Related papers: Upper bound for the counting function of interior …

We study nodal sets of Steklov eigenfunctions in a bounded domain with $\mathcal{C}^2$ boundary. Our first result is a lower bound for the Hausdorff measure of the nodal set: we show that for $u_{\lambda}$ a Steklov eigenfunction, with…

There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision…

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…

In physical-layer security, one of the most fundamental issues is the secrecy capacity. The objective of this paper is to determine the secrecy capacity for an indoor visible light communication system consisting of a transmitter, a…

The logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound

Let us consider the following minimum problem \[ \lambda_\alpha(p,r)= \min_{\substack{u\in W_{0}^{1,p}(-1,1)\\ u\not\equiv0}}\dfrac{\displaystyle\int_{-1}^{1}|u'|^{p}dx+\alpha\left|\int_{-1}^{1}|u|^{r-1}u\, dx\right|^{\frac…

Let $\Omega\subset\mathbb{R}^{n}$ be a smooth bounded domain and $m\in C(\overline{\Omega})$ be a sign-changing weight function. For $1<p<\infty$, consider the eigenvalue problem $$ \left\{ \begin{array} [c]{ll} -\Delta_{p}u=\lambda…

This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.

Let $\Omega$ be an $n$-dimensional compact Riemannian manifold $(n \geq 3)$ with $C^\infty$ boundary, and consider $L^2$-normalized eigenfunctions $ - \Delta \phi_{\lambda} = \lambda^2 \phi_\lambda$ with Dirichlet or Neumann boundary…

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are…

The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires…

Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-\frac{1}{2}$, $0<\gamma<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We…

Although prone to fabrication error, the nanowire crossbar is a promising candidate component for next generation nanometer-scale circuits. In the nanowire crossbar architecture, nanowires are addressed by controlling voltages on the…

In this article, we show that $$ \left| N (T) - \frac{T}{ 2 \pi} \log \left( \frac{T}{2\pi e}\right) \right| \le 0.1038 \log T + 0.2573 \log\log T + 9.3675 $$ where $N(T)$ denotes the number of non-trivial zeros $\rho$, with $0<\Im(\rho)…

The paper presents an improved upper bound (achievability result) on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load for distributed computing MapReduce systems in certain ranges of the parameters. The upper…

Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant…

Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature $T_c$ are obtained for the $\gamma$ model…

We investigate the interior nodal sets $\mathcal{N}_\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\lambda$. The singular sets…

We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in \mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some…