To investigate effects of agomelatine and mirtazapine on sleep disturbances in patients with major depressive disorder. A total of 30 depressed patients with sleep disturbances, 27 of which completed the study, took agomelatine or mirtazapine for 8 weeks. Subjective scales were administered, and polysomnography was performed at baseline and at the end of week 1 and 8. Functional magnetic resonance imaging was performed at baseline and at the end of week 8. Compared with baseline, scores on the Hamilton Depression Scale, Hamilton Anxiety Scale, Pittsburgh Sleep Quality Index, Sleep Dysfunction Rating Scale, and Insomnia Severity Index after 8 weeks of treatment significantly decreased in both groups, with no significant differences between groups, accompanied by significant increases in total sleep time, sleep efficiency, and rapid eye movement (REM) sleep and significant decrease in wake after sleep onset. Mirtazapine treatment increased N3 sleep at week 1 compared with agomelatine treatment, but this difference disappeared at week 8. The increases in the percentage and duration of N3 sleep were positively correlated with increases in connectivity between right dorsal lateral prefrontal cortex (dlPFC) and right precuneus and between left posterior cingulate cortex and right precuneus in both groups, respectively. Functional connectivity (FC) between right dlPFC and left precuneus in mirtazapine group was higher compared with agomelatine group after 8 weeks of treatment. These findings indicated that both agomelatine and mirtazapine improved sleep in depressed patients, and the effect of mirtazapine was greater than agomelatine with regard to rapidly increasing N3 sleep and gradually improving FC in the brain.

We prove the global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism on the stress tensor in R d for the small initial data. Our proof is based on the observation that the behaviors of Green's matrix to the system of u, (−∆) − 1 2 P∇ · τ as well as the effects of τ change from the low frequencies to the high frequencies and the construction of the appropriate energies in different frequencies.

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By means of the Littlewood‐Paley decomposition and the div‐curl Theorem by Coifman‐Lions‐Meyer‐Semmes, we prove an Osgood type regularity criterion for the 2D incompressible Oldroyd‐B model, that is, sup2≤N<+∞∫0Tfalse∑|j|≤N‖normalΔ˙jτfalse‖L∞NlogNds, where trueΔ˙j denotes the Fourier localization operator whose spectrum is supported in the shell {|ξ|≈2j}.