Approximation du temps local des surfaces gaussiennes

Summary LetX be a centered stationary Gaussian stochastic process with ad-dimensional parameter (d2),F its spectral measure, (x denotes the Euclidean norm ofx). We consider regularizations of the trajectories ofX by means of convolutions of the formX (t)=( *X)(t) where stands for an approximation of unity (as tends to zero) satisfying certain regularity conditions.The aim of this paper is to recover the local time ofX at a given levelu, as a limit of appropriate normalizations of the geometric measure of theu-level set of the regular approximating processesX . A part of the difficulties comes from the fact that the geometric behavior of the covariance of the Gaussian processX can be a complex one as approaches O.The results are onL ²-convergence and include bounds for the speed of convergence.L ^presults may be obtained in similar ways, but almost sure convergence or simultaneous convergence for the various values ofu do not seem to follow from our methods. In Sect. 3 we have included examples showing a diversity of geometric behaviors, especially in what concerns the dependence on the thickness of the set in which the covariance of the original processX is irregular.Some technical results of analytic nature are included as appendices in Sect. 4.     

Semiclassical study of collision-induced predissociation: Comparison of the Landau-Zener model with the method of analytic continuation

Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I₂. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.     

Diphosphacarbollide analogues of the C5H5- anion: isolation of the nido-di- and triphosphacarboranes 7,8,9-P2CB8H10, [7,8,9-P2CB8H9]-, [7,8,10-P2CB8H9]-, and 7,8,9,10-P3CB7H8

Treatment of a solution of excess PCl(3) and PS (PS = "proton sponge" = 1,8-dimethylamino naphthalene) with arachno-4-CB(8)H(14) (1) in CH(2)Cl(2), followed by hydrolysis of the reaction mixture, resulted in the isolation of the eleven-vertex diphosphacarbaborane nido-7,8,9-P(2)CB(8)H(10) (2) (yield 34%) as the main product. Other products isolated from this reaction were the phosphacarboranes nido-7,8,9,10-P(3)CB(7)H(8) (3) (yield 5%) and closo-2,1-PCB(8)H(9) (4) (yield 15%). Compound 2 can be deprotonated by PS in CH(2)Cl(2) or NaH in diethyl ether to give the [nido-7,8,9-P(2)CB(8)H(9)](-) (2(-)()) anion, which gives back the original compound, 2, upon re-protonation. Thermal rearrangement of anion 2(-) (Na(+) salt) at 350 degrees C for 2 h produced the isomeric [nido-7,8,10-P(2)CB(8)H(9)](-) (5(-)()) anion, which was isolated as a PPh(4)(+) salt (yield 86%). Multinuclear ((1)H, (11)B, (31)P, and (13)C), two-dimensional [(11)B-(11)B] COSY, (1)H{(11)B(selective)}, (1)H{(31)P(selective)}, and gradient-enhanced ([(1)H-(13)C] HSQC) magnetic resonance measurements led to complete assignments of all resonances which are in excellent agreement with the structures proposed. Coupling constants, (1)J((31)P,(13)C), (2)J((31)P,C,(1)H), and (1)J((31)P,(31)P), were calculated using the DFT method B3LYP/6-311+G(d,p). The molecular geometries of all compounds were optimized ab initio at a correlated level of theory (RMP2(fc)) using the 6-31G basis set, and their correctness was assessed by comparison of the experimental (11)B and (13)C chemical shifts with those calculated by the GIAO-SCF/II//RMP2(fc)/6-31G method. The computations also include the structures and chemical shieldings of the still unknown isomers [nido-7,10,8-P(2)CB(8)H(9)](-) (6(-)) and [nido-7,9,8-P(2)CB(8)H(9)](-) (7(-)).     

New insight into solvent effects on the formal HOO. + HOO. reaction

The 2,2'-azobis(isobutyronitrile)(AIBN)-induced autoxidation of gamma-terpinene (TH) at 50 degrees C produces p-cymene and hydrogen peroxide in a radical-chain reaction having HOO* as one of the chain-carrying radicals. The kinetics of this reaction in cyclohexane and tert-butyl alcohol show that chain termination involves the formal HOO. + HOO. self-reaction over a wide range of gamma-terpinene, AIBN, and O2 concentrations. However, in acetonitrile this termination process is accompanied by termination via the cross-reaction of the terpinenyl radical, T., with the HOO. radical under conditions of relatively high [TH] (140-1000 mM) and low [O2] (2.0-5.5 mM). This is because the formal HOO. + HOO. reaction is comparatively slow in acetonitrile (2k approximately 8 x 10(7) M(-1) s(-1)), whereas, this reaction is almost diffusion-controlled in tert-butyl alcohol and cyclohexane, 2k approximately 6.5 x 10(8) and 1.3 x 10(9) M(-1) s(-1), respectively. Three mechanisms for the bimolecular self-reaction of HOO. radicals are considered: 1) a head-to-tail hydrogen-atom transfer from one radical to the other, 2) a head-to-head reaction to form an intermediate tetroxide, and 3) an electron-transfer between HOO. and its conjugate base, the superoxide radical anion, O2-.. The rate constant for reaction by mechanism (1) is shown to be dependent on the hydrogen bond (HB) accepting ability of the solvent; that by mechanism (2) is shown to be too slow for this process to be of any importance; and that by mechanism (3) is dependent on the pH of the solvent and its ability to support ionization. Mechanism (3) was found to be the main termination process in tert-butyl alcohol and acetonitrile. In the gas phase, the rate constant for the HOO. + HOO. reaction (mechanism (1)) is about 1.8 x 10(9) M(-1) s(-1) but in water at pH< or =2 where the ionization of HOO. is completely suppressed, this rate constant is only 8.6 x 10(5) M(-1) s(-1). The very large retarding effect of water on this reaction has not previously been explained. We find that it can be quantitatively accounted for by using Abraham's HB acceptor parameter, beta(2)(H), for water of 0.38 and an estimated HB donor parameter, alpha(2)(H), for HOO. of about 0.87. These Abraham parameters allow us to predict a rate constant for the HOO. + HOO. reaction in water at 25 degrees C of 1.2 x 10(6) M(-1) s(-1) in excellent agreement with experiment.     

