A localisation theorem for singularity categories of proper dg algebras

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of their singularity categories. This allows us to recover and generalise some known results on singularity categories of finite-dimensional algebras.Comment: Section 3 is new, and in Section 4 the base ring is changed from a field to a commutative noetherian ring and in Section 6 the base ring is changed from a field to an arbitrary commutative rin

Solar charge controller in solar street light

Recently, with the rapid development of scientific technology, the conventional energy cannot meet the requirement of human beings. People are looking for the utilization of renew energy. Solar en-ergy as a new clean energy has attract the eyes of people. The applications of solar energy are popular to human society. Solar street light is a good example. This thesis will focus on a deeper research of the popular and ubiquitous solar street light in China. However, solar charge controller as a core determines the quality of solar street light, therefore it is worthwhile to make a research. The controller is based on microcontroller, which using PWM pulse modulation control and protection technology. In order to achieve charge and discharge control. The microcontroller sends all kinds of wresting signal according to the charge and discharge pa-rameter of voltage and current. This thesis also gives the the block program and the circuitry to explain the working principle of the system clearly, and there are also some calculations which can show the economical value of solar street light. Solar charge controller is a core of the system, and this design gives an excellent example in solar street light. It is valuable to make a promotion to the market, which can give the elevation of effi-ciency than the traditional controller