On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems

This paper is concerned with the study of the proto-differentiability of the multifunction associated with the feasible points of optimization problems. It is proved under some natural conditions that the proto-differentiability of the data multifunctions ensure that of the resulting multifunctions of feasible points.     

Interface growth mechanism in ion beam sputtering-deposited Mo/Si multilayers

Despite the technological importance of metal/Si multilayer structures in microelectronics, the interface reactions occurring during their preparation are not yet fully understood. In this work, the interface intermixing in Mo/Si multilayer coatings has been studied with respect to their preparation conditions. Various samples, prepared at room temperature with different Mo deposition rates (0.06–0.43?Å?s^?1) and a constant Si rate, have been investigated by detailed TEM observations. Contrary to the Si-on-Mo interface where no evidence of chemical intermixing could be found, the Mo-on-Si interface presents a noticeable interface zone whose thickness was found to noticeably decrease (from 4.1 to 3.2?nm) when increasing the Mo deposition rate. Such intermixing phenomena correspond to diffusion mechanisms having coefficients ranging from 0.25?×?10^?15 to 1.2?×?10^?15?cm²?s^?1 at room temperature. By assuming a diffusion mechanism mainly driven by Mo–Si atomic exchanges to minimize the surface energy, the diffusion dependence with Mo deposition rate has been successfully simulated using a cellular automaton. A refined simulation including Mo cluster formation is also proposed to explain the scenario leading to the full crystallization of Mo layers.     

Carbonylation of C−N Bonds in Tertiary Amines Catalyzed by Low‐Valent Iron Catalysts

The first iron catalysts able to promote the formal insertion of CO into the C?N bond of amines are reported. Using low‐valent iron complexes, including K₂[Fe(CO)₄], amides are formed from aromatic and aliphatic amines, in the presence of an iodoalkane promoter. Inorganic Lewis acids, such as AlCl₃ and Nd(OTf)₃, have a positive influence on the catalytic activity of the iron salts, enabling the carbonylation at a low pressure of CO (6 to 8 bars).     

Transition‐Metal‐Free Acceptorless Decarbonylation of Formic Acid Enabled by a Liquid Chemical‐Looping Strategy

The selective decarbonylation of formic acid was achieved under transition‐metal‐free conditions. Using a liquid chemical‐looping strategy, the thermodynamically favored dehydrogenation of formic acid was shut down, yielding a pure stream of CO with no H₂ or CO₂ contamination. The transformation involves a two‐step sequence where methanol is used as a recyclable looping agent to yield methylformate, which is subsequently decomposed to carbon monoxide using alkoxides as catalysts.     

[N]-Isotopic labeling: a suitable tool to study the reactivity of bis lactams

The unexpected reactivity of 2,5-diketopiperazines under basic conditions, thanks to N-Boc activation, allows access to valuable pharmacological scaffolds, such as original statine derivatives. Toward this transannular rearrangement of activated lactams (TRAL), we report here the study of bis lactam reactivity using [¹⁵N]-isotopic labeling.     

Constructive Tensor Field Theory: the {T^4_3} Model

In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be Lagrangian. This paper investigates index pairings of projections and unitaries submitted to such symmetries. Various scenarios emerge: Noether indices can take either arbitrary integer values or only even integer values or they can vanish and then possibly have secondary \({{\mathbb {Z}_{2}}}\)-invariants. These general results are applied to prove index theorems for the strong invariants of disordered topological insulators. The symmetries come from the Fermi projection (K-theoretic part of the pairing) and the Dirac operator (K-homological part of the pairing depending on the dimension of physical space).     

One‐Electron Oxidation of [M(PtBu3)2] (M=Pd,Pt): Isolation of Monomeric [Pd(PtBu3)2]+ and Redox‐Promoted C−H Bond Cyclometalation

Oxidation of zero‐valent phosphine complexes [M(P^tBu₃)₂] (M=Pd, Pt) has been investigated in 1,2‐difluorobenzene solution using cyclic voltammetry and subsequently using the ferrocenium cation as a chemical redox agent. In the case of palladium, a mononuclear paramagnetic Pd^I derivative was readily isolated from solution and fully characterized (EPR, X‐ray crystallography). While in situ electrochemical measurements are consistent with initial one‐electron oxidation, the heavier congener undergoes C−H bond cyclometalation and ultimately affords the 14 valence‐electron Pt^II complex [Pt(κ²_PC‐P^tBu₂CMe₂CH₂)(P^tBu₃)]⁺ with concomitant formation of [Pt(P^tBu₃)₂H]⁺.     

Q-branch linewidths of N2 perturbed by H2: experiments and quantum calculations from an ab initio potential

In this work the authors present an experimental and theoretical study about the Q-branch lines' broadening coefficients of N2 perturbed by H2. Experimental values for these parameters have been obtained at 440 and 580 K, and quantum calculations have been performed using a new ab initio potential energy surface, obtained by quantum chemistry methods. The results of these calculations are compared to experimental data obtained previously at 77 and 298 K [L. Gomez et al., Mol. Phys. 104, 1869 (2006)] and to the present measurements. A satisfactory agreement is obtained for the whole range of temperatures used in the experiments.