A case of oligomerization on attempted chlorination of an α-hydroxy acetal with the triphenylphosphine tetrachloromethane reagent

Treatment of methyl 3,5-dideoxy-β-$\text{D}$-$\text{erythro}$-pentofuranoside $\text{8}$ with the Ph₃P-CCl₄ reagent gave none of the expected 2-chloro derivative but a mixture of l→2 linked oligosaccharides, $\text{9}$, $\text{10}$ with some higher homologues, terminated by αa 2-chloro-2,3,5-trideoxy-α-$\text{D}$-$\text{threo}$-pentofuranosyl unit at the non reducing end.     

When Ramification points meet

Summary This paper contains three applications of the technique of limit series (our [1986]) to the theory of ramification of linear series on smooth curves, and curves of compact type, overC.Let {L _t t|<}, be a family of linear series on a smooth family of smooth curves {C _t }, and letp ₁(t),p ₂(t)C _t be sections of the family which coincide (only) att=0. Setp=p ₁())=p ₂(0)C ₀.We first give a condition related to the Schubert calculus which must be satisfied by the ramification series and the . We then take up the converse problem: In what ways can a given ramification point arise as a limit? We show that if the ramification point isdimensionally proper in the sense of our [1986], then families of every kind allowed by the Schubert calculus condition can actually be constructed. Finally, we prove that dimensional propriety is in a strong sense an open condition, so that ramification points constructed as above are again dimensionally proper.In the body of the paper we work not with pairs of points, as above, but with arbitrary finite collections of points approaching (possibly) several points of the limit curve. Further, by their nature, the results are valid for families of curves of compact type.     

Self-avoiding random walk: A Brownian motion model with local time drift

Summary A natural model for a self-avoiding Brownian motion inR ^d, when specialised and simplified tod=1, becomes the stochastic differential equation , where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that exists almost surely, and to identify the limit.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Multiqueue System with Non-Exhaustive Cyclic Service Modelled as a Linear-Programming Problem

In modern processor-controlled systems, it is common to find a central processor polling a number of message queues, where at most one message is processed from each queue during one polling cycle. This paper shows how one important parameter can be estimated quickly, namely the cycle-time distribution. This is the distribution of times taken for the cyclic server to perform one complete cycle in its continuous scan of a number of queues. The method of solution is to identify various constraints which will determine the cycle-time distribution, formulate them as linear inequality and equality constraints and, by determining an appropriate objective function, apply the simplex method to find upper and lower bounds on the values taken by the cycle-time distribution itself. A great strength of this technique is its overall simplicity, which enables it to be used to obtain important results very quickly and cheaply.     

Further evidence for magnetic charge from meson spectroscopy

Recently evidence was presented for the existence of magnetic charge from Zeeman splitting in meson states. The model by Akers predicted the existence of a new meson at 1814 MeV withI ^G(J ^PC )=0⁺(0^–+). Experimental evidence for this new meson is cited and discussed.