Randić index and lexicographic order

Let T be a tree and consider the Randi index (T)= ), where v _i –v _j runs over all edges of T and (v _i ) denotes the degree of the vertex v _i . Using counting arguments we show that the Randi index, is monotone increasing over the well (lexicographic order) ordered sequence of trees with unique branched vertex.     

Serine protease mechanism-based mimics. Direct evidence for a transition state bridge proton in stable potentials

We have synthesized 1-(2-hydroxyacetyl)piperidine-2-one (2) and 1-(2-hydroxyacetyl)azepan-2-one (3). Equilibrium (K(f)) between the free alcohol (open form) and the tetrahedral intermediate (cyclol) is readily established, and both forms are observed in the D(2)O (1)H NMR spectra of 2 and 3. Therefore, their interconversion can be considered as an almost thermoneutral non-identical one. Pseudo-first-order rate constants (k(obs)) were obtained by simulating the AB (1)H NMR system observed for the cyclol. By best fitting the experimental points of a k(obs) versus pD profile to the equation k(obs) = 0.5k(0r) + 0.5k(r) K(ac)/(K(ac) + [D(+)]) + 0.5k(f)K(ao)/(K(ao)+ [D(+)]), the parameters involved were obtained: rate constants of rupture and formation (k(0r) and k(0f) = K(f)k(0r)) catalyzed by water, rate constants of rupture (k(r)) and formation (k(f)) from the conjugated bases of the cyclol form and the open form, and their acidity equilibrium constants K(ac) and K(ao). The system studied mimics the serine alcohol attack on the peptide bond and its reverse reaction in serine protease enzymes. In fact, the reaction rates are similar or perhaps even faster than the ones obtained for enzymatic reactions. The results also show the participation of water molecules forming catalytic proton bridges in stable potentials with the two interconverted forms. The position change of the bridged proton is sensitive to lactam ring size, and it is manifested by considerable change in the pKa values of both cyclol and open forms. Other evidence such as kinetics, DeltaS degrees , DeltaS, and proton inventory experiments and semiempirical molecular calculations support this proposal.     

Theoretical calculations of homogeneous catalysis in the gas phase: elimination kinetics of 2,2-dimethoxypropane in the presence of HCl,F3CCOOH and CH3COOH

The mechanisms of gas-phase elimination kinetics of 2,2-dimethoxypropane in the presence of hydrogen chloride, trifluoroacetic acid and acetic acid were studied using Moller Plesset, ab initio combined method Complete Basis Set (CBS)-QB3 and various density functional theory methods with 6-311G(d,p) and 6-311++G(d,p) basis sets. The M06-2X/6-311++G(d,p) method provided reasonable agreement with the experimental enthalpy and energy of activation. Formation of 2-methoxypropene and methanol products occurs through six-membered cyclic ring transition state (TS) structure. The TS was characterised by single imaginary frequency, and confirmed through intrinsic reaction coordinate (IRC) calculations. The IRC calculations suggest the development of a van der Waal complex between the 2, 2-dimethoxy propane and the acid catalyst, leading to the TS formation. The process of decomposition in the absence of the acid catalyst requires much higher temperature with an energy of activation above 200 kJ/mol. This fact appears to be a consequence of a four-membered cyclic TS-type of mechanism in the non-catalysed reaction. Structural parameters, analyses of natural bond orbital charges and bond orders of the acid-catalysed elimination reactions in this study suggest that the polarisation of the C–O bond, in the direction C^δ+—O^δ?, is rate-determining in the TS. These reactions are non-synchronous concerted polar in nature.     

Pristine and Al-doped hematite printed films as photoanodes of <Emphasis Type="Italic">p</Emphasis>-type dye-sensitized solar cells

We hereby propose a non-expensive method for the deposition of pure and Al-doped hematite photoanodes in the configuration of thin films for the application of dye-sensitized solar cells (DSSC). The electrodes have been prepared from hematite nanoparticles that were obtained by thermal degradation of a chemical precursor. The particles have been used in the preparation of a paste, suitable for both screen printing and doctor blade deposition. The paste was then spread on fluorine-doped tin oxide (FTO) to obtain porous hematite electrodes. The electrodes have been sensitized using N3 and D5 dyes and were characterized through current/voltage curves under simulated sun light (1 sun, AM 1.5) with a Pt counter electrode. Al-doping of hematite showed interesting changes in the physical and electrochemical characteristics of sensitized photoanodes since we could notice the growth of AlFe₂O₄ (hercynite) as a secondary crystal phase into the oxides obtained by firing the mixtures of two chemical precursors at different molar ratios. Pure and Al-doped hematite electrodes have been used in a complete n-type DSSCs. The kinetics of charge transfer through the interface dye/electrolyte was studied and compared to that of a typical p-type DSSC based on NiO photocathodes sensitized with erythrosine B. The results suggest a potential application of both Fe₂O₃ and Fe₂O₃/AlFe₂O₄ as photoanodes of a tandem DSSC.     

