A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition tha...

Most student modelling systems seek to develop a model of the internal operation of the cognitive system. In contrast, Input-Output Agent Modelling (IOAM) models an agent in terms of relationships between the inputs and outputs of the cognitive system. Previous IOAM systems have demonstrated high predictive accuracy in the domain of elementary subtraction. These systems use zeroth-order inducti...

Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At same time, some only a zeroth-order oracle is available. In this paper, we propose several algorithms solve smooth (strongly) convex-concave saddle-point oracles and estimate their convergence ra...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole, I discuss a perturbative solution of the Heun equation. The analytical results are...

The problem of event pileup in single-photonÈcounting CCD cameras (e.g., in the X-ray regime) is discussed, and a solution to the problem is proposed. The resulting pileup equation includes the e†ects of grade migration and presents itself as a nonlinear modiÐcation to the standard integral equation used by forward-folding spectral-Ðtting programs. The e†ectiveness of the model is demonstrated ...

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Till now, different constitutive models have been applied to model the hot deformation flow curves of different materials. In this research, the hot deformation flow stress of API X65 pipeline steel was modeled using the power law equation with strain dependent constants. The results was compared with the results of the other previously examined constitutive equations including the Arrhenius eq...