A theoretical approach to the thermochemistry of the polymerization of some derivatives of the monomers CH2X (X = CH2, NH,O)

In this work, we have calculated the thermodynamic parameters of the polymerization of some derivatives of the species CH₂X (X = CH₂, NH, O), using ab initio methods of quantum chemistry and the usual formalism of statistical thermodynamics. It is shown that the Gibbs functions ΔG(l, c) corresponding to CH₂NOCH₃, CNCHNCN, CF₂O and all the percyano derivatives are largely positive which indicates that the spontaneous (radical or ionic) chain polymerization of these monomers is thermodynamically prohibited.     

Formation of β-distonic oxonium ions: Study of ROCH2CH2OR′ radical cations

Radical cations derived from the ethers ROCH₂CH₂OR′ (R, R′ = H, CH₃, C₂₅) were studied, since β-distonic oxonium ions are often prepared from ionized ethers of glycol. The first step in the fragmentation is a 1,5-transfer of an α-hydrogen to oxygen of a terminal alkoxy group leading to a δ-distonic oxonium ion. This step is thermo-neutral and reversible in the ROCH₂CH₂OH radical cations and exothermic and irreversible in the dialkyl ether radical cations. Depending on R and R,′ these δ-distonic oxonium ions fragment by three reactions: the loss of an alcohol or a water molecule, the formation of a β-distonic oxonium ion ˙CH₂CH₂O(H)⁺R and a 1,4-H migration between carbon atoms. Competition between these processes is discussed.     

Note sur le mécanisme réactionnel de la transposition de Dimroth. Une étude ab initio

An ab initio study of the Dimorth rerarrangement of the -amino-1,2,3,4-tetrazole leads to the conclusion teht in vapour phase the rate determining step is not the ring-chain isomerism, but is either the Z-E iomerism around the C?N double bond or the 1,3-sigmatropic shift of the proton.     

Spectroscopic investigation of ground state pyrrole (C4H5N): the NH stretch

We have recorded the infrared absorption spectrum of pyrrole at 0.005 cm⁻¹ spectral resolution using a Fourier transform interferometer. The rotational analysis of the fundamental N---H stretch (1¹₀) at 3530.811343(82) cm⁻¹ was performed. A set of 13 upper state rovibrational parameters was determined, allowing the 2715 assigned rovibrational lines to be reproduced with a standard deviation of 1.3 10⁻³ cm⁻¹. An attempt to record the fundamental band under slit-jet conditions is reported. The role of hot bands accompanying the series of the N---H stretch excitation is investigated. Effective vibrational parameters — ω⁰₁, X⁰₁₁, Y₁₁₁, X_1,24 — are obtained. The lower level in the hot band series is unambiguously identified as the V₂₄ = 1 level, by retrieving X_1,24 independently, from other spectral data. The observation of the complex band pattern accompanying the N---H series in the higher overtone range is discussed with the help of new data, recorded around the 1⁵₀ band at different temperatures using intracavity laser optoacoustic spectroscopy.     

Note on 2-rational fields

We give an alternative computation of the Galois group of the maximal 2-ramified and complexified pro-2-extension of any 2-rational number field (Theorem 2), a particular case of results of Movahhedi-Nguyen Quang Do. This short Note is motivated by the paper [J. Jossey, Galois 2-extensions unramified outside 2, J. Number Theory 124 (2007) 42-76] and, at this occasion, we bring into focus some classical technics of abelian ?-ramification which, unfortunately, are often ignored, especially those developed by J.-F. Jaulent with the ?-adic class field theory, and by G. Gras in his book on class field theory, and which considerably simplify the study of such subjects; for instance, our proof of Theorem 2 generalizes the purpose of Jossey's paper in such a way using a result of Herfort-Zalesskii. This Note is mainly an attempt of clarification about ?-rationality.     

Labeling the -path with a condition at distance two

For integer r≥2, the infinite r-path P_∞(r) is the graph on vertices …v₋₃,v₋₂,v₋₁,v₀,v₁,v₂,v₃… such that v_s is adjacent to v_t if and only if |s−t|≤r−1. The r-path on n vertices is the subgraph of P_∞(r) induced by vertices v₀,v₁,v₂,…,v_n−1. For non-negative reals x₁ and x₂, a λ_x1,x2-labeling of a simple graph G is an assignment of non-negative reals to the vertices of G such that adjacent vertices receive reals that differ by at least x₁, vertices at distance two receive reals that differ by at least x₂, and the absolute difference between the largest and smallest assigned reals is minimized. With λ_x1,x2(G) denoting that minimum difference, we derive λ_x1,x2(P_n(r)) for r≥3, 1≤n≤∞, and . For , we obtain upper bounds on λ_x1,x2(P_∞(r)) and use them to give λ_x1,x2(P_∞(r)) for r≥5 and . We also determine λ_x1,x2(P_∞(3)) and λ_x1,x2(P_∞(4)) for all .     

Dual role of price and myopia in a marketing channel

In this paper we study a dynamic two-player channel where the manufacturer controls the wholesale price and the investment in quality and the retailer chooses the retail price. We consider that the retail price affects both the demand and the perceived quality of the brand and that its variations contribute to the building of an internal reference price. One of the model’s distinctive features is that it accounts for the two meanings of price, i.e., its classical objective measure of the cost of acquiring a particular quantity of the product, and its subjective roles as an assessment of the quality of the product and an evaluation of gains or losses (deal vs. sacrifice) resulting from buying a “cheap” or an “expensive” product. This dual computation is done with respect to the internal reference price.     

Modeling of rod-structures in nonlinear elasticity

This Note deals with the modeling of a structure made of straight elastic rods whose thickness tends to 0. We show that, upon an adequate scaling, the infimum of the total elastic energy tends to the minimum of a functional which depends on fields defined on the centerlines of the rods.