A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

A Mechanistically and Operationally Simple Route to Metal–N-Heterocyclic Carbene (NHC) Complexes

We have been puzzled by the involvement of weak organic and inorganic bases in the synthesis of metal–N-heterocyclic carbene (NHC) complexes. Such bases are insufficiently strong to permit the presumed required deprotonation of the azolium salt (the carbene precursor) prior to metal binding. Experimental and computational studies provide support for a base-assisted concerted process that does not require free NHC formation. The synthetic protocol was found applicable to a number of transition-metal- and main-group-centered NHC compounds and could become the synthetic route of choice to form M–NHC bonds.     

Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems

Numerical Algorithms - Recently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods...     

On some auxiliary mappings generated by nonexpansive and strictly pseudo-contractive mappings

Starting by a finite family of mappings, we define the concept of procedure with Lipschitzian dependence of the coefficients. We give seven concrete examples of such procedures and prove the strong convergence of two viscosity methods.     

Some noncoercive parabolic equations with lower order terms in divergence form

This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div(uE), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $.AMS Subject Classification: 35K10, 35K15, 35K65.     

On a discrimination problem for a class of stochastic processes with ordered first‐passage times

Consider the Bayes problem in which one has to discriminate if the random unknown initial state of a stochastic process is distributed according to either of two preassigned distributions, on the base of the observation of the first‐passage time of the process through 0. For processes whose first‐passage times to state 0 are increasing in the initial state according to the likelihood ratio order, such problem is solved by determining the Bayes decision function and the corresponding Bayes error. The special case of fixed initial values including a family of first‐passage times with proportional reversed hazard functions is then studied. Finally, various applications to birth‐and‐death and to diffusion processes are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

The electrostatics of Einstein’s unified field theory

When sources are added at their right-hand sides, and g_(ik) is a priori assumed to be the metric, the equations of Einstein’s Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_(ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_(ik), however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély’s physically correct metric is adopted.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

Blended implicit methods for solving ODE and DAE problems,and their extension for second-order problems

The use of implicit numerical methods is mandatory when solving general stiff ODE/DAE problems. Their use, in turn, requires the solution of a corresponding discrete problem, which is one of the main concerns in the actual implementation of the methods. In this respect, blended implicit methods provide a general framework for the efficient solution of the discrete problems generated by block implicit methods. In this paper, we review the main facts concerning blended implicit methods for the numerical solution of ODE and DAE problems.