"Let $P : \CI(M; E) \to F)$ be an order $\mu$ differential operator with coefficients $a$ and $P_k := P H^{s_0 + k +\mu}(M; k}(M; F)$. We prove polynomial norm estimates for the solution $P_0^{-1}f$ of form $$\|P_0^{-1}f\|_{H^{s_0 \mu}(M; E)} \le C \sum_{q=0}^{k} \, \| P_0^{-1} \|^{q+1} \,\|a \|_{W^{|s_0|+k}}^{q} f \|_{H^{s_0 - q}},$$ (thus in higher Sobolev spaces, which amounts also to a para...

Abstract In a colouring of $${\mathbb {R}}^d$$ R d pair $$(S,s_0)$$ ( S , s 0 ) with $$S\subseteq {\mathbb ⊆</mml:...

Let $$V_{n,d}$$ be the variety of equations for hypersurfaces degree d in $${\mathbb {P}}^n({\mathbb {C}})$$ with singularities not worse than simple nodes. We prove that orbit map $$G'=SL_{n+1}({\mathbb {C}}) \rightarrow V_{n,d}$$ , $$g\mapsto g\cdot s_0$$ $$s_0\in is surjective on rational cohomology if $$n>1$$ $$d\ge 3$$ and $$(n,d)\ne (2,3)$$ . As a result, Leray–Serre spectral sequence fro...

We study monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. first derive the inequality unified-(q, s) for multi-qubit states under arbitrary bipartition, then obtain $$\alpha $$ th ( $$0\le \alpha \le \frac{r}{2}, r\ge \sqrt{2}$$ ) power formation tripartite their generalizations states. also generalize bipartition. Moreover, we investigate $$\beta \ge ...

Abstract In this work, by assuming a spatially flat Universe, we have tested 8 kinematic parametrization models with H ( z ) data from Cosmic Chronometers and SNe Ia Pantheon compilation. Our aim is obtain the current values for Hubble constant $$H_0$$ H 0 ), decelerati...

We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying double $D(G)$ symmetry, where $G$ is finite group. provide projection operators its quasiparticles content as irreducible representations of and combine this $D(G)$-bimodule properties open ribbon excitation spaces $L(s_0,s_1)$ to show how ribbons can be used teleport information between their e...

In this paper, we consider the defocusing mass-supercritical, energy-subcritical nonlinear Schrodinger equation, $$\begin{aligned} i\partial _{t}u+\Delta u= |u|^p u, \quad (t,x)\in {\mathbb {R}}^{d+1}, \end{aligned}$$ with $$p\in (\frac{4}{d},\frac{4}{d-2})$$ . We prove that under some restrictions on d, p, any radial function in rough space $$H^{s_0}({\mathbb {R}}^d),\textit{for } s_0<s_c$$ ...