Mean2-Bounded Operators on Hilbert Space and Weight Sequences of Positive Operators

We introduce and study the class of mean₂-bounded operators on Hilbert space. These operators, which are characterized by a uniform boundedness condition on the 'quadratic averages' of their powers, are intimately related to operator-valued weight sequences and weighted norm inequalities. Mean₂-bounded operators exhibit a lively interplay with the discrete Hilbert transform in an array of settings. Under appropriate circumstances, mean₂-bounded operators have a rich spectral theory leading to powerful transference properties.     

用谱方法数值模拟槽道内的气固两相流动

在数值模拟领域内,谱方法具有收敛快、分辨率高和精度高的优点．谱方法处理边界方便,随着数值方法的改善和计算机的发展,它在数值模拟中的作用愈加重要．这里采用谱方法数值求解三维Ｎ—Ｓ方程,用这一方法计算了直槽道内流体的流动．计算得到的层流和湍流结果与理论结果符合地较好．在此基础之上进一步模拟了几种不同槽道内的三维粘性流体层流流动,特别在弯曲槽道内的流动计算中,发展了源项处理方法,正确地反映了弯曲固壁对流体流动的影响．通过对湍流计算获得的脉动速度场的统计可以得到湍流运动的许多统计量,正确地反映了湍流运动的特征,说明可以用模拟得到的流场来代替真实的流场．进行了气固两相流动的研究,由直接模拟得到的流体瞬时速度场对固体粒子的作用进行了粒子运动的模拟计算,得到了颗粒在真实流场中运动的浓度,轨道等有用信息和运动特性,得到了令人鼓舞的结果．     

Ionospheric plasma by VHF waves

The amplitude scintillations of very high frequency electromagnetic wave transmitted from geo-stationary satellite at 244.168 MHz have been recorded at Varanasi (geom. lat. 14′ 55′N) during 1991 to 1999. The data are analyzed to determine the statistical features of overhead ionospheric plasma irregularities which are mostly of small duration <30 minutes and are predominant during pre-midnight period. The increase of solar activity generally increases the depth of scintillation. The auto-correlation functions and power spectra of scintillations predict that the scale length of these irregularities varies from 200–500 m having velocity of movement between 75 m/sec to 200 m/sec. These results agree well with the results obtained by other workers.     

利用拉曼散射测量燃烧场的组分浓度及温度

介绍了利用拉曼散射测量燃烧流场温度及组分浓度的物理方法和实验测量结果。利用可调谐KrF准分子激光激发振动拉曼散射（VRS）测量了甲烷－空气燃烧火焰内不同空间的主要组分分子（CH4、N2、O2、H2O等）浓度及温度,测量误差小于10％;另外用N2的拉曼谱拟合测量了火焰的温度,测量精度高于5％。在实验中采用了偏振技术及波长调谐提高了信噪比和测量精度。     

Biomedical Applications of Translational Optical Imaging: From Molecules to Humans

Light is a powerful investigational tool in biomedicine, at all levels of structural organization. Its multitude of features (intensity, wavelength, polarization, interference, coherence, timing, non-linear absorption, and even interactions with itself) able to create contrast, and thus images that detail the makeup and functioning of the living state can and should be combined for maximum effect, especially if one seeks simultaneously high spatiotemporal resolution and discrimination ability within a living organism. The resulting high relevance should be directed towards a better understanding, detection of abnormalities, and ultimately cogent, precise, and effective intervention. The new optical methods and their combinations needed to address modern surgery in the operating room of the future, and major diseases such as cancer and neurodegeneration are reviewed here, with emphasis on our own work and highlighting selected applications focusing on quantitation, early detection, treatment assessment, and clinical relevance, and more generally matching the quality of the optical detection approach to the complexity of the disease. This should provide guidance for future advanced theranostics, emphasizing a tighter coupling—spatially and temporally—between detection, diagnosis, and treatment, in the hope that technologic sophistication such as that of a Mars rover can be translationally deployed in the clinic, for saving and improving lives.     

A spectral solution of the magneto‐convection equations in spherical geometry

A fully three‐dimensional solution of the magneto‐convection equations—the nonlinearly coupled momentum, induction and temperature equations—is presented in spherical geometry. Two very different methods for solving the momentum equation are presented, corresponding to the limits of slow and rapid rotation, and their relative advantages and disadvantages are discussed. The possibility of including a freely rotating, finitely conducting inner core in the solution of the momentum and induction equations is also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

The N‐limit of spectral gap of a class of birth–death Markov chains

We extend Zeifman's method for bounding the spectral gap and obtain the asymptotical behaviour, as N→∞, of the spectral gap of a class of birth–death Markov chains known as random walks on a complete graph of size N. Copyright © 2000 John Wiley & Sons, Ltd.     

A numerical study of flow through wavy-walled channels

A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.     

Approximation of Navier–Stokes incompressible flow using a spectral element method with a local discretization in spectral space

A spectral element technique is examined, which builds upon a local discretization within the spectral space. To approximate a given system of equations the domain is subdivided into nonoverlapping quadrilateral elements, and within each element a discretization is found in the spectral space. The difference is that the test functions are divided into the higher-order polynomials, which have zero boundaries and lower-order polynomials, which are nonzero on one boundary. The method is examined for Navier–Stokes incompressible flow for fluid flow within a driven cavity and for flow over a backstep. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 587–599, 1997     

可迹图的规范拉普拉斯谱半径

根据图的阶数和边数, 本文给出了图可迹的一些充分条件. 作为应用, 得到了可迹图的规范拉普拉斯谱条件.