We study persistence in one-dimensional ferromagnetic and antiferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) approximately 1/t(straight theta(p)) with straight theta(p) approximately 0.75 numerically. A mapping to the dynamics of ...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

We present a derivative free method of fourth order convergence for solving systems of nonlinear equations. The method consists of two steps of which first step is the well-known Traub’s method. First-order divided difference operator for functions of several variables and direct computation by Taylor’s expansion are used to prove the local convergence order. Computational efficiency of new met...

We construct analogues of theta series, Eisenstein series and Poincaré series for function fields of one variable over finite fields, and prove their basic properties.

Moire systems offer an exciting playground to study many-body effects of strongly correlated electrons in regimes that are not easily accessible conventional material settings. Motivated by a recent experiment on $\text{WSe}_2/\text{WS}_2$ moire bilayers [Y. Tang et al., Nature 579, 353-358 (2020)], which realizes triangular superlattice with small hopping (of approximately 10 Kelvin), tunable ...

This paper is mainly concerned with whether the almost sure exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical method. Under the global Lipschitz condition, we first show that the SDE is pth moment exponentially stable (for p ∈ (0, 1)) if and only if the stochastic theta method is pth moment exponentially stable for a sufficiently small step siz...

The method of finite-gap integration was created to solve the periodic KdV initial problem. Its development during last 30 years, combining the spectral theory of differential and difference operators with periodic coefficients, the algebraic geometry of compact Riemann surfaces and their Jacobians, the Riemann theta functions and inverse problems, had a strong impact on the evolution of modern...

The effect of stimuli predicting danger (DS) and safety (SS) in Pavlovian aversive conditioning on hippocampal local field potentials (LFP) was studied in 25 partially restrained adult male rats (Long-Evans). DS lasting 5 s preceded tail-shock, while SS overlapping DS during DS last 3 s predicted omission of shock. The power spectra of LFPs during trials were analyzed in theta and delta frequen...

Introduction: There have been multiple explorations for the finding of biological markers of suicide. Some studies indicated the association of neurophysiological markers with suicidal ideation (SI). In previous studies, antidepressant treatment-emergent SI was associated with theta value in midline right frontal region, and pretreatment assessment of frontal quantitative EEG (QEEG) may be asso...