<p style='text-indent:20px;'>We examine the following degenerate elliptic system:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\Delta_{s} u \! = v^p, \quad v\! u^\theta, \;\; u, v>0 \;\;\mbox{in }\; \mathbb{R}^N \mathbb{R}^{N_1}\times \mathbb{R}^{N_2}, \quad\mbox{where}\;\; s \geq 0\;\; \mbox{and} \;\;p...

Abstract We study a spin 1/2 fermion in thick braneworld the context of teleparallel f ( T , B ) gravity. Here, is such that $$f_1(T,B)=T+k_1B^{n_1}$$ f 1 ( T , B ) =...

Sums of the form $\sum_{q \leq N_1 < \cdots N_m n}{a_{(m);N_m}\cdots a_{(2);N_2}a_{(1);N_1}}$ date back to sixteen century when Vi\`ete illustrated that relation linking roots and coefficients a polynomial had this form. In more recent years, such sums have become increasingly used with diversity applications. paper, we develop formulae help manipulating (which will refer as multiple sums). We ...

We study a family of non-convex functionals $\{\mathcal{E}\}$ on the space measurable functions$u: \Omega_1\times\Omega_2 \subset \mathbb{R}^{n_1}\times\mathbb{R}^{n_2} \to \mathbb{R}$. These vanish subset $S(\Omega_1\times\Omega_2)$ formed by functions form $u(x_1,x_2)=u_1(x_1)$ or $u(x_1,x_2)=u_2(x_2)$. investigate under which conditions converse implication $\mathcal{E}(u) = 0 \Rightarrow u ...

We report a strong nonlinear optical response of 2D MoSe$_2$ nanoflakes (NFs) through spatial self-phase modulation (SSPM) and cross-phase (XPM) induced by nonlocal coherent light-matter interactions. The interaction light NFs creates the SSPM laser beams, forming concentric diffraction rings. refractive index ($n_2$) third-order broadband susceptibility ($\chi^{(3)}$) are determined from self ...