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- 저자 : Qiuxia Hu (검색결과 3 건)
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On four new mock theta functions
QiuXia Hu 대한수학회 2020 대한수학회보 Vol.57 No.2
In this paper, we first give some representations for four new mock theta functions defined by Andrews \cite{Andrews} and Bringmann, Hikami and Lovejoy \cite{BHL} using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of $_2\psi_2$ series \[\sum_{n=-\infty}^\infty\frac{(a,c;q)_n}{(b,d;q)_n}z^n\] and Ramanujan's sum \[\sum_{n=-\infty}^\infty\frac{(a;q)_n}{(b;q)_n}z^n.\]
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ON FOUR NEW MOCK THETA FUNCTIONS
Hu, QiuXia Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of <sub>2</sub>𝜓<sub>2</sub> series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.
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TEST SCENARIO DESIGN FOR INTELLIGENT DRIVING SYSTEM ENSURING COVERAGE AND EFFECTIVENESS
Qin Xia,Jianli Duan,Feng Gao,Qiuxia Hu,Yingdong He 한국자동차공학회 2018 International journal of automotive technology Vol.19 No.4
Intelligent vehicle greatly benefits traffic safety, efficiency and driving comfortable. With the development of intelligent driving technology and its application, it is becoming increasingly important to do effective and comprehensive tests before putting on the market. Comprehensively considering the cost of test, an automatic generation method of test scenarios is proposed to ensure both coverage and effectiveness. Based on the analyzed key infuence factors of an intelligent driving system, the analytic hierarchy process (AHP) is used to determine their importance and accordingly an complex index is defined, based on which an improved test case generation algorithm based on the pairwise independent combinatorial testing tool (PICT) is proposed to ensuring both combinational coverage and complexity of test cases. Finally, the test scenario is generated by clustering these discrete test cases considering similarity and complexity. The high complex test cases are preferred to be combined together and conducted preferentially to increase the test efficiency. The effectiveness of this method is validated by applying it on a lane departure warning system (LDW).
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