We establish an optimal $$L^p$$ -regularity theory for solutions to fourth order elliptic systems with antisymmetric potentials in all supercritical dimensions $$n\ge 5$$ : $$\begin{aligned} \Delta ^2 u=\Delta (D\cdot \nabla u)+\text {div}(E\cdot u) +(\Delta \Omega +G)\cdot u +f \qquad \ \mathrm{{in}}\ B^n, \end{aligned}$$ where $$\Omega \in W^{1,2}(B^n, so_m)$$ is and $$f\in L^p(B^n)$$ , $$D, ...

We report the first demonstration of integrated electro-optic (EO) phase shifters based on racetrack microresonators a 3C-silicon-carbide-on-insulator (SiCOI) platform working at near-infrared (NIR) wavelengths. By applying DC voltage in crystalline axis perpendicular to waveguide plane, we have observed optical shifts from whose loaded quality (Q) factors are ~ 30,000. show length-product (V${...

We consider the watchman route problem for a k-transmitter watchman: standing at point p in polygon P, can see $$q\in P$$ if $$\overline{pq}$$ intersects P’s boundary most k times—q is k-visible to p. Traveling along route, either all points P or discrete set of $$S\subset must be watchman. aim minimizing length route. show that even simple polygons shortest NP-complete and cannot approximated ...

The aim of this work is to introduce and study the nondegenerate inner product $<\cdot , \cdot >_{det}$ induced by determinant map on space $Sym(2)$ symmetric $2\times 2$ real matrices. This bilinear form index $2$ defines a rational function pairs rays in plane an associated $2$-torus can be expressed with usual Hopf bundle projection $S^3\rightarrow S^2(\frac{1}{2})$. Also, trea...

Let $(u, v)$ be a nonnegative solution to the semilinear parabolic system $$ \mbox{(P)} \qquad \left\{ \begin{array}{ll} \partial_{t} u = D_{1} \Delta + v^{p}, \quad x \in \mathbf{R}^{N}, \ t > 0,\\ v D_{2} u^{q}, (u(\cdot,0), v(\cdot,0)) (\mu, \nu), \end{array} \right. where $D_{1}$, $D_{2} 0$, $0 < p \leq q$ with $pq 1$ and $(\mu, \nu)$ is pair of Radon measures or measurable functions in $\m...

Obtaining a precise theoretical description of the spectral properties liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost Koopmans-compliant functionals with respect to Green's function methods allows simulations many MD trajectories, close state-of-art quasi-particle self-consistent GW plus vertex corrections method (QS...

Let $\mathcal{C}_n =\left [\chi_{\lambda}(\mu)\right]_{\lambda, \mu}$ be the character table for $S_n,$ where indices $\lambda$ and $\mu$ run over $p(n)$ many integer partitions of $n.$ In this note we study $Z_{\ell}(n),$ number zero entries $\chi_{\lambda}(\mu)$ in $\mathcal{C}_n,$ is an $\ell$-core partition For every prime $\ell\geq 5,$ prove asymptotic formula form $$ Z_{\ell}(n)\sim \alph...

Abstract We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $$H\in (0,1)$$ H ∈ ( 0 , 1 )...

&lt;p style='text-indent:20px;'&gt;In this paper, we study the following three species predator-prey model with prey-taxis:&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label&gt;*&lt;/label&gt; &lt;tex-math id="E1"&gt; \begin{document}$ \left\{ \begin{array}{lll} u_t = d_1\Delta u+\chi_1\nabla\cdot(u\nabla v)+r_1u(1-u-kv-b_1w), &amp;amp;\quad x\in \Omega, t&amp;gt;0, \\ ...