Hadronic Decays of the Spin-Singlet Heavy Quarkomium under the Principle of Maximum Conformality

The principle of maximum conformality （PMC） provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying the PMC scale setting, all non-conformal terms in a perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In this study, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay （into light hadrons） at the next-to-leading order. After applying the PMC scale setting, the decay widths for all those cases are ahnost independent of the initial renormalization scales. The PMC scales for ηc and he decays are below 1 GeV; to achieve a confidential pQCD estimation, we adopt several low-energy running coupling models to carry out the estimation. By taking the MPT model, we obtain Г（ηc → LH） = 25.09 -4.28^＋5.52 MeV, F（ηb →LH） 14.34-0.84^＋0.92 feV, Г（hc →LH） = 0.54-0.04^＋0.06 MeV and Г（hb →LH） = 39.89-0.46^＋0.28 keV, where the errors are calculated by taking mc E[1.4OGeV, 1.60GeV] and mb C[4.50GeV, 4.70GeV]. These decay widths agree with the principle of minimum sensitivity estimations, in which the decay widths of ηc,b are also consistent with the measured ones.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Structural stability and electrical properties of AIB2-type MnB2 under high pressureStructural stability and electrical properties of AIB2-type MnB2 under high pressureStructural stability and electrical properties of AIB2-type MnB2 under high pressureStructural stability and electrical properties of AIB2-type MnB2 under high pressure

The structural stability and electrical properties of A1B2-type MnB2 were studied based on high pressure angle- dispersive x-ray diffraction, in situ electrical resistivity measured in a diamond anvil cell （DAC） and first-principles calcu- lations under high pressure. The x-ray diffraction results show that the structure of A1B2-type MnB2 remains stable up to 42.6 GPa. From the equation of state of MnB2, we obtained a bulk modulus value of 169.9~3.7 GPa with a fixed pressure derivative of 4, which indicates that A1B2-type MnB2 is a hard and incompressible material. The electrical resistance un- dergoes a transition at about 19.3 GPa, which can be explained by a transition of manganese 3d electrons from localization to delocalization under high pressure.     

Banach空间中线性算子核逆的一致有界性与收敛性（英文）

本文主要研究Banach空间中线性算子核逆的一致有界性与收敛性之间的关系.首先证明核逆的一致有界性与收敛性的等价性,给出了核逆的表达式.其次,利用稳定扰动,证明核逆的稳定扰动与连续性是等价的.作为应用,我们还给出有限秩算子核逆的连续性特征,并给出扰动算子的核逆具有最简表达式的充分必要条件.     

谈高一新课程"函数的零点"教学的几个问题

2006年9月下旬绍兴市优质课在上虞举行，课题是《方程的根与函数的零点》笔者有幸听了6位老师的精彩上课，颇有收获，多数教师在教学中体现了先进正确的教学理念：“以学生为本”、“问题引导学习”、“教与学重心前移”、“教会学生数学地思维”、“改进教学方式”、“促进学生主动，探究学习”等等．但由于准备时间仓促，每节课中总会或多或少有点遗憾，下面结合教学实例谈一下自己对几个问题粗浅的认识．     

数学建模中的类比方法

本文通过实例论述了类比方法在数学建模中的作用．     

矩函数及其在旋成面叶栅气动反命题及杂交命题中的应用

本文首先对旋转的任意旋成面上的理想可压缩流动引入一新通用函数——矩函数,并论证它的主要性质,接着将它推广到粘性气体的情况。然后,提出一个基于矩函数的旋成面叶栅气动反命题及A型杂交命题的通用解法。研究表明,矩函数对求解杂交命题(反命题是其特例)和跨声速流动具有明显的优越性。     

Feasibility of similarity coefficient map for improving morphological evaluation of T2* weighted MRI for renal cancer

The purpose of this paper is to investigate the feasibility of using a similarity coefficient map(SCM) in improving the morphological evaluation of T2* weighted(T2*W) magnatic resonance imaging(MRI) for renal cancer.Simulation studies and in vivo 12-echo T2*W experiments for renal cancers were performed for this purpose.The results of the first simulation study suggest that an SCM can reveal small structures which are hard to distinguish from the background tissue in T2*W images and the corresponding T2* map.The capability of improving the morphological evaluation is likely due to the improvement in the signal-to-noise ratio(SNR) and the carrier-to-noise ratio(CNR) by using the SCM technique.Compared with T2* W images,an SCM can improve the SNR by a factor ranging from 1.87 to 2.47.Compared with T2* maps,an SCM can improve the SNR by a factor ranging from 3.85 to 33.31.Compared with T2*W images,an SCM can improve the CNR by a factor ranging from 2.09 to 2.43.Compared with T2* maps,an SCM can improve the CNR by a factor ranging from 1.94 to 8.14.For a given noise level,the improvements of the SNR and the CNR depend mainly on the original SNRs and CNRs in T2*W images,respectively.In vivo experiments confirmed the results of the first simulation study.The results of the second simulation study suggest that more echoes are used to generate the SCM,and higher SNRs and CNRs can be achieved in SCMs.In conclusion,an SCM can provide improved morphological evaluation of T2*W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T2*W MR images and T2* maps.Furthermore,in practical applications,for a fixed total sampling time,one should increase the number of echoes as much as possible to achieve SCMs with better SNRs and CNRs.