41 problems

The computed curves describe triply periodic surfaces parametrized by volume fraction, with points $B$ and $C$ marking portions that the numerical method was unable to reproduce. A…

Consider a time grid … For Bermudan option pricing, let the exercise dates be equidistant and coincide with time points in this grid. The option price is approximated using the Alm…

Conjecture concerning YBC 7289. The scheme

Let $u_b$ denote the upper control bound, and consider the optimal controls for the bang-bang control problem studied in the paper. Bang-bang control conjecture. Optimal controls a…

The paper considers summation-by-parts (SBP) properties in discrete derivative operators and notes that the Active Flux method uses upwinding, with upwind SBP operators providing a…

Approximate multiplier convergence conjecture. Under the direct-adjoining and secant-function-augmentation formulations, $\tilde{\eta}_i$ approaches $\eta_i$ as $\rho_i\to 0$:

In a moist atmospheric simulation, compare a standard coarse-grid simulation with a finer-grid benchmark, and consider the spurious clouds produced by the coarse simulation. Coarse…

Let the Riemann xi function be the function whose roots are being studied, and let BNQN denote the Backtracking New Q-Newton method. Suppose there is a method that proves that…

Let $\xi$ be the Riemann xi function, let $z^*$ be one of its zeros, and let the Voronoi cell of $z^*$ be its cell in the Voronoi diagram of all zeros of $\xi$. Let the basin of at…

Let $\bar{y}_i^{k-1}$ and $y_i^k$ denote the two possible initial guesses used to evaluate the best-response mapping $\textbf{BR}_{\lambda^k}(x_i)$ in the numerical algorithm, with…

CA-EC applicability conjecture. CA-EC is expected to work for quantum systems involving more particles, as well as in conjunction with techniques other than complex scaling.

Let $g\in\{7,8\}$, let $p$ be the percentile used by the $p$-quantile algorithm to construct the set of penultimate histograms, and let efficiency mean the fraction of most likely…

Let $\zeta=100$ be the discretization level, let $g$ be the number of genotypes, and let $p(g)$ denote the smallest percentile that enables full efficiency of the $p$-quantile algo…

For a numerical scheme, let the mass flux denote its mass-flux function and let the pressure term denote the pressure contribution to that flux. Liou's conjecture. Schemes with a m…

The coupled envelope evolution equations (CEEEs) are being compared with the second-order accurate envelope equations of Li et al. for weakly nonlinear surface gravity waves. Let…

Let $E$ denote the deterministic Lévy area correction appearing when approximating a stochastic system by smooth processes, so that the limiting stochastic integral has the form ……

The method of manufactured solutions (MMS) is being compared with its use in traditional finite-volume and finite-element methods, and the smoothed particle hydrodynamics (SPH) met…

Let $St(n,p)$ denote the Stiefel manifold equipped with the Riemannian metric parametrized by $\alpha$, and let an algorithm compute the Riemannian logarithm…

Shot-noise numerical-methods conjecture. The shot noise representation has the potential to offer effective numerical methods for stochastic delay differential equations with jumps…

Effectiveness conjecture. The proposed method can be equally effective for a very wide range of FDE optimization problems.

Let an optimization procedure solve a differential equation whose solution contains large-scale and fine-scale features. Introduce a large numerical viscosity so that the equation…

The self-approximating method uses a marginal importance sampler, and some simulated draws may fall outside the support of $Z_t\mid Z_{t-1}=z$ for a given $z$, so they are not used…

Let $G\in\mathcal{H}^{\circ}$ be a target histogram, let $h(y,G)$ denote the norm of the cost gradient, and let $y_0\in\mathcal{H}^{0}$. For small $m$, define $y^*$ approximately b…

Let $PEN$ be a finite set of interior histograms and, for each $y\in PEN$, define the local mesh size $LMS(y)$ by … For a target histogram $G\in\mathcal{H}^{\circ}$, let…

The regularized Euler evolution equations for density $\rho$, momentum density $u_i$, entropy density $s$, pressure $p$, and velocity $v_i=u_i/\rho$ are given by the displayed syst…