On Newton’s method for solving equations containing Fréchet-differentiable operators of order at least two

We provide sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear operator equation containing operators that are Fréchet-differentiable of order at least two, in a Banach space setting. Numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot [J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method, J. Comput. Appl. Math. 79(1997) 131-145; Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5 (1985) 71-84].     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

17O NMR studies of electronic and steric interactions of substituted quinoxaline-2(1H),3(4H)-diones

¹⁷O nmr studies, at natural abundance, of substituted quinoxaline-2(1H),3(4H)-diones demonstrate that the ¹⁷O chemical shift data can provide new insights into steric and electronic interactions due to long range substituent effects on the aromatic ring. The role of considerable “keto” character and torsion angle deformation of the diamide group in solution is emphasized.     

Theoretical study of gallium nitride molecules, GaN2 and GaN4

The electronic and geometric structures of gallium dinitride GaN 2, and gallium tetranitride molecules, GaN 4, were systematically studied by employing density functional theory and perturbation theory (MP2, MP4) in conjunction with the aug-cc-pVTZ basis set. In addition, for the ground-state of GaN 4( (2)B 1) a density functional theory study was carried out combining different functionals with different basis sets. A total of 7 minima have been identified for GaN 2, while 37 structures were identified for GaN 4 corresponding to minima, transition states, and saddle points. We report geometries and dissociation energies for all the above structures as well as potential energy profiles, potential energy surfaces and bonding mechanisms for some low-lying electronic states of GaN 4. The dissociation energy of the ground-state GaN 2 ( X (2)Pi) is 1.1 kcal/mol with respect to Ga( (2)P) + N 2( X (1)Sigma g (+)). The ground-state and the first two excited minima of GaN 4 are of (2)B 1( C 2 v ), (2)A 1( C 2 v , five member ring), and (4)Sigma g (-)( D infinityh ) symmetry, respectively. The dissociation energy ( D e) of the ground-state of GaN 4, X (2)B 1, with respect to Ga( (2)P) + 2 N 2( X (1)Sigma g (+)), is 2.4 kcal/mol, whereas the D e of (4)Sigma g (-) with respect to Ga( (4)P) + 2 N 2( X (1)Sigma g (+)) is 17.6 kcal/mol.     

Theoretical study on the electronic states of NaLi

Configuration interaction calculations have been carried out on electronic states of the NaLi molecule and the cation NaLi(+). Potential energy curves are presented for the lowest nine (1)Sigma(+), seven (1)Pi, four (1)Delta, eight (3)Sigma(+), seven (3)Pi, and four (3)Delta states of NaLi as well as for the lowest ten (2)Sigma(+), six (2)Pi, and two (2)Delta states of NaLi(+). The results of the present many-electron configuration interaction calculations on the cation are in support of previous core-polarization effective potential calculations. The present calculations on the NaLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously as well as an investigation of nonadiabatic effects leading to spectral perturbations. Furthermore, ab initio potential energy curves of the neutral and the ground state of the cation are employed to determine quantum defect that may be employed to generate potential energy curves for nd and (n+1)p (for n>3) Rydberg states of NaLi. The present results on the 3 (1)Pi and 4 (1)Pi states are in good agreement with recent experimental work, whereas on the basis of theoretical data, the recently observed state 5 (1)Pi is better described as 6 (1)Pi.     

The phytochemical analysis and antioxidant activity assessment of orange peel (Citrus sinensis) cultivated in Greece-Crete indicates a new commercial source of hesperidin

The flavonoid content of several methanolic extract fractions of Navel orange peel (flavedo and albedo of Citrus sinensis) cultivated in Crete (Greece) was first analysed phytochemically and then assessed for its antioxidant activity in vitro. The chemical structures of the constituents fractionated were originally determined by comparing their retention times and the obtained UV spectral data with the available bibliographic data and further verified by detailed LC-DAD-MS (ESI+) analysis. The main flavonoid groups found within the fractions examined were polymethoxylated flavones, O-glycosylated flavones, C-glycosylated flavones, O-glycosylated flavonols, O-glycosylated flavanones and phenolic acids along with their ester derivatives. In addition, the quantitative HPLC analysis confirmed that hesperidin is the major flavonoid glycoside found in the orange peel. Interestingly enough, its quantity at 48 mg/g of dry peel permits the commercial use of orange peel as a source for the production of hesperidin. The antioxidant activity of the orange peel methanolic extract fractions was evaluated by applying two complementary methodologies, DPPH(*) assay and the Co(II)/EDTA-induced luminol chemiluminescence approach. Overall, the results have shown that orange peel methanolic extracts possess moderate antioxidant activity as compared with the activity seen in tests where the corresponding aglycones, diosmetin and hesperetin were assessed in different ratios.     

