A note on recursive completions of the countable atomless Boolean algebras

The Baire category theorem for compact Hausdorff spaces is used to show that any recursive completion ℬ^ϕof the countable atomless Boolean algebra ℬ is ℬrecursively closed." Also, a theorem of R.D. Anderson on the simplicity of Aut(ℬ) is used to show that uncountably many automorphisms of ℬ extend to ℬ^ϕ. This revised version was published online in June 2006 with corrections to the Cover Date.     

低能X射线工业CT图像杯状伪影校正

为了去除X射线工业CT图像中的杯状伪影,提高CT图像的识别能力和量化分析精度,提出一种基于分度投影和权函数的射束硬化校正方法。首先分析得出杯状伪影主要是由X射线连续谱穿过被测物体过程中出现的射束硬化所导致。然后扫描阶梯模型,采集不同厚度下的投影数据并求出线衰减系数,通过拟合曲线,得到硬化模型函数和权函数校正模型函数,并确定权函数。接着,扫描被测圆柱形工件,采集不同分度下的投影数据。最后,针对每一个分度投影数据,采用权函数与当前分度投影数据乘积的方法进行硬化校正。对含有杯状伪影的实际CT图像进行了校正实验,结果表明,与多项式拟合法相比,该方法校正后的灰度图像没有放大噪声,且信噪比提高3.29%,有效地消除了杯状伪影,同时较好地保留了图像边界细节。     

The Mathematics of Internet Search Engines

This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.     

水杨酰肼Schiff碱的合成、表征及抑菌活性

Sehiff碱具有多个氧、氮配位原子,是一类重要的生物配体,某些Schiff碱具有抗癌、抗病毒、抑制细菌生长等生物活性。本文制备了两个水杨酰肼类Schiff碱化合物,并探讨了结构组成、波谱性能及抑菌活性。     

图C4n＋2×P4k＋3的优美性

It is shown that the product graph C_4n＋2×P_4k＋3 is graceful.     

Preparation and Solid-State Characterization of Eltrombopag Crystal Phases

Eltrombopag, of C₂₅H₂₂N₄O₄ chemical formula, is a drug used against thrombocytopenia, marketed worldwide under different tradenames in the form of its bis-olamine salt. The free acid (CAS no. 496775-61-2) is an intermediate species used for the final drug isolation and is reported to crystallize in more than 20 distinct crystal forms, including a large number of hydrates and solvates. Their identification, and, ultimately, their quantification in industrial lots require the usage of accurately measured X-ray powder diffraction pattern, as well as the assessment of the metrical features (crystal symmetry and lattice parameters), nowadays accessible by powerful crystallographic software. Here, the complete indexing of 13 monophasic samples, prepared using literature or newly tailored crystallization methods, jointly to simultaneous thermogravimetric and calorimetric analyses and to variable temperature X-ray diffraction studies, provide a clear picture of the stability fields of the different crystal phases and their mutual interconversion processes, leading, in a few cases, to new and unexpected crystalline polymorphs or solvates of the pristine unsolvated Form I.     

Lanczos and the Riemannian SVD in information retrieval applications

Variations of the latent semantic indexing (LSI) method in information retrieval (IR) require the computation of singular subspaces associated with the k dominant singular values of a large m × n sparse matrix A, where k?min(m,n). The Riemannian SVD was recently generalized to low‐rank matrices arising in IR and shown to be an effective approach for formulating an enhanced semantic model that captures the latent term‐document structure of the data. However, in terms of storage and computation requirements, its implementation can be much improved for large‐scale applications. We discuss an efficient and reliable algorithm, called SPK‐RSVD‐LSI, as an alternative approach for deriving the enhanced semantic model. The algorithm combines the generalized Riemannian SVD and the Lanczos method with full reorthogonalization and explicit restart strategies. We demonstrate that our approach performs as well as the original low‐rank Riemannian SVD method by comparing their retrieval performance on a well‐known benchmark document collection. Copyright 2004 John Wiley & Sons, Ltd.     

综合评价试卷质量分析方法

试卷综合评价分析是提高教学质量的重要环节,也是目前高等院校办学水平和教学质量评估的一项重要的基础性工作.传统的试卷评价分析方法只是一般意义上的正态分布检验,层次是粗浅的.本文将从知识点覆盖率、题量、难度系数、区分度、稳定性和目标效果等方面探索对试卷进行综合评价分析的深层次方法.     

Grammar compressed sequences with rank/select support

Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly repetitive sequences, and classical statistical compression proves ineffective. We introduce, instead, grammar-based representations for repetitive sequences, which use up to 6% of the space needed by statistically compressed representations, and support direct access and rank/select operations within tens of microseconds. We demonstrate the impact of our structures in text indexing applications.