The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot typ...The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.展开更多
In recent years, triboelectric nanogenerators have attracted much attention because of their unique potential in self-powered nanosensors and nanosystems. In this paper, we report a cylindrical spiral tdboelectric nan...In recent years, triboelectric nanogenerators have attracted much attention because of their unique potential in self-powered nanosensors and nanosystems. In this paper, we report a cylindrical spiral tdboelectric nanogenerator （S-TENG）, which not only can produce high electric output to power display devices, but also can be used as a self-powered displacement sensor integrated on a measurement ruler. At a sliding speed of 2.5 m/s, S-TENG can generate a short-circuit current （Isc） of 30 μA and an open-circuit voltage （Voc） of 40 V. As the power source, we fabricate a transparent and flexible hand-driven S-TENG. Furthermore, we demonstrate a self-powered S-TENG-based measuring tapeline that can accurately measure and display the pulled-out distance without the need for an extra battery. The results obtained indicate that TENG-based devices have good potential for application in self-powered measurement systems.展开更多
文摘The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.
基金Acknowledgements Thanks for the support from the ＂thousands talents＂ program for pioneer researcher and his innovation team, China, National Natural Science Foundation of China （Nos. 51432005 and 61405131）, Beijing Natural Science Foundation （No. 4154090）, Beijing City Committee of science and technology （Nos. Z131100006013004 and Z131100006013005）.
文摘In recent years, triboelectric nanogenerators have attracted much attention because of their unique potential in self-powered nanosensors and nanosystems. In this paper, we report a cylindrical spiral tdboelectric nanogenerator （S-TENG）, which not only can produce high electric output to power display devices, but also can be used as a self-powered displacement sensor integrated on a measurement ruler. At a sliding speed of 2.5 m/s, S-TENG can generate a short-circuit current （Isc） of 30 μA and an open-circuit voltage （Voc） of 40 V. As the power source, we fabricate a transparent and flexible hand-driven S-TENG. Furthermore, we demonstrate a self-powered S-TENG-based measuring tapeline that can accurately measure and display the pulled-out distance without the need for an extra battery. The results obtained indicate that TENG-based devices have good potential for application in self-powered measurement systems.
