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1.
Jacob Fox 《Journal of Combinatorial Theory, Series A》2006,113(1):84-100
We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a1,a2, and a3 are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a1x1+a2x2+a3x3=0, then for every finite coloring of the positive integers there is a monochromatic solution to a1x1+a2x2+a3x3=0. 相似文献
2.
R. P. Sundarraj P. S. Sundararaghavan Dale R. Fox 《The Journal of the Operational Research Society》1994,45(5):549-558
Several production and flexible manufacturing systems can naturally be modelled using queueing networks. In this paper, we consider the problem of acquiring servers for the nodes of an open queueing network, so as to optimize the steady-state mean virtual system parameters subject to a budget constraint. A partial enumeration scheme and a heuristic method have been proposed to solve this problem. Empirical results based on randomly generated test problems are used to identify a class of problems for which the heuristic performs well. 相似文献
3.
Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure. 相似文献
4.
Current reform documents in mathematics education recommend that teachers help students develop both conceptual and procedural understandings. However, teachers often do not possess the in-depth mathematical reasoning necessary to accomplish this goal. The purpose of this article is to provide one way in which preservice teachers can come to better understand the mathematics they will teach. 相似文献
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7.
Malkinson JP Anim MK Zloh M Searcey M Hampshire AJ Fox KR 《The Journal of organic chemistry》2005,70(19):7654-7661
[reaction: see text] In this article, the first solid-phase-based total synthesis of TANDEM, a synthetic analogue of triostin A, is described. In initial studies, the synthesis incorporated depsipeptide formation, introduction of chromophores, and disulfide bond formation on the solid phase, prior to a final solution-phase macrolactamization, to give the target molecule. Although pure TANDEM was obtained in an overall yield comparable to those for all syntheses to date, the yield of the final cyclization was low (11%). A more efficient approach involved removal from the solid phase prior to disulfide bond formation. The resulting linear peptide underwent macrolactamization under mild conditions and high dilution. Final disulfide bond formation was essentially quantitative and gave the target molecule, TANDEM, in an overall yield of 18%. The final compound was assessed for its ability to bind to 5'-TpA sequences on DNA by DNase I footprinting. This efficient synthesis sets the stage for a study of the structure-activity relationship of TANDEM and the natural product triostin A, with analogues containing "point mutations" at every site within the cyclic compounds. 相似文献
8.
The 1D- and 2D-6Li, 6Li-INADEQUATE experiments are described as new tools for the detection of scalar coupled nonequivalent 6Li nuclei in organolithium clusters. Practical applications of these sequences are demonstrated for the 6Li-NMR spectra of (E)-1-lithio-2-(2-lithiophenyl)-1-phenylhex-1-ene ( 1 ) and (E)-2-lithio-1-(2-lithiophenyl)-1-phenylpent-1-ene ( 2 ), where signals due to dimers and monomers can be distinguished. The performance of the 2D-6Li, 6Li-INADEQUATE and the 6Li, 6Li-COSY-45-LR experiment are compared. The 6Li chemical shifts of 1 and 2 are discussed. 相似文献
9.
Photosensitization by Erythrosin B of a TiO2 colloidal dispersion in acetonitrile has been studied by fast kinetic spectroscopy. The dye molecules adsorbed on the TiO2 surface had a significantly shorter lifetime (2̃ 250 ps) compared to those in homogeneous solution (≈ 1.6 ns) in acetonitrile. The photosensitization of TiO2 occurred more efficiently from the singlet than from the triplet state of the dye. 相似文献
10.
Electrical conductance measurements are reported for aqueous NaCl solutions at 25°C as a function of concentration up to 0.02M and pressures up to 2000 atm. The data were analyzed with the Fuoss-Hsia-Fernandez-Prini (FHFP) equation. The standard error of fit, , varies from 0.04 at 1 atm to 0.10 at 2000 atm. The increase of with pressure arises from increasing non-randomness in the distribution of errors about the FHFP equation suggesting that modifications in the theory are necessary. The pressure dependence of O for NaCl and KCl is nearly identical.Contribution of the Scripps Institution of Oceanography, New Series 相似文献