Spectroscopic and magnetic properties of copper(II) complexes derived from pyridine-2-carbaldehyde thiosemicarbazone. Structures of [Cu(NO3)(C7H8N4S)(H2O)](NO3) and [{Cu(NCS)(C7H7N4S)}2]

Complexes with the formula CuX(L) (X=N₃ 1, NCO 2 and NCS 3) and [Cu(NO₃)(HL)(H₂O)](NO₃) 4, where HL=C₇H₈N₄S, (pyridine-2-carbaldehyde thiosemicarbazone), have been characterised. Single-crystal X-ray diffraction studies on compounds 3 and 4 have been carried out. The structure of compound 4 consists of monomeric distorted square pyramidal copper(II) species. The copper(II) ions are coordinated to the NNS atoms from the tridentate thiosemicarbazone ligand and one oxygen atom of a nitrate group in the equatorial position. The oxygen atom of the water molecule occupies the apical position. The structure of compound 3 consists of non-centrosymmetric {Cu₂(μ-SR)₂} entities in which the copper(II) ions exhibit five-coordinate square–pyramidal geometry. The thiosemicarbazone ligand and one nitrogen atom from the thiocyanate ion are in a basal position. The sulfur atom of the tridentate ligand acts as a bridge occupying the apical position. Structural and spectroscopic results suggest the presence of relevant σ ligand-to-metal charge transfer and metal-to-ligand π-backdonation character in these compounds. The ESR spectra of compounds 3 and 4 show rhombic symmetry. For complexes 1 and 2 the ESR spectra exhibit axial signals. Magnetic measurements on compounds 1, 2 and 3 show antiferromagnetic couplings. The susceptibility data were fitted by the Bleaney–Bowers’ equation for copper(II) dimers. The obtained J/k values are −4.22, −6.10 and −7.33 K for compounds 1, 2 and 3, respectively.     

A Straightforward Synthesis of Six‐Membered‐Ring Heterocyclic α‐Aminophosphonic Acids from N‐Acyliminium Ions

A convenient synthesis of phosphonic analogues of pipecolic acid and its heterocyclic analogues is reported. The major step of the elaborated procedure is the introduction of the phosphonate group into the skeleton of the appropriate cyclic amide through N‐acyliminium ions. The former ones were obtained by preparation of the hemiaminals or their methyl ethers from the N‐protected cyclic amides. Finally, the reaction with trimethyl phosphite in the presence of BF₃·OEt₂ afforded the desired phosphonates, which were converted into phosphonic acids by the hydrolysis of phosphonate moiety with simultaneous cleavage of the nitrogen protecting groups.     

Piperidine-Iodine as Efficient Dual Catalyst for the One-Pot,Three-Component Synthesis of Coumarin-3-Carboxamides

A simple and efficient one-pot, three-component synthetic method for the preparation of coumarin-3-carboxamides was carried out by the reaction of salicylaldehyde, aliphatic primary/secondary amines, and diethylmalonate. The protocol employs piperidine-iodine as a dual system catalyst and ethanol, a green solvent. The main advantages of this approach are that it is a metal-free and clean reaction, has low catalyst loading, and requires no tedious workup.     

Majoration du Nombre de Zéros D’Une Fonction Méromorphe en Dehors D’Une Droite Verticale et Applications

We study the distribution of the zeros of functions of the form f(s) = h(s) ± h(2a − s), where h(s) is a meromorphic function, real on the real line, a is a real number. One of our results establishes sufficient conditions under which all but finitely many of the zeros of f(s) lie on the line ℜs = a, called the critical line for the function f(s), and that they are simple, provided that all but finitely many of the zeros of h(s) lie on the half-plane ℜs < a. This result can be regarded as a generalization of the necessary condition of stability for the function h(s), in the Hermite-Biehler theorem. We apply our results to the study of translations of the Riemann Zeta Function and L functions, and integrals of Eisenstein Series, among others.     

Pharmacological activities of a propylthiouracil compound structurally modified by coordination with copper(II)

For the first time, pharmacological activities for propylthiouracil (actually used as antithyroid drug) were determined. In addition, a new propylthiouracil copper(II) complex ([Cu(PTU)₂]₂) was synthesized and characterized by FTIR, EPR, UV–visible, and diffuse reflectance spectroscopies including elemental analysis, dissolution profiles, and stability studies. Taking into account the correlation between Graves’ disease and the formation of reactive oxygen species (ROS) and other free radicals, the ligand and the complex were tested for their antioxidant effects on O₂^·? and OH^· radicals. A significant increase in the disruption of OH^· radical was observed for PTU and its copper(II) complex, but neither of them have the ability to dismutate the O₂^·? radical. Antimicrobial activities were also determined observing that the complex is very active against Gram-positive bacteria. In addition, the ability of PTU and its complex to inhibit acid and alkaline phosphatases were analyzed. Results showed that PTU had no effect, while the complex behaved as a potent ALP (alkaline phosphatases) inhibitor. Finally, albumin interaction experiments denoted high affinity towards the complex in contrast with PTU with a constant binding value two hundred times higher than the ligand and bearing two binding sites. Based on this study, it has been hypothesized that ([Cu(PTU)₂]₂ would be a promising candidate for further evaluation as an antioxidant, antimicrobial and phosphatase alkaline inhibitor agent.