In this paper the numerical solution of the one dimensional heat conduction equation is investigated, by applying Dirichlet boundary condition at the left hand side and Neumann boundary condition was applied at the right hand side. To the discretization in space, we apply the linear finite element method and for the time discretization the wellknown theta-method. The aim of the work is to deriv...

Abstract. This is the third and final installment in our series of papers applying the method of Atkin and Swinnerton-Dyer to deduce formulas for rank differences. The study of rank differences was initiated by Atkin and Swinnerton-Dyer in their proof of Dyson’s conjectures concerning Ramanujan’s congruences for the partition function. Since then, other types of rank differences for statistics ...

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate a...

The effects of initial conditions on the evolution Richtmyer–Meshkov instability (RMI) at early to intermediate times are analysed, using numerical simulations an idealised version recent shock tube experiments performed University Arizona (Sewell et al. , J. Fluid Mech. vol. 917, 2021, A41). experimental results bracketed by performing both implicit large-eddy high-Reynolds-number limit as wel...

We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, th...

In this paper we study the theta contants appeared in [S] those induced the modular function for the family of Picard curves C(ξ) given by (1). Our theta constants θk(u, v) (k = 0, 1, 2) , given by (3), are ”Neben type” modular forms of weight 1 defined on the complex 2-dimensional hyperball B, given by (2), with respect to a index finite subgroup Γθ of the Picard modular group Γ = PGL(M,Z[exp(...

Hippocampal theta oscillations are postulated to support mnemonic processes in humans and rodents. Theta oscillations facilitate encoding and spatial navigation, but to date, it has been difficult to dissociate the effects of volitional movement from the cognitive demands of a task. Therefore, we examined whether volitional movement or cognitive demands exerted a greater modulating factor over ...

This paper establishes that a class of $ N $-player stochastic games with singular controls, either bounded velocity or finite variation, can both be approximated by mean field (MFGs) controls velocity. More specifically, it shows (i) the optimal control to an MFG \theta is shown \epsilon_N $-NE game velocity, = O(\frac{1}{\sqrt{N}}) $, and (ii) this (\epsilon_N + \epsilon_{\theta}) where \epsi...

OBJECTIVE The aim of this study was to assess and compare the effect of two neurofeedback protocols (SMR/theta and beta/theta) on ADHD symptoms, selective attention and EEG (electroencephalogram) parameters in children with ADHD. METHOD The sample consisted of 16 children (9-15 year old: 13 boys; 3 girls) with ADHD-combined type (ADHD-C). All of children used methylphenidate (MPH) during the ...

We study the convergence and rates of a multi-block proximal alternating direction method multipliers (PADMM) for solving linearly constrained separable nonconvex nonsmooth optimization problems. This algorithm is an important variant (ADMM) which includes term in each subproblem, to cancel out complicated terms applications where subproblems are not easy solve or do admit simple closed form so...