Intercalation of α,ω-alkyldiamines in layered α-zirconium phosphate and the inclusion behaviour of some of the intercalates obtained

The paper reports a study on the intercalation mechanism of NH₂(CH₂) _n NH₂ (withn=2, 4, 6, 8, 10) diamines in layered Zr(HOPO₃)₂·H₂O, performed by titrating the host with aqueous solutions of amines at 80°C. The intercalation reactions occur stepwise according to the ‘moving boundary’ model, with the formation of a number of intermediate intercalation compounds of formula Zr(HOPO₃)₂·xNH₂(CH₂) _n NH₂ (0<x<1) before obtaining the fully intercalated ones (x=1). For each diamine the batch titration curve and a diagram of the phases involved in the interaclation reaction are reported. Twenty-two intercalation compounds have been isolated and characterized by their composition, XRD patterns and thermal behaviour, and information on the disposition of the guests within the interlayer region have been derived. At full intercalation the diamines form a monolayer of extended molecules with their axis inclined at 58° to the plane of the sheet. The terminal amino groups are protonated by the —POH groups of the host, thus each diamine binds adjacent layers and, in a sense, transforms a layered structure into a framework structure that may have an accessible or potentially accessible porosity. The intercalation compound Zr(HOPO₃)₂·0.5NH₂(CH₂)₈NH₂ is indeed able to include polar molecules such as water and short chain alkanols.     

On the electronic states of macrocycles of the extended porphyrin family and their coordination compounds

The electronic absorption spectra of Ni, Zn and Mg hemiporphyrazine derivatives are presented and discussed together with theoretical results obtained by INDO/S computations. The absorption spectra of all the metal derivatives show marked red shifts of the lowest energy absorption bands with respect to those of the metal free hemiporphyrazine. The possible explanation that in metal derivatives low lying excited states with a fully conjugated π electron system are present is supported by theoretical computations.     

The Chemistry of Coumarin Derivatives. Part 5. Unusual course of the reaction of 4-hydroxycoumarin and aliphatic aldehydes

The reaction of 4-hydroxycoumarin and certain aliphatic aldehydes affords 1:1 or complex 2:2 adducts besides (or in place) of the expected 2:1 bis(coumarin) adducts. Reaction with heptanal, cyclohexanecarbaldehyde, and pivalaldehyde are reported as representative. The structure of the reaction products was established by spectroscopical techniques, including X-ray analysis, and their formation was mechanistically rationalized. Some of the 1:1 adducts are synthetically useful for the preparation of 3-alkyl-4-hydroxycoumarins.     

Electron Transfer Spectra of Some Adducts of Niobium (V), Tantalum (V), Titanium (IV) and Zirconium (IV) Halides with Lewis Bases

The electron transfer spectra of adducts of the title metal halides with a series of ligands (nitriles, dialkylchalcogenides, phosphoryl and thiophosphoryl ligands and phosphines) have been studied. The effect of halogen substitution on the halogen metal transitions is discussed by comparing the spectra of the adducts with those of the hexahalometalates. The origin of the two ligand-metal transitions observed in most adducts is discussed, and the splitting of the metal d levels in these almost octahedral adducts is estimated. For each metal halide, the series of adducts with dialkyl chalcogenides show a linear relationship of slope one between the ligand ionisation potential and the ligand-metal charge transfer energy. The ligand optical electronegativities have been estimated.     

Quelques considérations sur la structure électronique du naphtalène

Theπ electronic structure of naphtalene is studied, using a semi-empirical approximation for coulombic and resonance integrals; forH andS (H, hamiltonian;S, overlap) the complete matrices are adopted, together withKohlrausch's nuclear effective charges. A non uniform charge distribution is obtained, with charge accumulation at the tertiary carbons. Bond orders between non neighboring atoms indicate contributions to the fundamental state from other structures besides the classical ones. A comparative study of the obtained interatomic distances is carried. It is shown that [H, S]=0 is not a sufficient condition for the identity of the bond orders for the fundamental state calculated with and without overlap.     

An Extensive Assessment of Network Embedding in PPI Network Alignment

Network alignment is a fundamental task in network analysis. In the biological field, where the protein–protein interaction (PPI) is represented as a graph, network alignment allowed the discovery of underlying biological knowledge such as conserved evolutionary pathways and functionally conserved proteins throughout different species. A recent trend in network science concerns network embedding, i.e., the modelling of nodes in a network as a low-dimensional feature vector. In this survey, we present an overview of current PPI network embedding alignment methods, a comparison among them, and a comparison to classical PPI network alignment algorithms. The results of this comparison highlight that: (i) only five network embeddings for network alignment algorithms have been applied in the biological context, whereas the literature presents several classical network alignment algorithms; (ii) there is a need for developing an evaluation framework that may enable a unified comparison between different algorithms; (iii) the majority of the proposed algorithms perform network embedding through matrix factorization-based techniques; (iv) three out of five algorithms leverage external biological resources, while the remaining two are designed for domain agnostic network alignment and tested on PPI networks; (v) two algorithms out of three are stated to perform multi-network alignment, while the remaining perform pairwise network alignment.