Sharp essential self-adjointness of relativistic Schrödinger operators with a singular potential

This paper is devoted to the study of essential self-adjointness of a relativistic Schrödinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient and necessary condition for essential self-adjointness.     

Synthesis, spectral and thermal study on new Fe(III) complexes with N,N-dimethylbiguanide as antibacterial agents

New complexes [FeO(DMBG)]₂ and [Fe(DMBG)₂]Cl·0.5H₂O (HDMBG: N,N-dimethylbiguanide) have been synthesized and characterized by microanalytical, IR and UV–Vis data. Electronic spectra of the complexes are characteristic for a tetrahedral stereochemistry, whilst the modifications in the IR spectra indicate the presence of the DMBG anion as chelate. The thermal decomposition investigated in air by thermal analysis confirmed the proposed formulas for the complexes and provided information concerning the modifications during heating and also the thermodynamic effects accompanying them. The thermal transformations are complex, according to TG and DTG curves including dehydration, hydrochloric acid elimination, oxidative degradation and condensation of –C=N– unit. The final product of decomposition was iron (III) oxide as powder XRD indicates. Complexes were screened for their antimicrobial properties against Gram-positive, Gram-negative bacterial, as well as fungal pathogenic strains. The results indicate that Fe(III) complexes exhibit an improved antibacterial activity against S. aureus and E. coli strains in comparison with free biguanide. The Fe(III) complexes also inhibit the ability of S. aureus, B. subtilis, P. aeruginosa and E. coli strains to colonize the inert substratum, accounting for their possible use as anti-biofilm agents.     

Physico-chemical and thermal characterisation of new Co(II) complexes with pyrazole derivatives

Four new complexes having general formula [CoL₂(acr)₂] (L: 1H-pyrazole (Hpz) (1); 3-methyl-1H-pyrazole (3-Me-Hpz) (2); 4-methyl-1H-pyrazole (4-Me-Hpz) (3); 3,5-dimethyl-1H-pyrazole (Hdmpz) (4); acr: acrylato ion) were synthesised and characterised. The infrared and UV–vis spectral data indicate that these pyrazole derivatives act as unidentate while acrylato ions act as bidentate chelate ligands generating Co(II) complexes with octahedral stereochemistry. TG experiments revealed the nature of complex species as anhydrous and confirmed those compositions. The biological assays revealed a good activity against Bacillus subtilis for all complexes.     

Probing the reactivity of nebularine N1-oxide. A novel approach to C-6 C-substituted purine nucleosides

A novel approach to the synthesis of purine nucleoside analogues, featuring the reaction of the C6-N1-O⁻ aldonitrone moiety of 9-ribosyl-purine (nebularine) N1-oxide with some representative dipolarophiles, as well as Grignard reagents, is reported. Addition of Grignard reagents to the electrophilic C-6 carbon of the substrate allows a facile access to C-6 C-substituted purine nucleosides without using metal catalysts. 1,3-Dipolar cycloaddition processes lead to novel nucleoside analogues via opening, degradation or ring-enlargement of the pyrimidine ring of the base system of the first-formed isoxazoline or isoxazolidine cycloadduct.     

Dynamics of vibrational overtone excited pyruvic acid in the gas phase: line broadening through hydrogen-atom chattering

The dynamics of overtone-excited pyruvic acid (PA) is studied using a combination of experimental and theoretical methods. It is experimentally observed that high overtone excitation of the OH-stretching mode of PA in the gas phase leads to a unimolecular decarboxylation reaction. An RRKM analysis of the rate is consistent with previous experiments for the thermal reaction but is inconsistent with the present overtone chemistry; from this it is concluded that the overtone-induced reaction is likely to be a direct reaction. Using a Fourier transform infrared spectrometer and a cavity ring-down spectrometer, the spectrum for the OH-stretch fundamental and overtone transitions is measured. We assign two conformers of PA in the spectrum, the Tc and Tt, corresponding to distinct orientations of the OH-group. The spectral peaks for the Tc-conformer broaden dramatically at the third and fourth overtones while those of the Tt-conformer remain relatively narrow. Using a three-mode quantum mechanical model for the vibrational states, the line positions and intensities are well reproduced by theory. The line widths, and the associated dynamical interpretation, are provided by a direct dynamics calculation, where the potential is computed "on-the-fly" and all degrees of freedom are included. It is found that the line broadening is due to the onset of H-atom chattering between the two O-atoms, an effect that occurs for the Tc-conformer but not the Tt-conformer. This H-atom-transfer process is the first step of the decarboxylation reaction mechanism, which subsequently involves breaking the C-C bond. The theoretical and experimental line widths agree but do not correspond to the full reaction time which is much longer than the initial chattering step.     

