A two-scale model for the periodic homogenization of the wave equation

We present a new mathematical object designed to analyze the oscillations occurring on both microscopic and macroscopic scales in a wave equation with oscillating coefficients and data. Through a Bloch wave homogenization method, our study addresses typical problems of two-scale convergence in the interior of the domain, and sheds some light on the behavior near the boundary. A decoupled system of (systems of) transport equations is derived in each energy band, and the total energy field is approximated. We also recover previously known results in homogenization as a restricted part of our model.     

A <Emphasis Type="Italic">q</Emphasis>-analog of Schläfli and Gould identities on Stirling numbers

In this paper, we present a simple combinatorial proof of Jacobi’s triple product identity.     

Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero

We determine the stationary distribution of a one-sided Markov-Modulated Brownian Motion (MMBM) of which the behaviour is modified during the intervals between a visit to level zero and the next visit to a fixed positive level b. We use the semi-regenerative structure of the process, and we also use the fluid approximation for MMBMs introduced by Latouche and Nguyen in 2015. Finally, we show how the expressions can be simplified in some interesting special cases and we conclude by providing some numerical illustrations.     

Note on the fall of an axisymmetric body in a perfect fluid over a horizontal ramp

In this note, we consider the fall of an axisymmetric body in a perfect fluid over a ramp. It was shown in [12] that the possibility of a collision between the body and the ramp is related to the asymptotics of the so-called added mass when the distance between the ramp and the body goes to 0. We propose here a new method to compute this added mass, which provides simultaneously an approximation of an associated fluid velocity field in the gap between the ramp and the body.     

endo-6-(Hydroxymethyl)bicyclo[3.1.0]hept-3-en-2-one esters and the photochemical challenge: [2+2] cycloaddition versus skeletal rearrangement

The photochemical reactivity of enantiomerically pure bicyclo[3.1.0]hept-3-en-2-ones has been examined to determine whether a [2+2] cycloaddition with an alkene could be achieved without interference from a photochemically induced skeletal rearrangement. The formation of a tricyclo[5.2.0.0^2,5]nonan-6-one was indeed the major pathway, exclusively providing the cis-anti-cis isomer. However, the formation of norbornenones was also observed, as was stereochemical scrambling at C6 in the starting material.     

Design and synthesis of a self-assembled photochemical dyad based on selective imidazole recognition

The unique recognition properties of phenanthroline-strapped zinc porphyrin 1, which displays extremely high affinity for N-unsubstituted imidazoles, has been used as the driving force for the assembly of a photochemical dyad involving a zinc(II) porphyrin as energy donor and a free base porphyrin as energy acceptor. The synthesis of the imidazole-substituted porphyrin is described together with the assembly of the dyad. (1)H NMR titrations confirm the formation of a 1/1 complex between 1 and 6, as well as insertion of the imidazole of the acceptor within the phenanthroline strap of the donor. Preliminary fluorescence quenching measurements show that efficient energy transfer occurs between the self-assembled components.     

Reactions of a Transient Carbonyl(chloro)(hydrido)ruthenium(II) Complex with Ethylene,Alkynes, and CO; Chemistry of the New Anion [Ru2(CO)4Cl5]−

A 97% yield of [Ru ₃ (CO) ₁₂ ] (2) in 20 minutes is obtained simply by treating [Ru(CO)₃Cl₂(thf)] with KOH under CO (1 atm). The reduction to Ru⁰ can be explained in terms of the facile reductive elimination of HCl from the transient hydrido complex 1 . Though elusive, the latter can be intercepted by olefins or alkynes to produce trappable alkyl or alkenyl complexes such as 3 and 4 .█ denotes a vacant coordination site.     

Self-absorption effects in radially and axially viewed inductively coupled plasma-atomic emission spectrometry – the key role of the operating conditions

Self-absorption effects leading to curvatures of the upper part of calibration graphs were investigated in multichannel detection ICP–AES. A dual view Optima 3000 ICP system was used to enable the simultaneous determination of 38 lines for both radial and axial viewing. Resonance and non-resonance lines were selected for both atomic and ionic lines. The concentrations of 22 standards were in the range 0.1–100 mg L^–1 and two sets of operating conditions, namely power and carrier gas flow rate, were used to evaluate their influence. It was found that these two conditions, and in particular the carrier gas flow rate, play a major role in self-absorption effects. Except for strongly absorbing lines, it was possible, under suitable conditions, to reduce or to suppress differences between self-absorption effects in radial and axial viewing, enabling extension of the range of linearity of axial viewing to higher concentrations. A diagnostic tool, based on emission line ratios, is proposed for detection of self-absorption. A calibration procedure is given for strongly absorbing lines affected by self-absorption even when operating conditions were optimized.