Fuzzy dark matter (FDM) is a well-motivated candidate for (DM) as its tiny mass and large de-Broglie wavelength suppress small-scale fluctuations, thereby solving some of the discrepancies in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Although it has been ruled out single component DM by several observables, there still region FDM parameter space (the ``FDM window,'' ${10}^{\ensuremath{-}25}\...

0.1 Proofs of Theorems 4.1, 4.2 & 5.2 Proof of Theorem 4.1: Let bn = pn+ln, where pn = b √ nc. Define a block of observations as Bn(i) = i + bn(0, 1], i ∈ Z. We first divide Rn into non-overlapped blocks of observations. Let Kn = {k ∈ Z : Bn(bnk) ⊂ Rn} represents the index set of all complete blocks Bn(bnk) = bn(k + (0, 1]) lying inside Rn. For each k ∈ Kn, we further divide each block into lar...

a new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. we use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. then, we linearized this identified model at each sampling time to have an approximate linear time varying system. in order to stabilize...