Photothermal and photocatalytic processes on TiO2 based materials prepared by sol-gel method

In the present work, Fe³⁺ doped TiO₂ coatings on glass substrates were prepared by dip-coating from a sol-gel solution. The influence of the dopant concentration on the structure, optical, photocatalytic and photothermal properties of the films was studied. The results obtained have shown a strong correlation between the catalytic properties and the amount of iron dopant and the temperature of the thermal treatment.     

Host-guest complexes between an aromatic molecular tweezer and symmetric and unsymmetric dendrimers with a 4,4'-bipyridinium core

We have investigated the spectroscopic and electrochemical behavior of symmetric and unsymmetric first-, second-, and third-generation dendrimers comprising an electron-acceptor 4,4'-bipyridinium core (viologen type) and electron-donor 1,3-dimethyleneoxybenzene (Fréchet-type) dendrons. The quite strong fluorescence of the symmetrically and unsymmetrically disubstituted 1,3-dimethyleneoxybenzene units of the dendrons is completely quenched as a result of donor-acceptor interactions that are also evidenced by a low-energy tail in the absorption spectrum. In dichloromethane solution, the 4,4'-bipyridinium cores of the investigated dendrimers are hosted by a molecular tweezer comprising a naphthalene and four benzene components bridged by four methylene units. Host-guest formation causes the quenching of the tweezer fluorescence. The association constants, as measured from fluorescence and (1)H NMR titration plots, (i) are of the order of 10(4) M(-1), (ii) decrease on increasing dendrimer generation, and (iii) are slightly larger for the unsymmetric than for the symmetric dendrimer of the same generation. The analysis of the complexation-induced shifts of the temperature-dependent (1)H NMR signals of the host and guest protons confirms that the bipyridinium core is positioned inside the tweezer cavity and allows the conclusions that (i) shuttling of the tweezer from one to the other pyridinium ring is fast (DeltaG < 10 kcal/mol), (ii) in the case of the unsymmetric dendrimers, the less substituted pyridinium ring is preferentially complexed in apolar solvents, and (iii) complexation of the 4,4'-bipyridinium core proceeds by clipping for the symmetric dendrimers and by threading in the case of unsymmetric ones. Host-guest formation causes a displacement of the first reduction wave of the 4,4'-bipyridinium unit toward more negative potential values, whereas the second reduction wave is unaffected. These results show that the host-guest complexes between the tweezer and the dendrimers are stabilized by electron donor-acceptor interactions and can be reversibly assembled/disassembled by electrochemical stimulation.     

A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems

In this paper we propose a new algorithm for solving difficult large-scale global optimization problems. We draw our inspiration from the well-known DIRECT algorithm which, by exploiting the objective function behavior, produces a set of points that tries to cover the most interesting regions of the feasible set. Unfortunately, it is well-known that this strategy suffers when the dimension of the problem increases. As a first step we define a multi-start algorithm using DIRECT as a deterministic generator of starting points. Then, the new algorithm consists in repeatedly applying the previous multi-start algorithm on suitable modifications of the variable space that exploit the information gained during the optimization process. The efficiency of the new algorithm is pointed out by a consistent numerical experimentation involving both standard test problems and the optimization of Morse potential of molecular clusters.     

A Note on Local Asymptotics of Solutions to Singular Elliptic Equations via Monotonicity Methods

This paper concerns the asymptotic behavior of solutions and their gradients to linear and nonlinear elliptic equations with singular coefficients of fuchsian type.