Existence and multiplicity of solutions for semilinear elliptic equations with Hardy terms and Hardy–Sobolev critical exponents

AbstractSome existence and multiplicity results are obtained for solutions of semilinear elliptic equations with Hardy terms, Hardy–Sobolev critical exponents and superlinear nonlinearity by the variational methods and some analysis techniques

Clinical study of 23G <i>vs</i> 20G vitreous surgery combined with phacoemulsification and IOL implantation for macular epiretinal membrane with cataract

AIM: To evaluate the effects of 23G vs 20G pars plana vitrectomy(PPV)combined with internal limiting membrane peeling, phacoemulsification and intraocular lens implantation for macular epiretinal membrane with cataract. METHODS: Totally 45 eyes of 45 patients with macular epiretinal membrane and cataract were enrolled in this retrospective non-randomized controlled clinical study. All eyes were treated with PPV combined with internal limiting membrane peeling, phacoemulsification and intraocular lens implantation. There were 20 eyes in 23G PPV group, and 25 eyes in 20G PPV group. The best corrected visual acuity(BCVA), intraocular pressure(IOP), counting of corneal endothelial cells(CEC)and central retinal thickness(CRT)were examined before surgery. BCVA results were converted to the logarithm of the minimum angle of resolution(LogMAR)visual acuity. All operations were performed by the same doctor. Operation time for vitrectomy and membrane peeling, average ultrasound energy(AVE)and effective phacoemulsification time(EPT)were recorded. BCVA and CRT were observed postoperatively at 30d and 90d, counting of CEC was observed postoperatively at 90d. IOP was observed postoperatively at 1d and 7d.RESULTS: The mean operation time for vitrectomy were 12.57±1.35min in 23G group and 17.30±1.19min in 20G group. The difference was statistically significant(t=-12.488, Pt=-0.68,-1.186,-0.737,P=0.500, 0.242,0.465). On 1d after surgery, IOP in 23G group was lower than that in 20G group, the difference was statistically significant(t=-2.345, P=0.024). The BCVA and CRT of the two groups both improved after operations. There were no statistically significant differences between two groups in terms of IOP, BCVA, and CRT(F=0.465, 1.895, 0.689; P=0.499, 0.176, 0.411). IOP, BCVA and CRT were significant statistical different in different time-point within each group(F=291.245, 103.06, 665.402, PF=13.245, PF=1.212, 2.293; P=0.283, 0.129). The counting CEC in 23G group was more than that in 20G group postoperatively at 90d, the difference was statistically significant(t=2.049, P=0.048). CONCLUSION: The 23G PPV combined with internal limiting membrane peeling, phacoemulsification, intraocular lens implantation for macular epiretinal membrane with cataract is effective. Compared with 20G PPV, 23G PPV has advantages in operation time for vitrectomy and counting CEC. But lower IOP is likely in 23G PPV on 1d after surger

Break the efficiency limitations of dissipative Kerr soliton using nonlinear couplers

Dissipative Kerr soliton (DKS) offers a compact solution of coherent comb sources and holds huge potential for applications, but has long been suffering from poor power conversion efficiency when driving by a continuous-wave laser. Here, a general approach to resolving this challenge is provided. By deriving the critical coupling condition of a multimode nonlinear optics system in a generalized theoretical framework, two efficiency limitations of the conventional pump method of DKS are revealed: the effective coupling rate is too small and is also power-dependent. Nonlinear couplers are proposed to sustain the DKS indirectly through nonlinear energy conversion processes, realizing a power-adaptive effective coupling rate to the DKS and matching the total dissipation rate of the system, which promises near-unity power conversion efficiencies. For instance, a conversion efficiency exceeding $90\:\%$ is predicted for aluminum nitride microrings with a nonlinear coupler utilizing second-harmonic generation. The nonlinear coupler approach for high-efficiency generation of DKS is experimentally feasible as its mechanism applies to various nonlinear processes, including Raman and Brillouin scattering, and thus paves the way of micro-solitons towards practical applications.Comment: 8 pages, 3 figure