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• The intermodal interference of microfiber was enhanced by forming the micro-arched transition region. • The RI sensitivity of the sensor was up to 12,620.0 nm/RIU in the RI range of 1.3940–1.3980, respectively. • The sensor showed a sensitivity of 0.3 nm/(mg/ml) to the concentration of bovine serum albumin solution. A novel refractive index (RI) sensor based on micro-fiber with micro-arched transition (MMAT) was proposed. The power extinction ratio of interference spectra was enhanced by the micro-arched transition. Although the waist diameter of micro-fiber was less than 6 μm, the power extinction ratio was larger than 10 dB, which was critical to the spectral dip measurement. The relationship between waist diameter of micro-fiber and RI sensitivity was systematically investigated. It turned out that higher RI sensitivity of MMAT could be obtained by decreasing the waist diameter of micro-fiber. While the waist diameter was 5.6 μm, the RI sensitivities of MMATs were up to 2739.8 nm/RIU, 4515.7 nm/RIU and 12,620.0 nm/RIU in the RI range of 1.333–1.3580, 1.3705–1.3905 and 1.3940–1.3980 respectively. The sensor was applied to detecting the concentrations of bovine serum albumin (BSA) solutions and showed the sensitivity of 0.3 nm/(mg/ml). Owing to its small volume and high sensitivity, this kind of senor can be expected to widely apply in fields of biology, chemistry and physics. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with subquadratic homogeneity elliptic problems with VMO-coefficients in divergence form. We obtain that the weak solution u is locally Hölder continuous besides a singular set by using A -harmonic approximation, where the Hölder exponent α ∈ ( 0 , 1 ) . The Hausdorff dimension of the singular set is less than n − p . [ABSTRACT FROM AUTHOR]