AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We establish the coefficient sign patterns in the Third Borwein conjecture and the modulus-three Cubic Borwein conjecture. The analytic arguments apply for $n\ge1750$ and $n\ge500$, respectively. They combine exact dissections and positive coefficient identities near the boundary with saddle point estimates that preser...
For a positive integer $m$ and a real parameter $\alpha>-1$, consider the generalized Ces\`aro matrix on $\ell^2(\mathbb N_0)$ with entries $m(n-j+1)_{m-1}/(n+\alpha+1)_m$ for $j\le n$. We give a computer-assisted proof that this operator is hyponormal if and only if $\alpha\ge0$. The main algebraic ingredient is an ex...
Let $\mathcal H_g f(z)=\int_0^1 f(t)g'(tz),dt$, and let $2<p<\infty$. Set $t=2p/(p-2)$ and $X_j=2^{-j/p'}\Delta_j g'$, where $\Delta_j$ is the hard dyadic Taylor projection. We prove that $\mathcal H_g:H^p\to H^p$ is bounded if and only if $h\mapsto(X_jh)_{j\geq0}$ is bounded from $H^t$ to $\ell^t(H^2)$. The square of...
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