One-sided Grothendieck quotients

We introduce one-sided thick subcategories of an arbitrary preadditive category and define a quotient category . When is abelian, this concept specializes to Grothendieck’s quotient for two-sided thick . We determine the left noetherian rings for which the injective modules form a left thick subcategory. We exhibit a class of one-sided thick subcategories in categories of coherent functors which are ubiquitous in representation theory. Received: 14 November 2006 Revised: 12 March 2007     

Use of multitoxin immunoaffinity columns for determination of aflatoxins and ochratoxin A in ginseng and ginger

Conditions were optimized for the simultaneous, alkaline, aqueous methanol extraction of aflatoxins (AFL), i.e., B1 (AFB1), B2 (AFB2), G1 (AFG1), and G2 (AFG2), and ochratoxin A (OTA) with subsequent purification, isolation, and determination of the toxins in ginseng and ginger. Powdered roots were extracted with methanol-0.5% NaHCO3 solution (7 + 3). After shaking and centrifugation, the supernatant was diluted with 100 mM phosphate buffer containing 1% Tween 20 and filtered through glass microfiber filter paper. The filtrate was then passed through an immunoaffinity column, and the toxins were eluted with methanol. The AFL were separated and determined by reversed-phase liquid chromatography (RPLC) with fluorescence detection after postcolumn UV photochemical derivatization. OTA was separated and determined by RPLC with fluorescence detection. Recoveries of AFL added at 2-16 ng/g and OTA added at 1-8 ng/g to ginseng were 72-80 and 86-95%, respectively. Recoveries of AFL and OTA added to ginger were similar to those for ginseng. A total of 39 commercially available ginger products from 6 manufacturers were analyzed. Twenty-six samples were found to be contaminated with AFL at 1-31 ng/g and 29 samples, with OTA at 1-10 ng/g. Ten samples contained no AFL or OTA. Ten ginseng finished products were also analyzed; 3 contained AFL at 0.1 ng/g and 4 contained OTA at levels ranging from 0.4 to 1.8 ng/g. LC/tandem mass spectrometry with multiple-reaction monitoring of 3 collisionally induced product ions from the protonated molecular ions of OTA, AFB1, and AFG1 was used to confirm the identities of the toxins in extracts of the finished products.     

Convenient Synthesis of Acyloins from Saturated Ethoxyethyl-Protected Cyanohydrins and α,β-Unsaturated Aldehydes

Functionalized acyloins have been synthesized via Umpolung from saturated ethoxyethyl-protected cyanohydrins and α,β-unsaturated aldehydes.     

Computing predecessor and successor in rounding to nearest

We give simple and efficient methods to compute and/or estimate the predecessor and successor of a floating-point number using only floating-point operations in rounding to nearest. This may be used to simulate interval operations, in which case the quality in terms of the diameter of the result is significantly improved compared to existing approaches.      

视频通信的未来趋势

本文讨论了视频通信的发展现状及今后的发展方向。     

Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices

In this paper, the problem of inverting regular matrices with arbitrarily large condition number is treated in double precision defined by IEEE 754 floating point standard. In about 1984, Rump derived a method for inverting arbitrarily ill-conditioned matrices. The method requires the possibility to calculate a dot product in higher precision. Rump's method is of theoretical interest. Rump made it clear that inverting an arbitrarily ill-conditioned matrix in single or double precision does not produce meaningless numbers, but contains a lot of information in it. Rump's method uses such inverses as preconditioners. Numerical experiments exhibit that Rump's method converges rapidly for various matrices with large condition numbers. Why Rump's method is so efficient for inverting arbitrarily ill-conditioned matrices is a little mysterious. Thus, to prove its convergence is an interesting problem in numerical error analysis. In this article, a convergence theorem is presented for a variant of Rump's method.