Muricatetrocins A and B and Gigantetrocin B: Three New Cytotoxic Monotetrahydrofuran-Ring Acetogenins from Annona muricata

Extracts from the seeds of Annona muricata yielded three new Annonaceous acetogenins: muricatetrocin A (= (5S)-3-{(2R)-2-hydroxy-9-{(2R,5S)-tetrahydro-5-[(1S,4S,5S)-1,4,5-trihydroxyheptadecyl]furan-2-yl}nonyl}-5-methylfuran-2(5H)-one; 1 ), muricatetrocin B (= (5S)-{(2R)-2-hydroxy-9-{(2S,5S)-tetrahydro-5-[(1S,4S,5S)-1,4,5-trihydroxyheptadecyl]furan-2-yl}nonyl}-5-methylfuran-2(5H)-one; 2 ), and gigantetrocin B (= (5S)-3-{(2R)-2-hydroxy-7-{(2S,5S)-tetrahydro-5-[(1S,4R,5R)-1,4,5-trihydroxynonadecyl]furan-2-yl}heptyl}-5-methyl-furan-2(5H)-one; 3 ). Their C-skeletons were deduced by mass spectrometry. Configurations were determined by ¹H-NMR of ketal derivatives and 2D-NMR experiments utilizing Mosher esters. A previously described compound, gigantetrocin A (= (5S)-3-{(2R)-2-hydroxy-7-{(2S,5S)-tetrahydro-5-[(1S,4S,5S)-1,4,5-trihydroxynonadecyl]furan-2-yl}heptyl}-5-methylfuran-2-(5H)one; 4 ), was also isolated and is new to this species. Compounds 1–4 were all selectively cytotoxic for the HT-29 human colon-tumor cell line with potencies at least 10 times that of adriamycin.     

Existence results for non-autonomous multiple-fragmentation models

We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=U_n(t,t₀)f, t⩾t₀, where f is the known data at some fixed time t₀⩾0 and {U_n(t,s)} is a uniformly continuous evolution system. A limit evolution system {U(t,s)} is shown to exist. Depending on the form of the known data f at time t₀, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t₀)f](x) for a.e. x>0, t⩾t₀, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Disordered syn–anti hydrogen‐bonded chains in 3‐(ferrocenyl­carbonyl)­propionic acid

The title compound, [Fe(C₅H₅)(C₉H₉O₃)], has Fe–centroid distances of 1.6551 (11) and 1.6445 (11) Å to the cyclo­penta­dienyl rings. The carboxyl group forms hydrogen bonds in the extremely rare syn–anti chain motif, with O⋯O distances of 2.667 (3) and 2.655 (3) Å. The carboxyl group and the hydrogen‐bonded chains are disordered.     

Development of a volatile amine sensor for the monitoring of fish spoilage

A sensor with potential for the development of a “chemical barcode” for real-time monitoring of fish freshness is described. This on-package sensor contains a pH sensitive dye, bromocresol green, that responds through visible colour change to basic volatile spoilage compounds, such as trimethylamine (TMA), ammonia (NH₃) and dimethylamine (DMA) collectively known as Total Volatile Basic Nitrogen (TVB-N). The sensor characteristics were studied as well as its response with standard ammonia gas. Trials on cod and under-utilised species have verified that the sensor response correlates with bacterial growth patterns in fish samples thus enabling the “real-time” monitoring of spoilage in various fish species. The sensor response can be interrogated with a simple, inexpensive reflectance colorimeter that we have developed based on two light emitting diodes (LEDs) and a photodetector.     

Porphyrin-[(E)-1,2-Diethynylethene] Scaffolding: Synthesis and Optical and Electrochemical Properties of Multinanometer-Sized Porphyrin Arrays

Two series of linearly conjugated hybrid materials, consisting of (E)-1,2-diethynylethene (DEE; hex-3-ene-1,5-diyne) and Zn^II porphyrin components, were prepared by Pd⁰-catalyzed cross-coupling reactions. In one series, one or two DEE substituents were introduced into the meso-positions of the Zn^II porphyrins, leading from 5 ⋅ Zn , to 9 and 1 (Scheme 1). The second series contains the linearly π-conjugated molecular rods 1 – 3 that span a length range from 23 Å ( 1 ) to 53 Å ( 3 ) (Fig. 1). The larger rods 2 and 3 consist of two or three porphyrin moieties, respectively, that are bridged at the meso-positions by trans-enediynediyl (hex-3-ene-1,5-diyne-1,6-diyl) linkers (Scheme 2). The UV/VIS spectra in the series 5 ⋅ Zn , 9 , and 1 (Fig. 2) showed a strong bathochromic shift of both Soret and Q bands of the Zn^II porphyrin as a result of the addition of DEE substituents. Upon changing from 1 to 2 (Fig. 3), the Q band was further bathochromically shifted, whereas the Soret band remained nearly at the same position but became broadened and displayed a shoulder on the lower-wavelength edge as a result of excitonic coupling. The close resemblance between the UV/VIS spectra of 2 and 3 suggests that saturation of the optical properties in the oligomeric series already occurs at the stage of dimeric 2 . Stationary voltammetric investigations showed that the DEE substituents act as strong electron acceptors which induce large anodic shifts in the first reduction potential upon changing from 5 ⋅ Zn to 9 (ΔE=190 mV) and to 1 (ΔE=340 mV). Increasing the number of porphyrin moieties upon changing from 1 to 2 had no effect on the first reduction potential yet the first oxidation potential was substantially lowered (ΔE=110 mV). Large differences in the potentials for one-electron oxidation of the two porphyrin moieties in 2 (ΔE=200 mV) confirmed the existence of substantial electronic communication between the two macrocycles across the trans-enediynediyl bridge.     

A note on effective ultrapowers: Uniform failure of bounded collection

By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single Δ₁ formula that defeats “bounded collection” for any model of II₂ Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MSC: 03F30, 03C62.     

Strongly nonlinear modal equations for nearly integrable PDEs

Summary The purpose of this paper is the derivation of reduced, finite-dimensional dynamical systems that govern the near-integrable modulations ofN-phase, spatially periodic, integrable wavetrains. The small parameter in this perturbation theory is the size of the nonintegrable perturbation in the equation, rather than the amplitude of the solution, which is arbitrary. Therefore, these reduced equations locally approximate strongly nonlinear behavior of the nearly integrable PDE. The derivation we present relies heavily on the integrability of the underlying PDE and applies, in general, to anyN-phase periodic wavetrain. For specific applications, however, a numerical pretest is applied to fix the truncation orderN. We present one example of the reduction philosophy with the damped, driven sine-Gordon system and summarize our present progress toward application of the modulation equations to this numerical study.     

Smooth partitions of unity in preduals of WCG spaces

This paper is based on part of the author's Ph.D. thesis written under the supervision of Professor V. Zizler and has been supported in part by a Province of Alberta Graduate Fellowship     

The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [−1,1]

We consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1−x)^α(1+x)^βh(x), with α,β>−1 and h real analytic and strictly positive on [−1,1]. We obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval [−1,1], for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials. We also deduce asymptotic behavior for the Hankel determinants and for the monic orthogonal polynomials on the interval [−1,1]. For the asymptotic analysis we use the steepest descent technique for Riemann-Hilbert problems developed by Deift and Zhou, and applied to orthogonal polynomials on the real line by Deift, Kriecherbauer, McLaughlin, Venakides, and Zhou. In the steepest descent method we will use the Szeg? function associated with the weight and for the local analysis around the endpoints ±1 we use Bessel functions of appropriate order, whereas Deift et al. use Airy functions.