10,031 research outputs found

    On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations

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    Considered herein are the generalized Camassa-Holm and Degasperis-Procesi equations in the spatially periodic setting. The precise blow-up scenarios of strong solutions are derived for both of equations. Several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established. The exact blow-up rates are also determined. Finally, geometric descriptions of these two integrable equations from non-stretching invariant curve flows in centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are given.Comment: 26 page

    Statistical Constraints on the Error of the Leptonic CP Violation of Neutrinos

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    A constraint on the error of leptonic CP violation, which require the phase δCP\delta_{CP} to be less than π/4\pi/4 for it to be distinguishable on a 2π2\pi cycle, is presented. Under this constraint, the effects of neutrino detector 's distance, beam energy, and energy resolution are discussed with reference to the present values of these parameters in experiments. Although an optimized detector performances can minimize the deviation to yield a larger distinguishable range of the leptonic CP phase on a 2π2\pi cycle, it is not possible to determine an arbitrary leptonic CP phase in the range of 2π2\pi with the statistics from a single detector because of the existence of two singular points. An efficiency factor η\eta is defined to characterize the distinguishable range of δCP\delta_{CP}. To cover the entire possible δCP\delta_{CP} range, a combined efficiency factor η\eta^* corresponding to multiple sets of detection parameters with different neutrino beam energies and distances is proposed. The combined efficiency factors η\eta^* of various major experiments are also presented.Comment: 9 pages, 5 figure

    Remarks on Mizushima's Method for the Determination of Surface Area of Powders

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70158/2/JCPSA6-18-6-899-1.pd

    A Rho family GTPase controls actin dynamics and tip growth via two counteracting downstream pathways in pollen tubes.

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    Tip growth in neuronal cells, plant cells, and fungal hyphae is known to require tip-localized Rho GTPase, calcium, and filamentous actin (F-actin), but how they interact with each other is unclear. The pollen tube is an exciting model to study spatiotemporal regulation of tip growth and F-actin dynamics. An Arabidopsis thaliana Rho family GTPase, ROP1, controls pollen tube growth by regulating apical F-actin dynamics. This paper shows that ROP1 activates two counteracting pathways involving the direct targets of tip-localized ROP1: RIC3 and RIC4. RIC4 promotes F-actin assembly, whereas RIC3 activates Ca(2+) signaling that leads to F-actin disassembly. Overproduction or depletion of either RIC4 or RIC3 causes tip growth defects that are rescued by overproduction or depletion of RIC3 or RIC4, respectively. Thus, ROP1 controls actin dynamics and tip growth through a check and balance between the two pathways. The dual and antagonistic roles of this GTPase may provide a unifying mechanism by which Rho modulates various processes dependent on actin dynamics in eukaryotic cells