This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time version of the classical Black-Scholes-Merton (BSM) model, whe…
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or fe…
We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local ma…
"Q Zhang's Problem" is a teaching problem proposed by Qian Zhang, a science teacher at Dongjiao Minxiang Primary School in Dongcheng District, Beijing. In 2022, she proposed that: (1) when explaining the knowledge points of frequency in the "Sound" unit, experiments on the vibration of objects such …
Quantifying the neural signatures of consciousness remains a major challenge in neuroscience and AI. Although many theories link consciousness to rich, multiscale, and flexible neural organisation, robust quantitative measures are still lacking. This paper presents a theory-neutral framework that ch…
Membrane potential in a mathematical model of a cardiac myocyte can be formulated in different ways. Assuming a spatially homogeneous myocyte that is strictly charge-conservative and electroneutral as a whole, two methods will be compared: (1) the differential formulation dV/dt=-I/C_m of membrane po…
The nuclear electric quadrupole moment (NQM) of $^{87}$Sr has recently been revisited using high-precision relativistic atomic calculations [B. Lu et al., Phys. Rev. A 100, 012504 (2019)], indicating that the currently accepted value should be revised and that their result may serve as a new referen…
We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted…
This report addresses the moments, ${\mathfrak{G}_n}\left( {\mathbf{q}} \right) = \int_{ - \infty }^{ + \infty } {{ω^n}S\left( {\mathbf{q},ω} \right)\mathrm{d}ω},\,n \in \mathbb{N},\,n \geq - 1$, of the quantum mechanical dynamic structure factor $S\left( {\mathbf{q},ω} \right)$ for a one-compon…
Research of influence of collisions on Friedel oscillations in quantum degenerate collisional plasma (T=0) is carried out for the first time. It is shown that presence of collisions in plasma leads to exponential decreasing of amplitude and phase shift of the Friedel oscillations. In linear approxim…