Simultaneous determination of the flavonoid aglycones diosmetin and hesperetin in human plasma and urine by a validated GC/MS method: in vivo metabolic reduction of diosmetin to hesperetin

Diosmetin and hesperetin are the aglycones of the flavonoid glycosides diosmin and hesperidin which occur naturally in citrus fruit. A GC/MS method for the simultaneous determination of diosmetin and hesperetin in human plasma and urine has been developed and validated. The method was linear in the 2-300 ng/mL concentration range for both diosmetin and hesperetin in plasma and urine (r > 0.999). The precision of the method was better than 6.01 and 7.16% for diosmetin and hesperetin, respectively, and the accuracy was 96.76-100.40% and 95.00-105.50% for diosmetin and hesperetin, respectively. The lower limit of quantitation was found to be 2 ng/mL for both analytes in plasma and urine. Recovery of diosmetin, hesperetin and internal standard naringenin was greater than 82.5%. The method has been applied for the determination of diosmetin and hesperetin in plasma and urine samples obtained from a healthy male subject following a single oral 1000 mg dose of the flavonoid glycoside diosmin. The presence of hesperetin in plasma and urine samples indicates the metabolic reduction of diosmetin to its flavanone analogue hesperetin through reduction of the 2,3 double bond of the C-ring by the enzymes of bacteria of the intestinal microflora.     

Design of a field flow system for the on-line spectrophotometric determination of phosphate, nitrite and nitrate in natural water and wastewater

This study describes the design and optimisation of a field flow system for the in-situ collection and on-line determination of phosphate, nitrate and nitrite by flow injection analysis-spectrophotometry. The method is based on the initial determination of phosphate as its phosphoantimonylmolybdenum blue complex which is then oxidized on-line by nitrite and the decrease in absorbance is monitored at 880 nm. Nitrate is determined as the difference between total and initial nitrite content in a separate flow after reduction to nitrite in a cadmium reductive column. The calibration curves were linear in the range 0–2.00 mg L⁻¹ P-phosphate, 0–10.00 mg L⁻¹ nitrite and 0–7.00 mg L⁻¹ nitrate with correlation coefficients of 0.9979, 0.9993 and 0.9995, respectively. The detection limits, calculated as 3S/N, were 0.15 mg L⁻¹ for P-phosphate, 0.17 mg L⁻¹ for nitrite and 0.09 mg L⁻¹ for nitrate. The reproducibility was below 3.0% (n = 7). Method validation in the analysis of natural water and wastewater samples revealed that it can efficiently be applied to the determination of the target analytes, with recoveries in the range of 92–108%. Correspondence: Athanasios G. Vlessidis, Laboratory of Analytical Chemistry, Department of Chemistry, University of Ioannina, Ioannina 45110, Greece     

A criterion for dewetting initiation from surface disturbances on ultrathin polymer films

Nanoindentation-induced defects on ultrathin (h = 17 nm) polystyrene (PS) films that are spin cast on silicon (Si) substrates, with residual depths of penetration lower than the film thickness (<17 nm), can either grow to initiate dewetting or level, which results in a flat polymer surface, upon heating above the glass-transition temperature (T(g)). The excess surface energy (DeltaF(gamma)) of the system, which is added to the initially flat coating with the formation of an indent, provides a critical value, DeltaF(gamma,crit) = 6.1 x 10(-16) J, which determines indent evolution upon annealing. An indent grows when DeltaF(gamma) > DeltaF(gamma,crit) and levels when DeltaF(gamma) < DeltaF(gamma,crit). This conclusion is in agreement with previous reports, which used DeltaF(gamma) to distinguish the two (dewetting/leveling) opposing processes (1) in the case of indents deeper than the film thickness and (2) in the case of built-in ordered surface disturbances by capillary force lithography.     

Theory of the two step enantiomeric purification of 1,3 dimethylallene

An application of a recently proposed [P. Kral et al., Phys. Rev. Lett. 90, 033001 (2003)] two step optical control scenario to the purification of a racemic mixture of 1,3 dimethylallene is presented. Both steps combine adiabatic and diabatic passage phenomena. In the first step, three laser pulses of mutually perpendicular linear polarizations, applied in a "cyclic adiabatic passage" scheme, are shown to be able to distinguish between the L and D enantiomers due to their difference in matter-radiation phase. In the second step, which immediately follows the first, a sequence of pulses is used to convert one enantiomer to its mirror-imaged form. This scenario, which only negligibly populates the first excited electronic state, proves extremely useful for systems such as dimethylallene, which can suffer losses from dissociation and internal conversion upon electronic excitation. We computationally observe conversion of a racemic mixture of dimethylallene to a sample containing approximately 95% of the enantiomer of choice.