Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum $P(k)$. These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest {\it Planck} release suggests that $P(k)$ has a hard cutoff, $k_{\rm min}\not=0$, inconsistent with this conventional picture. Here we demonstrate quantitatively that most---perhaps all---slow-roll inflationary models fail to accommodate this minimum cutoff. We show that the small parameter $\epsilon$ must be $\gtrsim 0.9$ throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an $\epsilon$ predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications to---not only fit the measured fluctuation spectrum, but to simultaneously also---fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.

Poor interlaminar fracture toughness has been a major issue in glass fiber-reinforced epoxy resin (GF/EP) laminate composites. In this paper, soft carboxy-terminated liquid nitrile (CTBN) rubber particles and rigid nano-SiO2 are used to toughen the epoxy resin (EP) matrix to improve the interlayer properties of GF/EP laminate composites. The effects of adding two toughening agents on the mechanical and interlayer properties of GF/EP laminates were studied. The results showed that adding the two kinds of particles improved the mechanical properties of the epoxy matrix. When the additional amount of flexible CTBN rubber particles was 8wt%, and the rigid nano SiO2 was 0.5wt%, the fracture toughness of the matrix resin was increased by 215.8%, and the tensile strength was only decreased by 2.3% compared with the pure epoxy resin. On this basis, the effects of two kinds of particles on the interlayer properties of GF/EP composites were studied. Compared with the unmodified GF/EP laminates, the interlayer shear strength and mode Ⅰ interlayer fracture toughness is significantly improved by toughening agent, and the energy release rate GIC of interlayer shear strength and interlayer fracture toughness is increased by 109.2%, and 86.8%, respectively.