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91.
For positive integers s and k1,k2,…,ks, the van der Waerden number w(k1,k2,…,ks;s) is the minimum integer n such that for every s-coloring of set {1,2,…,n}, with colors 1,2,…,s, there is a ki-term arithmetic progression of color i for some i. We give an asymptotic lower bound for w(k,m;2) for fixed m. We include a table of values of w(k,3;2) that are very close to this lower bound for m=3. We also give a lower bound for w(k,k,…,k;s) that slightly improves previously-known bounds. Upper bounds for w(k,4;2) and w(4,4,…,4;s) are also provided. 相似文献
92.
93.
Nonlinear Dynamics, Psychology, and Life Sciences - 相似文献
94.
Greene P.A. Robertson S.H. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1990,18(2):228-230
A model for the shell current in a reversed field pinch which includes the current induced by the motion of the plasma is discussed. This model gives a good approximation to the magnitude and time dependence of a shell current measured experimentally 相似文献
95.
N. A. Robertson S. Hoggan J. B. Mangan J. Hough 《Applied physics. B, Lasers and optics》1986,39(3):149-153
An intensity-stabilisation system for an argon laser using an electro-optic modulator is described. We achieved a degree of stabilisation of up to 40 dB (factor of 100) for intensity fluctuations below a few kHz. The performance in this frequency range did not reach that expected from the available loop gain. We have identified two serious limiting factors to the performance of our system at low frequency: geometrical fluctuations and frequency fluctuations of the laser light. 相似文献
96.
97.
Chris C. Stowers J. Brian Robertson Hyunju Ban Robert D. Tanner Erik M. Boczko 《Applied biochemistry and biotechnology》2009,156(1-3):59-75
Four decades of work have clearly established the existence of autonomous oscillations in budding yeast culture across a range of operational parameters and in a few strains. Autonomous oscillations impact substrate conversion to biomass and products. Relatively little work has been done to quantify yield in this case. We have analyzed the yield of autonomously oscillating systems, grown under different conditions, and demonstrate that it too oscillates. Using experimental data and mathematical models of yeast growth and division, we demonstrate strategies to increase the efficient recovery of products. The analysis makes advantage of the population structure and synchrony of the system and our ability to target production within the cell cycle. While oscillatory phenomena in culture have generally been regarded with trepidation in the engineering art of bioprocess control, our results provide further evidence that autonomously oscillating systems can be a powerful tool, rather than an obstruction. 相似文献
98.
We describe the thermal rearrangement of aldehydes bearing an α-(allyl- or crotylsilyl)oxy substituent. The transformations are best described mechanistically as intramolecular silatropic ene reactions based on stereoselectivity, kinetic and computed transition state data. The overall process constitutes a stereospecific (meth)allylation of α-hydroxyaldehydes, under neutral conditions, in which the hydroxyl protecting group is also the (meth)allylating agent. 相似文献
99.
Crystals of Co3(AsO4)2 were grown from the melt of a mixture of Co2As2O7 and As2O5. The crystals are isostructural with Mg3(AsO4)2 and are tetragonal with a = 6.858(2), c = 18.872(5) Å, Z = 6, and space group . A total of 1048 independent reflections were measured by diffractometer and used in the full-matrix refinement to a final R value of 0.069. The structure contains two distinct AsO4 groups. Two of the cobalt ions are octahedrally coordinated and a third occupies a site with four short and four long CoO distances. The crystal structure of Co3 (AsO4)2 is not based on the continuous three-dimensional closest packing of oxygen atoms. Nevertheless the number of oxygen atoms per cubic centimeter is 5.4 × 1022, which falls in the range of values for hexagonal and cubic closest packed structures. A better measure of the degree to which closest packing is achieved by a structure is suggested. It is based on an analysis of the polyhedra of oxygen atoms which surround each of the oxygen atoms in a structure and their relation to the polyhedra in ideally closest packed structures. In order to facilitate the analysis, polytopes of 11- and 12-vertex polyhedra were studied. A new decahexahedral 11-vertex polyhedron was found. 相似文献
100.