In this article, we have proved the Darboux's theorem. This theorem is important to prove the Riemann integrability. We can replace an upper bound and a lower bound of a function which is the definition of Riemann integration with convergence of sequence by Darboux's theorem. We adopt the following rules: x, y are real numbers, i, j, k are natural numbers, and p, q are finite sequences of eleme...

This paper proposes an ultra-low power CMOS random number generator (RNG), which is based on an oscillator-sampling architecture. The noisy oscillator consists of a dual-drain MOS transistor, a noise generator and a voltage control oscillator. The dual-drain MOS transistor can bring extra-noise to the drain current or the output voltage so that the jitter of the oscillator is much larger than t...

Random number generation (RNG) requires executive control. A novel paradigm using the eight drum pads of an electronic drum set as an input device was used to test 15 healthy subjects who engaged in random or ordered number generation (ONG). Brain potentials time-locked to the drum-beats revealed a more negative response during RNG compared to ONG which had a left frontal distribution. Source a...

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessar...

The problem of efficiently disseminating data from a mobile stimulus (source) to multiple mobile users (sinks) in a large-scale sensor network has been challenging. We address this problem by proposing a minimum-energy tree-based data dissemination scheme, Dynamic Localized Minimum-Energy Agent Tree-Based Scheme (DLATS). We exploit the fact that sensor nodes are stationary and location-aware. I...