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정상태,S. Thirumalai Kumaran,Changping Li,쿠르니아완렌디,고태조 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.9
Micro-dimple formation improves the tribological behavior of a material. This study investigates dimple formation on a titanium (Ti-6Al-4V) alloy by using electrical discharge drilling. Input parameters, namely capacitance (C), pulse-on-time (Ton), and voltage (V), were varied to measure the output quality responses including dimple depth, burr height, and burr width. The experimental results indicated that the quality of the dimple is determined based on the spark energy and rate of material removal. A regression analysis was performed for each output response. The developed model confirmed the fitness at a 95 % confidence interval. The contribution of each factor and its significance was determined by using analysis of variance (ANOVA). Further, the optimum drilling condition was predicted by using desirability analysis (C = 10000 pF, Ton = 100 µs, and V = 180 V). The microscopic view of the dimple array and the micro-dimple geometry were analyzed by using scanning electron microscopy images.
Cartier operators on compact discrete valuation rings and applications
정상태 대한수학회 2018 대한수학회지 Vol.55 No.1
From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic $p.$ In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring $\Fq[[T]]$ in one variable $T$ over a finite field $\Fq$ of $q$ elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous $\Fq$-linear functions on $\Fq[[T]].$ According to the digit principle, every continuous function on $\Fq[[T]]$ is uniquely written in terms of a $q$-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the $p$-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on $\Zp.$