17 problems

Let $n$ be a positive integer, let $\{I,H\}^n$ denote the transform set consisting of $n$ choices between the identity transform $I$ and the Hadamard transform $H$, and let the cli…

Let $\widehat{\lambda}_{0,\delta_n}$ denote the AR(2)-based estimator of the spectral peak location for the stationary time series $\{X_{t,\delta_n},t\in\mathbb{Z}\}$. The estimato…

In an E-FSMC of order $n$, let $\{{b}_{\mathpzc{e}}(t)\}_{t\in\mathbb{Z}}$ be the branch process and let $\{\textbfit{x}^n(t)\}_{t\in\mathbb{Z}}$ be the block-output process, with…

Let $ll$ be an odd positive integer with $ll a 0 , (mathrm{mod}; 5)$, and write $ll=5m$. A Legendre pair is a pair $(A,B)$ of sequences of length $ll$, and $mathrm{PSD}A(m)$ an…

Let a time-series spectrum exhibit either a break or a smooth change of the form discussed above simultaneously at multiple frequencies. Multiple-frequency pooling conjecture. The…

Let $f$ be a real-valued non-monotone symbol on $[-\pi,\pi]$, and consider the points in $[-\pi,\pi]$ where the derivative of the symbol is zero. Local matrix-less methods conjectu…

Let $\deg>0$, $j>0$, and $z>0$. Let $\hat{f}_{z,j}$ be the symbol appearing in the paper, and let $\lambda”_{\rm min}(\hat{f}_{z,j})|_{0}$ denote the second derivative at $0$ of it…

Practical-relaxation conjecture. The requirement on $C$ in condition (2) of the theorem and the need for an $I$-eigen gap are more restrictive than what occurs in practical applica…

Physical conjecture. The field has an exponential decay due to the presence of the imaginary part of $k$ corresponding to absorption in the medium.

Let $K_{n,p}^{{\mathbb{Q}}_\mu}$ be the stiffness matrix considered above, and let $\lambda_j(K_{n,p}^{{\mathbb{Q}}_\mu})$ denote its $j$-th smallest eigenvalue. Asymptotic eigenva…

The paper considers the unresolved phase-transition question for sample covariance eigenvalues as signal strengths vary from weak to strong, including how their asymptotic distribu…

Let $\xi_{2k-1,j}$ denote the zeros appearing in the polynomial representation of $\widetilde c_{2k-1}(\omega)$, with indices $k$ and $j$ as in the preceding construction. Conjectu…

The coefficient matrix ${\boldsymbol{\mathsf{A}}}_{{2{\boldsymbol{N}}-\boldsymbol{1}}}$ for Ga discretization can have eigenvalues outside the interval determined by the phase coef…

Let $q$ be the function defined by equation, and let $(\eta^{(j)}_P,\varphi^{(j)}_P)$ be the $j$th eigenpair of equation. The statement of Theorem for the case without torsion is c…

Quantum characteristic-function conjecture. In the high-energy, semiclassical scaling, for the relevant parameters $t$ and $q$,

Faster-decay conjecture. This improved linear decay property should hold for the Boltzmann equation without angular cutoff: for data satisfying $\mathbf{P}f_0=0$, the linear decay…

Changing-index conjecture. The value $\varepsilon=0$ is a point of changing index for the family $\{F_l\}$, and the result corresponding to Krasnosel'skii's Theorem 56.2 applies to…