental results are interpreted and compared with first-principles time-dependent density-functional theory calculations, which predict, for the considered systems, excitation and emission energies with an accuracy of 0.1 eV. It is found that the oxygenation strongly changes optical and photophysical properties. These effects are related to the modifications of the energetically lowest-unoccupied molecular orbital and the energetically second highest occupied one, which change the relative position of the two lowest singlet and triplet excited states.     

Synthesis and X-Ray Analysis of a Nickel Triphenyl-Cyclopropenyl Complex. A mo-interpretation of the geometry and bonding in the (C3H3)ML3-type of complexes

The reaction of [(C₃Ph₃)Ni(PPh₃)₂]ClO₄ with P(CH₂CH₂PPh₂)₃(pp₃) and NaBPh₄ yields the [(C₃Ph₃)Ni(pp₃)]BPh₄-complex. After long exposure of the solution of this compound in acetone/butanol to the air a new derivative [(C₃Ph₃)-Ni(pp₂po)]BPh₄· 0.5 C₄H₉OH, where pp₂po is (Ph₂PCH₂CH₂)₂P(CH₂ CH₂POPh₂), is obtained. Complete X-ray analysis has been carried out for the latter complex: a=18.303 (5); b=29.445 (6), c=13.305 (5) Å, β=112.70 (9)°; space group monoclinic, P2₁/a, Z=4. Disorder problems were encountered in the refinement of the structure. The best R is 0.093. One of the arms of the parent pp₃-molecule, not coordinated to the metal, undergoes oxidation. The Ni-atom, coordinated by the three remaining P-atoms of the ligand, is also linked in a roughly η³-mode to the cyclopropenium ligand. The geometry of the molecule is examined in detail. Extended HMO-calculations were performed to interpret how the variation of P? Ni? P angles affects the bonding between the NiP₃- and C₃H₃-fragments. The conclusion is that the overall energy of the complex may be lowered in spite of a weakening of the Ni-cyclopropenium linkage. Extensions are made to other systems containing a linkage between a metal and a X₃-ring (X=P,As).