Difference schemes on uniform grids performed by general discrete operators

Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form for suitable choices of q, and  . In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q, and  .     

Polymerization photoinitiated by carbonyl compounds. VI. Mechanism of benzil photoinitiation

The mechanism of the photoinitiation of the vinyl polymerization sensitized by benzil and 4,4′-dimethoxybenzil was studied. The monomers considered were methacrylic acid esters and styrene derivatives. All these monomers are efficient quenchers of the excited triplet benzil. However, the initiation efficiency of the benzil is important only when styrene derivatives are employed as monomers. The main polymerization process follows a simple free radical mechanism. The initiation step is a consequence of the interaction (triplet benzil–monomer double bond) through a charge transfer complex.     

Excited state enantiodifferentiating interactions between a chiral benzophenone derivative and nucleosides

Time-resolved measurements using nanosecond laser flash photolysis have revealed significant enantiodifferentiation in the interaction between ketoprofen (a chiral benzophenone derivative) and two relevant nucleosides, namely, thymidine and 2'-deoxyguanosine. In both cases, the highest quenching rate constants have been observed for (R)-ketoprofen, the enantiomer with lower pharmacological activity. Photoproduct studies performed in the case of thymidine suggest that the enantiodifferentiating process corresponds to a Paterno-Büchi reaction, leading to the formation of oxetanes. With 2'-deoxyguanosine, the quenching is associated with an electron-transfer process monitored through the generation of a ketyl radical.     

Electronic energy transfer and collection in luminescent molecular rods containing ruthenium(II) and osmium(II) 2,2':6',2"-terpyridine complexes linked by thiophene-2,5-diyl spacers

The electronic absorption spectra, luminescence spectra and lifetimes (in MeCN at room temperature and in frozen n-C3H7CN at 77 K), and electrochemical potentials (in MeCN) of the novel dinuclear [(tpy)Ru(3)Os(tpy)]4+ and trinuclear [(tpy)Ru(3)Os(3)Ru(tpy)]6- complexes (3 = 2,5-bis(2,2':6',2'-terpyridin-4-yl)thiophene) have been obtained and are compared with those of model mononuclear complexes and homometallic [(tpy)Ru(3)Ru(tpy)]4+, [(tpy)Os(3)Os(tpy)]4+ and [(tpy)Ru(3)Ru(3)Ru(tpy)]6+ Complexes. The bridging ligand 3 is nearly planar in the complexes, as seen from a preliminary X-ray determination of [(tpy)Ru(3)Ru(tpy)][PF6]4, and confers a high degree of rigidity upon the polynuclear species. The trinuclear species are rod-shaped with a distance of about 3 nm between the terminal metal centres. For the polynuclear complexes, the spectroscopic and electrochemical data are in accord with a significant intermetal interaction. All of the complexes are luminescent (phi in the range 10(-4)-10(-2) and tau in the range 6-340 ns, at room temperature), and ruthenium- or osmium-based luminescence properties can be identified. Due to the excited state properties of the various components and to the geometric and electronic properties of the bridge, Ru --> Os directional transfer of excitation energy takes place in the complexes [(tpy)Ru(3)Os(tpy)]4+ (end-to-end) and [(tpy)Ru(3)Os(3)Ru(tpy)]6+ (periphery-to-centre). With respect to the homometallic case, for [(tpy)Ru(3)Os(3)Ru(tpy)]6+ excitation trapping at the central position is accompanied by a fivefold enhancement of luminescence intensity.     

THE INTERACTION OF THE EXCITED STATES OF SAFRANINE T WITH ALIPHATIC AMINES IN ORGANIC SOLVENTS

Abstract—
The reactions of the excited states of safranine T with aliphatic amines have been studied in methanol and acetonitrile. Quenching of the singlet and triplet states occurs by different mechanisms. Whereas the former excited state is quenched by a charge-transfer mechanism, the triplet state is quenched through proton transfer from the excited dye to the amine. This process leads to the unprotonated form of the dye in the triplet state, which is later quenched by amines to form the corresponding semireduced species. The monoprotonated triplet also undergoes self-quenching in both solvents (k = 1.2 × 10⁸ M ^-1 s^-1).     

Boundary value problems on weighted networks

We present here a systematic study of general boundary value problems on weighted networks that includes the variational formulation of such problems. In particular, we obtain the discrete version of the Dirichlet Principle and we apply it to the analysis of the inverse problem of identifying the conductivities of the network in a very general framework. Our approach is based on the development of an efficient vector calculus on weighted networks which mimetizes the calculus in the smooth case. The key tool is an adequate construction of the tangent space at each vertex. This allows us to consider discrete vector fields, inner products and general metrics. Then, we obtain discrete versions of derivative, gradient, divergence and Laplace-Beltrami operators, satisfying analogous properties to those verified by their continuous counterparts. On the other hand we develop the corresponding integral calculus that includes the discrete versions of the Integration by Parts technique and Green’s Identities. Finally, we apply our discrete vector calculus to analyze the consistency of difference schemes used to solve numerically a Robin boundary value problem in a square.     

QUENCHING OF PYRENE FLUORESCENCE BY TRYPTOPHAN IN MICELLAR SOLUTIONS

Deactivation of excited pyrene incorporated to cationic (cetyltrimethylammonium chloride), anionic (sodium dodecyl sulfate) and neutral (Triton X-100) micelles by tryptophan has been investigated over a wide pH range. Data obtained allow an estimation of the tryptophan association to the micelles, of the tryptophan apparent p K in the micellar solutions, and of the dynamics of tryptophan incorporation to the micellar pseudophase. In particular, the data obtained at pH 7 allow an estimation of the effect of the micellar charge upon the binding capacity of the tryptophan zwitterion.     

Reactivity of tert-butoxyl radicals towards substituted indole derivatives

Tert-butoxyl radicals react with indole and methyl substituted derivatives by hydrogen abstraction. For those compounds which are unsubstituted at the N-atom, hydrogen abstraction takes place almost exclusively at the N? H bond. The reactivity of these compounds correlates with their donor electron capacity, pointing to significant contribution of charge transfer to the transition state stability. Substitution at the N atom considerably decreases the reactivity.     

Overdetermined partial boundary value problems on finite networks

In this study, we define a class of non-self-adjoint boundary value problems on finite networks associated with Schrödinger operators. The novel feature of this study is that no data are prescribed on part of the boundary, whereas both the values of the function and of its normal derivative are given on another part of the boundary. We show that overdetermined partial boundary value problems are crucial for solving inverse boundary value problems on finite networks since they provide the theoretical foundations for the recovery algorithm. We analyze the uniqueness and the existence of solution for overdetermined partial boundary value problems based on the nonsingularity of partial Dirichlet-to-Neumann maps. These maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed. We also execute full conductance recovery for spider networks.     

Photopolymerization initiated by carbonyl compounds. VII. Solvent effects on biacetyl photoinitiation

Biacetyl is solvated by methanol or water giving an α-substituted alkanone. Irradiation of the solvated species at 300 nm in the presence of vinyl acetate or vinyl pyrrolidone, produces a significant amount of polymer. The photoprocesses leading to active free radicals are considered to be a type I photocleavage of the α-substituted alkanone.