Weakly interacting particle systems on inhomogeneous random graphs

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The collection of neighbors of a given node changes dynamically over time and is determined through a time evolving random graph process. A law of large numbers and a propagation of chaos result is established for a multi-type population setting where at each instant the interaction between nodes is given by an inhomogeneous random graph which may change over time. This result covers the setting in which the edge probabilities between any two nodes are allowed to decay to 0 as the size of the system grows. A central limit theorem is established for the single-type population case under stronger conditions on the edge probability function.     

Rhodium(III)‐Catalyzed ortho Alkenylation of N‐Phenoxyacetamides with N‐Tosylhydrazones or Diazoesters through CH Activation

A coupling reaction of N‐phenoxyacetamides with N‐tosylhydrazones or diazoesters through Rh^III‐catalyzed C? H activation is reported. In this reaction, ortho‐alkenyl phenols were obtained in good yields and with excellent regio‐ and stereoselectivity. Rh–carbene migratory insertion is proposed as the key step in the reaction mechanism.     

Asymmetric NH Insertion of Secondary and Primary Anilines under the Catalysis of Palladium and Chiral Guanidine Derivatives

Efficient enantioselective N? H insertion reactions of secondary and primary anilines were catalyzed by palladium(0) in combination with chiral guanidine derivatives. A broad range of substituted anilines were tolerated, and the corresponding products were obtained in high yield (up to 99 %) with good enantioselectivity (up to 94 % ee) under mild reaction conditions. The N? H insertion mechanism was examined by the study of kinetic isotope effects, control experiments, HRMS, and spectroscopic analysis.     

Synthesis and Reaction of the First 1,2‐Oxaphosphetane Complexes

While P^V 1,2‐oxaphosphetanes are well known from the Wittig reaction, their P^III analogues are still unexplored. Herein, the synthesis and reactions of the first 1,2‐oxaphosphetane complexes are presented, which were achieved by reaction of the phosphinidenoid complex [Li(12‐crown‐4)(solv)][(OC)₅W{(Me₃Si)₂HCPCl}] with different epoxides. The title compounds appeared to be stable in toluene up to 100 °C, before unselective decomposition started. Acid‐induced ring expansion with benzonitrile resulted in selective formation of the first complex bearing a 1,3,4‐oxazaphosphacyclohex‐2‐ene ligand.     

Carbon‐Coated LiTi2(PO4)3: An Ideal Insertion Host for Lithium‐Ion and Sodium‐Ion Batteries

We report the extraordinary performance of carbon‐coated sodium super ion conductor (NASICON)‐type LiTi₂(PO₄)₃ as an ideal host matrix for reversible insertion of both Li and Na ions. The NASICON‐type compound was prepared by means of a Pechini‐type polymerizable complex method and was subsequently carbon coated. Several characterization techniques such as XRD, thermogravimetric analysis (TGA), field‐emission (FE) SEM, TEM, and Raman analysis were used to study the physicochemical properties. Both guest species underwent a two‐phase insertion mechanism during the charge/discharge process that was clearly evidenced from galvanostatic and cyclic voltammetric studies. Unlike that of Li (≈1.5 moles of Li), Na insertion exhibits better reversibility (≈1.59 moles of Na) while experiencing a slightly higher capacity fade (≈8 % higher than Li) and polarization (780 mV) than Li. However, excellent rate capability profiles were noted for Na insertion relative to its counterpart Li. Overall, the Na insertion properties were found to be superior relative to Li insertion, which makes carbon‐coated NASICON‐type LiTi₂(PO₄)₃ hosts attractive for the development of next‐generation batteries.     

Facile Insertion of Carbon Dioxide into Cu2(μ‐H) Dinuclear Units Supported by Tetraphosphine Ligands

Reactions of meso‐bis[(diphenylphosphinomethyl)phenylphosphino]methane (dpmppm) with Cu^I species in the presence of NaBH₄ afforded di‐ and tetranuclear copper hydride complexes, [Cu₂(μ‐H)(μ‐dpmppm)₂]X ( 1 ) and [Cu₄(μ‐H)₂(μ₄‐H)(μ‐dpmppm)₂]X ( 2 ) (X=BF₄, PF₆). Complex 1 undergoes facile insertion of CO₂ (1 atm) at room temperature, leading to a formate‐bridged dicopper complex [Cu₂(μ‐HCOO)(dpmppm)₂]X ( 3 ). The experimental and DFT theoretical studies clearly demonstrate that CO₂ insertion into the Cu₂(μ‐H) unit occurred with the flexible dicopper platform. Complex 2 also undergoes CO₂ insertion to give a formate‐bridged complex, [Cu₄(μ‐HCOO)₃(dpmppm)₂]X, during which the square Cu₄ framework opened up to a linear tetranuclear chain.     

Some of my favorite results with Endre Csáki and Pál Révész - A survey

Summary Some topics of our twenty some years of joint work is discussed. Just to name a few; joint behavior of the maximum of the Wiener process and its location, global and local almost sure limit theorems, strong approximation of the planar local time difference, a general Strassen type theorem, maximal local time on subsets.     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

A survey of retrial queues

We present a survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems. For the single channel case we consider the main model as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer. The stochastic processes arising from these models are considered in the stationary as well as the nonstationary regime. For multi-channel queues we survey numerical investigations of stationary distributions, limit theorems for high and low retrial intensities and heavy and light traffic behaviour.