A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

Hopping and optical absorption of electrons in nano-porous crystal 12CaO·7Al2O3

Recently it has been discovered that a nano-porous main group oxide 12CaO·7Al₂O₃ (C12A7) can be converted from a wide-gap insulator to a good transparent conductor. Using ab initio modelling we explain good conductivity of this material by very small barriers for hopping of localised electrons between neighbouring positive cages. We show that optical absorption of C12A7 in infrared region and at energies higher than 2.7 eV is due to inter-cage and intra-cage electron transitions, respectively. The proposed mechanisms can be useful in further search for conducting transparent media.     

影色迷人的小天地--夏新LC-17HWT1液晶电视

液晶电视具有图像逼真、画质细腻、层次丰富、立体感强，以及高亮度、宽视角、高清晰等优点；而且轻薄、省电、无闪烁、无辐射，可有效减轻人们的视觉疲劳；液晶电视的接口也极为丰富，可接驳电脑、DVD等音视频设备，现在一些厂家还将读取Flash卡的功能整合进了液晶电视，这让液晶电视具备了更多的数码味道。在一些发达国家，液晶电视已向许多家庭的厨房、起居室和浴室渗透，这让液晶电视的超薄、壁挂、平面、节能环保的优点充分显示出来。而夏新LC-17HWT1液晶电视则是这一方面的佼佼者。     

Relationship between haemodynamics and morphology in pulmonary hypertension. A quantitative intravascular ultrasound study

BACKGROUND: Intravascular ultrasound imaging of the pulmonary arteries has been demonstrated to be a reliable method of quantifying vessel diameter, luminal area and pulsatility. Simultaneous measurement of flow velocity and its response to vasodilators allows the relationship between morphology and functional compromise to be studied, especially endothelial dysfunction. METHODS: In 51 patients (mean age = 49.8 +/- 12.6 years, 17 female) we performed right heart catheterization and simultaneous intravascular ultrasound of pulmonary artery branches. The patients were divided in two groups: group 1 with normal pulmonary artery pressure and pulmonary vascular resistance, and group 2 with pulmonary hypertension (peak pulmonary artery pressure > 30 mmHg and/or mean pulmonary artery pressure > 20 mmHg). Vessel wall and lumen were studied using a 2.9 F intravascular ultrasound catheter with a 30 MHz phased array transducer. Measurement of blood flow velocity was accomplished by a Doppler flow wire (0.018 inch). The maximal flow change during acetylcholine infusion (adjusted to 10(-6); 10(-5), and 10(-4) M concentration in the blood vessel) was measured. RESULTS: There were no significant differences between groups 1 and 2 with respect to age (48.5 +/- 14.3 years vs 50.3 +/- 12.3 years; P = ns), gender (4 female/8 male vs 13 female/26 male; P = ns), luminal area of the vessel segment in which the intravascular ultrasound measurements were obtained (11.8 +/- 6.1 mm2 vs 16.7 +/- 14.3 mm2; P = ns), internal diameter (3.9 +/- 1.2 mm vs 4.2 +/- 1.7 mm; P = ns), and external diameter (6.1 +/- 1.3 mm vs 6.9 +/- 2.1 mm; P = ns). Cross-sectional images of the pulmonary artery wall demonstrated a single ring with high echodensity with a thin inner layer regarded as intima in group 1. In contrast, the majority of patients (n = 35/39) in group 2 demonstrated a thickening of the intimal layer and/or a disturbance of layering of the echogenic arterial wall. The relative wall thickness was higher in group 2 than in group 1 (22.5 +/- 10.4% vs 15.3 +/- 6.5%; P < 0.05). There were no significant correlations between pulmonary artery pressure and wall thickness pulmonary artery pressure and area change in the cardiac cycle, acetylcholine-dependent increase in pulmonary flow and morphological changes in the vessel wall. CONCLUSION: We conclude that intravascular ultrasound is capable of detecting morphological changes in the pulmonary vessel wall in pulmonary hypertension and that vessel wall hypertrophy of small pulmonary segment arteries, as detected by intravascular ultrasound, is not predictive of functional vasodilatory response of resistance vessels of the same vessel area.     

Management of multidimensional discrete data

Spatial database management involves two main categories of data: vector and raster data. The former has received a lot of in-depth investigation; the latter still lacks a sound framework. Current DBMSs either regard raster data as pure byte sequences where the DBMS has no knowledge about the underlying semantics, or they do not complement array structures with storage mechanisms suitable for huge arrays, or they are designed as specialized systems with sophisticated imaging functionality, but no general database capabilities (e.g., a query language). Many types of array data will require database support in the future, notably 2-D images, audio data and general signal-time series (1-D), animations (3-D), static or time-variant voxel fields (3-D and 4-D), and the ISO/IEC PIKS (Programmer's Imaging Kernel System) BasicImage type (5-D). In this article, we propose a comprehensive support ofmultidimensional discrete data (MDD) in databases, including operations on arrays of arbitrary size over arbitrary data types. A set of requirements is developed, a small set of language constructs is proposed (based on a formal algebraic semantics), and a novel MDD architecture is outlined to provide the basis for efficient MDD query evaluation.     

The aditi deductive database system

Deductive databases generalize relational databases by providing support for recursive views and non-atomic data. Aditi is a deductive system based on the client-server model; it is inherently multi-user and capable of exploiting parallelism on shared-memory multiprocessors. The back-end uses relational technology for efficiency in the management of disk-based data and uses optimization algorithms especially developed for the bottom-up evaluation of logical queries involving recursion. The front-end interacts with the user in a logical language that has more expressive power than relational query languages. We present the structure of Aditi, discuss its components in some detail, and present performance figures.