Given any finite direction set $\Omega$ of cardinality $N$ in Euclidean space, we consider the maximal directional Hilbert transform $H_{\Omega}$ associated to this set. Our main result provides an essentially sharp uniform bound, depending only on $N$, for $L^2$ operator norm dimensions 3 and higher. The ingredients proof consist polynomial partitioning tools from incidence geometry almost-ort...

We present an algorithm for constructing analytically approximate integrals of motion in simple time-periodic Hamiltonians the form $$H=H_{0}+\varepsilon H_{i}$$ , where $$\varepsilon$$ is a perturbation parameter. apply our Hamiltonian system whose dynamics governed by Mathieu equation and examine detail orbits their stroboscopic invariant curves different values . find $$\varepsilon_{crit}$$ ...

This is the first of a series two articles where we construct version wrapped Fukaya category $\mathcal W\mathcal F(M\setminus K;H_{g_0})$ cotangent bundle $T^*(M \setminus K)$ knot complement $M K$ compact 3-manifold $M$, and do some calculation for case hyperbolic knots $K \subset M$. For construction, use wrapping induced by kinetic energy Hamiltonian $H_{g_0}$ associated to cylindrical adju...

Topological crystalline metals/semimetals (TCMs) have stimulated a great research interest, which broaden the classification of topological phases and provide valuable platform to explore superconductivity. Here, we report discovery superconductivity features in Pb-intercalated transition-metal dichalcogenide Pb$_{1/3}$TaS$_2$. Systematic measurements indicate that Pb$_{1/3}$TaS$_2$ is quasi-tw...

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k