On the minimal number of critical points of functions on h-cobordisms

Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.Comment: 7 pages, Late

Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure

Author name used in this publication: Chun-Tian ChengAuthor name used in this publication: K. W. ChauAuthor name used in this publication: Xin-yu Wu2005-2006 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Producing innovation: Comments on Lee and Yu (2010)

The purpose of the article being reviewed (Lee and Yu, 2010), a survey by questionnaire with 182 valid responses, is to analyze “how different relationship styles of employees in the hi-tech industry influence innovation performance” and indeed its conclusions are that “the relationship style of an organization has a significant positive effect on innovation performance”. We see Lee and Yu (2010) as being similar to another highly cited article by Morgan and Hunt in so far as both articles are about relationships, cooperation and trust

Remarks on the number of tubulin dimers per neuron and implications for Hameroff-Penrose Orch OR

Stuart Hameroff has wrongly estimated that a typical brain neuron has 10^7^ tubulin dimers and wrongly attributed this result to Yu and Baas, J. Neurosci. 1994; 14: 2818-2829. In this letter we show that Hameroff’s estimate is based on misunderstanding of the results provided by Yu and Baas, who actually measured the total microtubule length in a single axonal projection with length of 56 μm in a differentiating in vitro stage 3 embryonic hippocampal neuron. In order to visualize how big Hameroff’s error is, we have reconstructed two of the studied by Yu and Baas embryonic hippocampal neurons with Neuromantic v1.6.3 and compared them with previously published reconstructions of adult hippocampal neurons. Correct calculations show that an adult differentiated pyramidal neuron in vivo has approximately 1.3×10^9^ tubulin dimers incorporated in cytoskeletal microtubules. This estimate has profound implications for the Hameroff-Penrose Orch OR model, because it sets limitations on the number of quantum coherent neurons and implies that if 100% of the neuronal microtubules are quantum coherent for 25 ms then Hameroff-Penrose Orch OR conscious events should involve only 15 pyramidal neurons

Mass-luminosity relation and pulsational properties of Wolf-Rayet stars

Evolution of Population I stars with initial masses from 70M_\odot to 130M_\odot is considered under various assumptions on the mass loss rate \dot M. The mass-luminosity relation of W-R stars is shown to be most sensitive to the mass loss rate during the helium burning phase \dot M_{3\alpha}. Together with the mass-luminosity relation obtained for all evolutionary sequences several more exact relations are determined for the constant ratio f_{3\alpha}=\dot M/\dot M_{3\alpha} with 0.5 \le f_{3\alpha} \le 3. Evolutionary models of W-R stars were used as initial conditions in hydrodynamic computations of radial nonlinear stellar oscillations. The oscillation amplitude is larger in W-R stars with smaller initial mass or with lower mass loss rate due to higher surface abundances of carbon and oxygen. In the evolving W-R star the oscillation amplitude decreases with decreasing stellar mass M and for M < 10M_\odot the sufficiently small nonlinear effects allow us to calculate the integral of the mechanical work W done over the pulsation cycle in each mass zone of the hydrodynamical model. The only positive maximum on the radial dependence of W is in the layers with temperature of T\sim 2e5K where oscillations are excited by the iron Z--bump kappa-mechanism. Radial oscillations of W-R stars with mass of M > 10M_\odot are shown to be also excited by the kappa-mechanism but the instability driving zone is at the bottom of the envelope and pulsation motions exist in the form of nonlinear running waves propagating outward from the inner layers of the envelope.Comment: 15 pages, 10 figures, submitted to Astronomy Letter