On the hot spots of a catalytic super-Brownian motion

Consider the catalytic super-Brownian motion X ^ϱ (reactant) in ℝ ^d , d≤3, which branching rates vary randomly in time and space and in fact are given by an ordinary super-Brownian motion ϱ (catalyst). Our main object of study is the collision local time L = L _[ϱ,Xϱ] (d(s,x) )of catalyst and reactant. It determines the covariance measure in themartingale problem for X ^ϱ and reflects the occurrence of “hot spots” of reactant which can be seen in simulations of X ^ϱ. In dimension 2, the collision local time is absolutely continuous in time, L(d(s,x) ) = ds K _s (dx). At fixed time s, the collision measures K _s (dx) of ϱ _s and X _s ^ϱ have carrying Hausdorff dimension 2. Spatial marginal densities of L exist, and, via self-similarity, enter in the long-term randomergodic limit of L (diffusiveness of the 2-dimensional model). We alsocompare some of our results with the case of super-Brownian motions withdeterministic time-independent catalysts. Received: 2 December 1998 / Revised version: 2 February 2001 / Published online: 9 October 2001     

Synthesis of Primary Amines by One-Pot Reductive Amination of Aldehydes

We report here a novel, one-pot, two-step reductive amination of aldehydes for the atom-economical synthesis of primary amines. The amination step has been carried out with hydroxylammonium chloride and does not require the use of a base. In the subsequent reduction step, a metal zinc/hydrochloride acid system has been used. This method is applicable to both aliphatic and aromatic aldehydes. The operational simplicity, the short reaction times, and the mild reaction conditions add to the value of this method as a practical alternative to the reductive amination of aldehydes.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Synthesis of Furoates and Furfurylic Alcohol Esters Under Very Mild Conditions Using Supported Base Catalysis

Sym-phthaloyl chloride under controlled cathodic reduction is converted into trans-[1(3H)-isobenzofuranone, 3-(3-oxo-1(3H)-isobenzofuranylidene)]: trans-biphthalyl in 65% yield.     

New Stereoselective Synthesis of Epoxyesters from Aldehydes by Solid-Liquid Phase Transfer Process in a Weakly Hydrated Organic Medium

The use of potassium carbonate leads to a stereoselective synthesis of epoxyesters in the presence of substituted thiolanium salt and a carbonyl compound in a solid-liquid low hydrated organic medium.     

Fragmentation associated with Lévy processes using snake

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is of its own interest.      

Location and base selectivity on fragmentation of brominated oligodeoxynucleotides

Bromine-modified oligodeoxynucleotides (ODNs) were fragmented in the electrospray source to study the influence of brominated bases on fragmentation. Several 13-mer ODNs containing a brominated pyrimidine base, BrdU (5-bromodeoxyuridine) or BrdC (5-bromodeoxycytidine), were analyzed. Low cone voltage fragmentation yields a loss of the brominated base with a preferential loss for the brominated base closer to the 5'-end (2-position > 4-position > 12-position) as well as a preferential loss of BrdU over BrdC. Higher cone voltage produces backbone fragmentation with complementary a(n)-base and w(m) ions close to the brominated base. On the basis of these observations, we located the brominated base in the sequence for all of the ODNs studied.     

Feller Property and Infinitesimal Generator of the Exploration Process

We consider the exploration process associated to the continuous random tree (CRT) built using a Lévy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale. The research of the second author was partially supported by NSERC Discovery Grants of the Probability group at Univ. of British Columbia.     

Synthesis of 2-Acylfurans in the Presence of Phosphonic Resins as Catalysts

The latest investigations on the acylation of aromatic and heteroaromatic structures (1,2,3) have shown that, in the case of furan, the yield and the selectivity observed are poor. Furylic ketones are however derivatives of major interest (4–6).     

An optical device to homogenize a laser beam

Based on segmentation-recombination principle, a specific optical device is designed to homogenize a highpower CO2 laser beam which is used as a heating source.