Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at $1$, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.Comment: 15page

An Ultra-Low-Power Oscillator with Temperature and Process Compensation for UHF RFID Transponder

This paper presents a 1.28MHz ultra-low-power oscillator with temperature and process compensation. It is very suitable for clock generation circuits used in ultra-high-frequency (UHF) radio-frequency identification (RFID) transponders. Detailed analysis of the oscillator design, including process and temperature compensation techniques are discussed. The circuit is designed using TSMC 0.18μm standard CMOS process and simulated with Spectre. Simulation results show that, without post-fabrication calibration or off-chip components, less than ±3% frequency variation is obtained from –40 to 85°C in three different process corners. Monte Carlo simulations have also been performed, and demonstrate a 3σ deviation of about 6%. The power for the proposed circuitry is only 1.18µW at 27°C

Dynamic microscopic structures and dielectric response in the cubic-to-tetragonal phase transition for BaTiO3 studied by first-principles molecular dynamics simulation

The dynamic structures of the cubic and tetragonal phase in BaTiO3 and its dielectric response above the cubic-to-tetragonal phase transition temperature (Tp) are studied by first-principles molecular dynamics (MD) simulation. It's shown that the phase transition is due to the condensation of one of the transverse correlations. Calculation of the phonon properties for both the cubic and tetragonal phase shows a saturation of the soft mode frequency near 60 cm-1 near Tp and advocates its order-disorder nature. Our first-principles calculation leads directly to a two modes feature of the dielectric function above Tp [Phys. Rev. B 28, 6097 (1983)], which well explains the long time controversies between experiments and theories