A high-speed dual-modulus divide-by-32/33 prescaler has been developed using 0.25 μm CMOS technology. The source-coupled logic (SCL) structure is used to reduce the switching noise and to ameliorate the power-speed t...A high-speed dual-modulus divide-by-32/33 prescaler has been developed using 0.25 μm CMOS technology. The source-coupled logic (SCL) structure is used to reduce the switching noise and to ameliorate the power-speed tradeoff. The proposed prescaler can operate at high frequency with a low-power consumption. Based on the 2.5 V, 0.25 μm CMOS model, simulation results indicate that the maximum input frequency of the prescaler is up to 3.2 GHz. Running at 2.5 V, the circuit consumes only 4.6 mA at an input frequency 2.5 GHz.展开更多
The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension ...The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension are developed for a time-independent potential consisting of an infinite wall and a repulsive delta function. The exact solutions are obtained by means of a superposition of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions for which the resulting integrals can be evaluated exactly. Square-integrability and the boundary conditions are satisfied. The simplest of the obtained solutions is presented and the probability for the particle to be found inside the potential well as a function of time is calculated. The system exhibits non-exponential decay for all times;the probability decreases at large times as . Other exact solutions found exhibit power law behavior at large times. The results are generalized to all normalizable solutions to this problem. Additionally, numerical solutions are obtained using the staggered leap-frog algorithm for select potentials exhibiting the prevalence of non-exponential decay at short times.展开更多
This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential ra...This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.展开更多
文摘A high-speed dual-modulus divide-by-32/33 prescaler has been developed using 0.25 μm CMOS technology. The source-coupled logic (SCL) structure is used to reduce the switching noise and to ameliorate the power-speed tradeoff. The proposed prescaler can operate at high frequency with a low-power consumption. Based on the 2.5 V, 0.25 μm CMOS model, simulation results indicate that the maximum input frequency of the prescaler is up to 3.2 GHz. Running at 2.5 V, the circuit consumes only 4.6 mA at an input frequency 2.5 GHz.
文摘The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension are developed for a time-independent potential consisting of an infinite wall and a repulsive delta function. The exact solutions are obtained by means of a superposition of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions for which the resulting integrals can be evaluated exactly. Square-integrability and the boundary conditions are satisfied. The simplest of the obtained solutions is presented and the probability for the particle to be found inside the potential well as a function of time is calculated. The system exhibits non-exponential decay for all times;the probability decreases at large times as . Other exact solutions found exhibit power law behavior at large times. The results are generalized to all normalizable solutions to this problem. Additionally, numerical solutions are obtained using the staggered leap-frog algorithm for select potentials exhibiting the prevalence of non-exponential decay at short times.
基金Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093)。
文摘This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.
