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We wish to solve the heat equation ut=Δu-qu in Id×(0,T), where I is the unit interval and T is a maximum time value, subject to homogeneous Dirichlet boundary conditions and to initial conditions u(·,0)=f over Id. We show that this problem is intractable if f belongs to standard Sobolev spaces, even if we have complete information about q. However, if f and q belong to a reproducing kernel Hilbert space with finite-order weights, we can show that the problem is tractable, and can actually be strongly tractable. 相似文献
14.
Synthesis of enantiomeric-pure cyclohexenyl nucleoside building blocks for oligonucleotide synthesis
Lipases were used for the resolution of (±) (4aR, 7R, 8aS)-2-phenyl-4a,7,8,8a-tetrahydro-4H-1,3-benzodioxine. This separation was carried out on preparative scale and used for the synthesis of eight phosphoramidites of cyclohexenyl nucleosides (d- and l-series). 相似文献
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Arthur Maki Robert L. Sams Jeffrey Barber Engelene t.H. Chrysostom Alfons Weber 《Journal of Molecular Spectroscopy》2004,225(2):109-122
Several new infrared absorption bands for 32S16O3 have been measured and analyzed. The principal bands observed were ν1+ν2 (at 1561 cm−1), ν1+ν4 (at 1594 cm−1), ν3+ν4 (at 1918 cm−1), and 3ν3 (at 4136 cm−1). Except for 3ν3, these bands are very complicated because of (a) the Coriolis coupling between ν2 and ν4, (b) the Fermi resonance between ν1 and 2ν4, (c) the Fermi resonance between ν1 and 2ν2, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A1′ and A2′ levels of ν3+ν4. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν3 band was an essential aid in fitting the ν3+ν4 transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A1′ vibrational level is 3.50 cm−1 above the A2′ level, i.e., r34=1.75236(7) cm−1. In the case of the 3ν3 band, the spectral analysis is straightforward and a weak Δk=±2, Δl3=±2 interaction between the l3=1 and l3=3 substates locates the latter A1′ and A2′ “ghost” states 22.55(4) cm−1 higher than the infrared accessible l3=1 E′ state. 相似文献
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Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data. 相似文献
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The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field. 相似文献
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We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation. 相似文献
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Kelley BD Booth J Tannatt M Wub QL Ladner R Yuc J Potter D Ley A 《Journal of chromatography. A》2004,1038(1-2):121-130
Polypeptides for use in affinity chromatography of factor VIII were identified using phage display technology. Phage libraries were designed to express polypeptide fusions containing five to seven residues flanked by two cysteines that form a disulfide bond. Individual bacteriophage were selected for the ability of these polypeptides to bind factor VIII, and then release the protein under mild elution conditions. Strong consensus sequences were observed that appear to be necessary for this reversible interaction. Chemically synthesized ligands identified by this screening were immobilized onto a chromatographic support and used for affinity purification of factor VIII from a complex feedstream. A chromatographic step was developed that provided a 10000-fold reduction in host cell proteins and DNA, while providing exceptional product recovery. 相似文献
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