P(RNCH2CH2)3N: catalysts for the head-to-tail dimerization of methyl acrylate

The dimerization of methyl acrylate to the head-to-tail 2-methylene-pentanedioic acid dimethyl ester product was realized in 82 and 85% yield in only 4 h at room temperature in THF in the presence of catalytic amounts of P(RNCH2CH2)3N (R = i-Bu and Bn, respectively). These phosphines are to our knowledge the best nonmetallic catalysts so far reported for this reaction. In contrast, less sterically hindered P(MeNCH2CH2)3N failed to catalyze this dimerization, giving oligomer or polymer instead.     

Baryon rapidity loss in relativistic Au + Au collisions

An excitation function of proton rapidity distributions for different centralities is reported from AGS Experiment E917 for Au+Au collisions at 6, 8, and 10.8 GeV/nucleon. The rapidity distributions from peripheral collisions have a valley at midrapidity which smoothly change to distributions that display a broad peak at midrapidity for central collisions. The mean rapidity loss increases with increasing beam energy, whereas the fraction of protons consistent with isotropic emission from a stationary source at midrapidity decreases with increasing beam energy. The data suggest that the stopping is substantially less than complete at these energies.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

Optimal design of an optical lens

We wish to construct an optimal optical lens, in the sense that it focuses all rays from a given source onto a given focal point. The construction can be reduced mathematically to a global study of a system of two nonlinear functional differential equations. We prove that this system has precisely two analytic solutions.     

Target‐Based Whole‐Cell Screening by 1H NMR Spectroscopy

An NMR‐based approach marries the two traditional screening technologies (phenotypic and target‐based screening) to find compounds inhibiting a specific enzymatic reaction in bacterial cells. Building on a previous study in which it was demonstrated that hydrolytic decomposition of meropenem in living Escherichia coli cells carrying New Delhi metallo‐β‐lactamase subclass 1 (NDM‐1) can be monitored in real time by NMR spectroscopy, we designed a cell‐based NMR screening platform. A strong NDM‐1 inhibitor was identified with cellular IC₅₀ of 0.51 μM , which is over 300‐fold more potent than captopril, a known NDM‐1 inhibitor. This new screening approach has great potential to be applied to targets in other cell types, such as mammalian cells, and to targets that are only stable or functionally competent in the cellular environment.     

Application of Uniform Asymptotics to the Second Painlevé Transcendent

In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection problems with minimal computational effort. Our method relies on finding uniform approximations of differ ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to the other Painlevé equations, and to the wider problem of the asymptotic behavio ur of the general solution to any of these equations. (Accepted May 15, 1997)     

A boundary value problem associated with the second painlevé transcendent and the Korteweg-de Vries equation

The differential equation considered is \(y'' - xy = y|y|^\alpha \) . For general positive α this equation arises in plasma physics, in work of De Boer & Ludford. For α=2, it yields similarity solutions to the well-known Korteweg-de Vries equation. Solutions are sought which satisfy the boundary conditions (1) y(∞)=0 (2) (1) $$y{\text{(}}\infty {\text{)}} = {\text{0}}$$ (2) $$y{\text{(}}x{\text{) \~( - }}\tfrac{{\text{1}}}{{\text{2}}}x{\text{)}}^{{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} \alpha }} \right. \kern-\nulldelimiterspace} \alpha }} {\text{ as }}x \to - \infty $$ It is shown that there is a unique such solution, and that it is, in a certain sense, the boundary between solutions which exist on the whole real line and solutions which, while tending to zero at plus infinity, blow up at a finite x. More precisely, any solution satisfying (1) is asymptotic at plus infinity to some multiple kA i(x) of Airy's function. We show that there is a unique k^*(α) such that when k=k^*(α) the condition (2) is also satisfied. If 0 ^*, the solution exists for all x and tends to zero as x→-∞, while if k>k ^* then the solution blows up at a finite x. For the special case α=2 the differential equation is classical, having been studied by Painlevé around the turn of the century. In this case, using an integral equation derived by inverse scattering techniques by Ablowitz & Segur, we are able to show that k^*=1, confirming previous numerical estimates.     

Amine- and sulfonamide-promoted wittig olefination reactions in water

Amine-promoted olefination: The reaction of a phosphonium salt and an aldehyde in water to yield alkenes with high E-configurational control is promoted by catalytic amounts of non-basic amines in aqueous bicarbonate media. Possible catalytic cycles involving imines and iminium intermediates are discussed.     

Imaging of Phospholipids in Formalin Fixed Rat Brain Sections by Matrix Assisted Laser Desorption/Ionization Mass Spectrometry

Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) is a valuable tool for the analysis of molecules directly from tissue. Imaging of phospholipids is gaining widespread interest, particularly as these lipids have been implicated in a variety of pathologic processes. Formalin fixation (FF) is the standard protocol used in histology laboratories worldwide to preserve tissue for analysis, in order to aid in the diagnosis and prognosis of diseases. This study assesses MALDI imaging of phospholipids directly in formalin fixed tissue, with a view to future analysis of archival tissue. This investigation proves the viability of MALDI-MSI for studying the distribution of lipids directly in formalin fixed tissue, without any pretreatment protocols. High quality molecular images for several phosphatidylcholine (PC) and sphingomyelin (SM) species are presented. Images correspond well with previously published data for the analysis of lipids directly from freshly prepared tissue. Different ionization pathways are observed when analyzing fixed tissue compared with fresh, and this change was found to be associated with formalin buffers employed in fixation protocols. The ability to analyze lipids directly from formalin fixed tissue opens up new doors in the investigation of disease profiles. Pathologic specimens taken for histologic investigation can be analyzed by MALDI-MS to provide greater information on the involvement of lipids in diseased tissue.