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In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition. 相似文献
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Integer compositions and related enumeration problems have been of interest to combinatorialists and number theorists for a long time. The cyclic and colored analogues of this concept, although interesting, have not been extensively studied. In this paper we explore the combinatorics of -color cyclic compositions, presenting generating functions, bijections, asymptotic formulas related to the number of such compositions, the number of parts, and the number of restricted parts. 相似文献
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Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain “twisted torus knots” originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings. 相似文献
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Elizabeth Finkelstein Yoav Moriah 《Transactions of the American Mathematical Society》2000,352(2):655-677
In this paper we show that given a knot or link in a -plat projection with and , where is the length of the plat, if the twist coefficients all satisfy then has at least nonisotopic essential meridional planar surfaces. In particular if is a knot then contains closed incompressible surfaces. In this case the closed surfaces remain incompressible after all surgeries except perhaps along a ray of surgery coefficients in .
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Sandy M Carter-Franklin JN Martin JD Butler A 《Chemical communications (Cambridge, England)》2011,47(44):12086-12088
Vanadium bromoperoxidase was isolated and cloned from the marine red alga Delisea pulchra. This enzyme catalyzes the bromolactonization of 4-pentynoic acid forming 5E-bromo-methylidenetetrahydro-2-furanone, a compound which is shown herein to inhibit quorum sensing in the engineered reporter strain, Agrobacterium tumefaciens NTL4. 相似文献
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We have developed a sensitive and stable electrochemical method for 17β-estradiol (E2) detection using fast-scan cyclic voltammetry (FSCV). Recently, E2 was proposed to function as a rapid synaptocrine signaling molecule in the brain; however, methods to directly monitor subsecond fluctuations in E2 are currently unavailable, limiting our understanding of the dynamics and mechanism of rapid E2 release. FSCV at carbon-fiber microelectrodes enables subsecond detection of electroactive neurochemicals directly in tissues like the brain. Here, we have electrochemically characterized E2 using FSCV for use in a tissue matrix. The limit of detection of E2 is 31.2±2.5 nM with FSCV, which will enable low nanomolar fluctuations in extracellular E2 to be monitored with hundred millisecond temporal resolution. We also identify specific parameters for waveform modification to improve future detection. This method will significantly improve E2 sensing capabilities and will have far-reaching impacts on improving our understanding of dynamic E2 signaling in the brain. 相似文献
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LetF be a free group andR≤F a characteristic subgroup. Automorphisms ofF/R which are induced by automorphisms ofF are called tame. In this paper we use theN-torsion invariant discovered by the first author and M. Lustig [LM] to show the existence of non-tame automorphisms of free
central extensions and free nilpotent extensions of Burnside groups.
Partially supported by the German Israel Foundation for Research and Development (G. I. F.).
Supported by a grant from the Israel Planning and Budgeting Committee. 相似文献
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Yoav Moriah 《Inventiones Mathematicae》1988,91(3):465-481
Summary In this paper we give a classification theorem of genus two Heegaard splittings of Seifert fibered manifolds overS
2 with three exceptional fibers, except for when two of the exceptional fibers hava the same invariants with opposite orientation. 相似文献