Hankel determinants, Pad\'e approximations, and irrationality exponents

The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary, and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han.Comment: International Mathematics Research Notices 201

Adaptive Weighted Morphology Detection Algorithm of Plane Object in Docking Guidance System

In this paper, we presented an image segmentation algorithm based on adaptive weighted mathematical morphology edge detectors. The performance of the proposed algorithm has been demonstrated on the Lena image. The input of the proposed algorithm is a grey level image. The image was first processed by the mathematical morphological closing and dilation residue edge detector to enhance the edge features and sketch out the contour of the image, respectively. Then the adaptive weight SE operation was applied to the edge-extracted image to fuse edge gaps and hill up holds. Experimental results show it can not only primely extract detail edge, but also superbly preserve integer effect comparative to classical edge detection algorithm

Study on the quality characteristics of a compounded system composed by highland barley flour and medium strength flour

Highland barley flour was selected as the research object and mixed with medium gluten wheat flour in this study. The correlation analysis of highland barley powders with different addition amounts on damaged starch, farino graphical properties, pasting property, solvent retention capacity were studied. The results showed that: with the increase of the proportion of highland barley flour, the damaged starch increased significantly (P<0.05), and was negatively correlated with the falling number; the water absorption of dough increased with the addition of 85%, and the maximum water absorption reached 73.10%, the water absorption and weakening degree increased significantly (P<0.05); The effect of different additions of highland barley powders on the stabilization time of the mixed powder is not significant; Peak viscosity, minimum viscosity, final viscosity, attenuation value and rebirth value decreased significantly (P<0.05), the falling number is positively correlated with peak viscosity; lactic acid SRC was significantly reduced (P<0.05), and was positive correlation with wet gluten content; sodium carbonate SRC, sucrose SRC and water SRC increased significantly (P<0.05), significant positive correlation was found between damaged starch and sodium carbonate SRC, sucrose SRC was positively correlated with water absorption and protein , and water SRC was positively correlated with protein

Does ISO 9000 certification benefit service firms?

This paper examines whether ISO 9000 certification benefits service firms in terms of their financial performance and promotes sustainable improvement. We argue that in a developing country setting such as China, the massive benefits brought by the signalling effect of the certification can discourage firms' motivation to fully implement the standard of certification and lead to the decline of investment on productivity-improving activities. In other words, the certification may have negative effects on the productivity of certified firms. We investigate 89,024 firms in Chinese service industries to assess the impacts of the certification on sales, productivity and profitability of these firms. To address the potential selection bias of ISO 9000 certification, the Propensity Score Matching method and Coarsened Exact Matching method were used. Our key findings are that the ISO 9000 certification does help to increase the total amount of sales, but it decreases the productivity and profitability of these certified service firms. We also find that earlier certifiers seem to gain larger advantage in sales but more reduction in productivity, and firms with higher level of technology intensity seem to obtain a larger increase in sales and less productivity loss after receiving their ISO 9000 certification