Solutions of a particle with fractional δ\delta-potential in a fractional dimensional space

A Fourier transformation in a fractional dimensional space of order \la (0<\la\leq 1) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order \a. This new method is applied for a particle in a fractional $\delta$-potential well defined by V(x) =- \gamma\delta^{\la}(x), where $\gamma>0$ and \delta^{\la}(x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0< \la<\a. The results for \la= 1 and \a=2 are in exact agreement with those presented in the standard quantum mechanics

Upregulation of FcyRIIb on monocytes is necessary to promote the superagonist activity of TGN1412

The anti-CD28 superagonist antibody TGN1412 caused life-threatening cytokine release syndrome (CRS) in healthy volunteers, which had not been predicted by preclinical testing. T cells in fresh peripheral blood mononuclear cells (PBMCs) do not respond to soluble TGN1412 but do respond following high-density (HD) preculture. We show for the first time that this response is dependent on crystallizable fragment gamma receptor IIb (Fc?RIIb) expression on monocytes. This was unexpected because, unlike B cells, circulating monocytes express little or no Fc?RIIb. However, Fc?RIIb expression is logarithmically increased on monocytes during HD preculture, and this upregulation is necessary and sufficient to explain TGN1412 potency after HD preculture. B-cell Fc?RIIb expression is unchanged by HD preculture, but B cells can support TGN1412-mediated T-cell proliferation when added at a frequency higher than that in PBMCs. Although low-density (LD) precultured PBMCs do not respond to TGN1412, T cells from LD preculture are fully responsive when cocultured with Fc?RIIb-expressing monocytes from HD preculture, which shows that they are fully able to respond to TGN1412-mediated activation. Our novel findings demonstrate that cross-linking by Fc?RIIb is critical for the superagonist activity of TGN1412 after HD preculture, and this may contribute to CRS in humans because of the close association of Fc?RIIb-bearing cells with T cells in lymphoid tissues