We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

This paper proposes statistic learning based Q-learning algorithm for Multi-Agent System, the agent can learn other agents’ action policies through observing and counting the joint action, a concise but useful hypothesis is adopted to denote the optimal policies of other agents, the full joint probability of policies distribution guarantees the optimal action choice to the learning agent. The a...

Continuous-time stochastic processes are approximations to physically realizable phenomena. We quantify one aspect of the approximation errors by characterizing the asymptotic distribution of the replication errors that arise from delta-hedging derivative securities in discrete time, and introducing the notion of temporal granularity which measures the extent to which discrete-time implementati...

In a search to unravel the fabric of space at short distances, many authors have explored variations on ordinary quantum mechanics based on q-deformations of the canonical commutation relation, q being a parameter in the interval (0, 1) where 1 corresponds to the Bose limit, see for instance [1], [2], [4] Time quantization was considered also, see [3], [13]. On an entirely different line of res...

background: prevention of slipping accidents requires provision of adequate friction through the use of suitable combinations of footwear and underfoot surfaces. shoe sole tread groove is one of the important factors on friction coefficient during walking. objective: to measure the effect of different shoe sole tread groove depths and different surfaces on the required quotient of friction (q),...