Search results for "Function"
showing 10 items of 14432 documents
1,3-Dipolar cycloadditions of electrophilically activated benzonitrile N-oxides. Polar cycloaddition versus oxime formation.
2006
The reactions of electrophilically activated benzonitrile N-oxides (BNOs) toward 3-methylenephthalimidines (MPIs) have been studied using density functional theory (DFT) at the B3LYP/6-31G* level. For these reactions, two different channels allowing the formation of the [3 + 2] cycloadducts and two isomeric (E)- and (Z)-oximes have been characterized. The 1,3-dipolar cycloadditions take place along concerted but highly asynchronous transition states, while formation of the oximes is achieved through a stepwise mechanism involving zwitterionic intermediates. Both reactions are initiated by the nucleophilic attack of the methylene carbon of the MPIs to the carbon atom of the electrophilically…
Integration of a Dirac comb and the Bernoulli polynomials
2016
Abstract For any positive integer n , we consider the ordinary differential equations of the form y ( n ) = 1 − Ш + F where Ш denotes the Dirac comb distribution and F is a piecewise- C ∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.
Turán type inequalities for generalized inverse trigonometric functions
2013
In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.
Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states
2019
Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously employed in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to get the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: the cell-averaged current density reveals the anomalous velocities whose integration leads to the conductivity quantum. Re…
PINCoC: a Co-Clustering based Method to Analyze Protein-Protein Interaction Networks
2007
Anovel technique to search for functionalmodules in a protein-protein interaction network is presented. The network is represented by the adjacency matrix associated with the undirected graph modelling it. The algorithm introduces the concept of quality of a sub-matrix of the adjacency matrix, and applies a greedy search technique for finding local optimal solutions made of dense submatrices containing the maximum number of ones. An initial random solution, constituted by a single protein, is evolved to search for a locally optimal solution by adding/removing connected proteins that best contribute to improve the quality function. Experimental evaluations carried out on Saccaromyces Cerevis…
Dependence of the Substituent Effect on Solvent Properties
2018
The influence of a solvent on the substituent effect (SE) in 1,4-disubstituted derivatives of benzene (BEN), cyclohexa-1,3-diene (CHD), and bicyclo[2.2.2]octane (BCO) is studied by the use of polarizable continuum model method. In all X–R–Y systems for the functional group Y (NO2, COOH, OH, and NH2), the following substituents X have been chosen: NO2, CHO, H, OH, and NH2. The substituent effect is characterized by the charge of the substituent active region (cSAR(X)), substituent effect stabilization energy (SESE), and substituent constants σ or F descriptors, the functional groups by cSAR(Y), whereas π-electron delocalization of transmitting moieties (BEN and CHD) is characterized by a geo…
New Reactions of Amino-Functionalized 3-Vinyl-1H-indoles and Tetrahydropyridin-4-yl Analogues with Dienophiles
1991
Reactions of 3-[2-(morpholin-4-yl)vinyl]-1H-indole (1), the 1,2-dihydro-9H-carbazole 2, as well as the 3-(tetrahydropyridin-4-yl)-1H-indoles 3a and 3b with some carbo- and heterodienophiles are described. The scope and limitations of the synthetic utility of these amino- (or homoamino)-functionalized 3-vinyl-1H-indoles are reported and some MO calculations for the qualitative prediction of their reactivities are presented. The reactions gave rise to substitution products, redox products, Diels-Alder adducts, ene adducts, and Michael-type adducts (Schemes 2 and 3).
Carbon nanotube supported aluminum porphyrin-imidazolium bromide crosslinked copolymer
2022
The increased awareness of the catastrophic consequences caused by the accumulation of greenhouse gases into the atmosphere has generated a large mobilization aimed at CO2 mitigation. Herein, in the spirit of the transformation of a waste as CO2 into value added products, we propose an efficient preparation of two different hybrid systems based on aluminum chloride tetrastyrylporphyrin (TSP-Al-Cl) and 1,4-butanediyl-3,3′-bis-1-vinylimidazolium dibromide copolymerized in the presence (MWCNT-TSP-AlCl-imi) and in absence (TSP-AlCl-imi) of multi-walled carbon nanotubes (MWCNTs) for the CO2 utilization in the synthesis of cyclic carbonates. The so-prepared materials have been thoroughly characte…
Estimation of total electricity consumption curves of small areas by sampling in a finite population
2016
International audience; Many studies carried out in the French electricity company EDF are based on the analysis of the total electricity consumption curves of groups of customers. These aggregated electricity consumption curves are estimated by using samples of thousands of curves measured at a small time step and collected according to a sampling design. Small area estimation is very usual in survey sampling. It is often addressed by using implicit or explicit domain models between the interest variable and the auxiliary variables. The goal here is to estimate totals of electricity consumption curves over domains or areas. Three approaches are compared: the rst one consists in modeling th…
A distance metric on binary trees using lattice-theoretic measures
1990
A so called height function which is a strictly antitone supervaluation is defined on binary trees. Via lattice-theoretic results and using the height function, we can define a distance metric on binary trees of size n which can be computed in expected time O(n 3/2 )