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The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
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Photoisomerisation in Aminoazobenzene‐Substituted Ruthenium(II) Tris(bipyridine) Complexes: Influence of the Conjugation Pathway
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![点击此处可从《Chemistry (Weinheim an der Bergstrasse, Germany)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Dr. Anissa Amar Dr. Paul Savel Dr. Huriye Akdas‐Kilig Dr. Claudine Katan Prof. Hacène Meghezzi Prof. Abdou Boucekkine Dr. Jean‐Pierre Malval Dr. Jean‐Luc Fillaut 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(22):8262-8270
Transition‐metal complexes containing stimuli‐responsive systems are attractive for applications in optical devices, photonic memory, photosensing, as well as luminescence imaging. Amongst them, photochromic metal complexes offer the possibility of combining the specific properties of the metal centre and the optical response of the photochromic group. The synthesis, the electrochemical properties and the photophysical characterisation of a series of donor–acceptor azobenzene derivatives that possess bipyridine groups connected to a 4‐dialkylaminoazobenzene moiety through various linkers are presented. DFT and TD‐DFT calculations were performed to complement the experimental findings and contribute to their interpretation. The position and nature of the linker (ethynyl, triazolyl, none) were engineered and shown to induce different electronic coupling between donor and acceptor in ligands and complexes. This in turn led to strong modulations in terms of photoisomerisation of the ligands and complexes. 相似文献
5.
Naphthalimide‐phthalimide derivative based photoinitiating systems for polymerization reactions under blue lights
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Pu Xiao Frédéric Dumur Jing Zhang Bernadette Graff Didier Gigmes Jean Pierre Fouassier Jacques Lalevée 《Journal of polymer science. Part A, Polymer chemistry》2015,53(5):665-674
Naphthalimide‐phthalimide derivatives (NDPDs) have been synthesized and combined with an iodonium salt, N‐vinylcarbazole, amine or 2,4,6‐tris(trichloromethyl)‐1,3,5‐triazine to produce reactive species (i.e., radicals and cations). These generated reactive species are capable of initiating the cationic polymerization of epoxides and/or the radical polymerization of acrylates upon exposure to very soft polychromatic visible lights or blue lights. Compared with the well‐known camphorquinone based systems used as references, the novel NDPD based combinations employed here demonstrate clearly higher efficiencies for the cationic polymerization of epoxides under air as well as the radical polymerization of acrylates. Remarkably, one of the NDPDs (i.e., NDPD2) based systems is characterized by an outstanding reactivity. The structure/reactivity/efficiency relationships of the investigated NDPDs were studied by fluorescence, cyclic voltammetry, laser flash photolysis, electron spin resonance spin trapping, and steady state photolysis techniques. The key parameters for their reactivity are provided. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 665–674 相似文献
6.
Beyond Stereoselectivity,Switchable Catalysis: Some of the Last Frontier Challenges in Ring‐Opening Polymerization of Cyclic Esters
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Dr. Sophie M. Guillaume Dr. Evgueni Kirillov Dr. Yann Sarazin Prof. Dr. Jean‐François Carpentier 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(22):7988-8003
Metal‐based catalysts and initiators have played a pivotal role in the ring‐opening polymerization (ROP) of cyclic esters, thanks to their high activity and remarkable ability to control precisely the architectures of the resulting polyesters in terms of molar mass, dispersity, microstructure, or tacticity. Today, after two decades of extensive research, the field is slowly reaching maturity. However, several challenges remain, while original concepts have emerged around new types or new applications of catalysis. This Review is not intended to comprehensively cover all of these aspects. Rather, it provides a personal overview of the very recent progress achieved in some selected, important aspects of ROP catalysis—stereocontrol and switchable catalysis. Hence, the first part addresses the development of new metal‐based catalysts for the isoselective ROP of racemic lactide towards stereoblock copolymers, and the use of syndioselective ROP metal catalysts to control the monomer sequence in copolymers. A second part covers the development of ROP catalysts—primarily metal‐based catalysts, but also organocatalysts—that can be externally regulated by the use of chemical or photo stimuli to switch them between two states with different catalytic abilities. Current challenges and opportunities are highlighted. 相似文献
7.
The main object of this note is to prove the following generalisation of a theorem of Serre. A simply connected space of finite
type whose mod. 2 cohomology is nilpotent (and non-trivial) has infinitely many homotopy groups which are not of odd torsion.
Incidentally we show that for every fibrationF(
→
ί
)E (
→
p
)B, satisfying certain mild conditions, the following holds. If a classx in the mod. 2 cohomology ofE belongs to the kernel ofi*, then some power ofx belongs to the ideal generated by the image underp* of the mod. 2 reduced cohomology ofB.
相似文献
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Jean Bellissard Anton Bovier Jean-Michel Ghez 《Communications in Mathematical Physics》1991,135(2):379-399
We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength. 相似文献
10.
We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C
1 transformation. 相似文献