Abstract. The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f (·, ε k ), and the derivative of f (·, ε k ) at x k is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global convergence and convenience in handling. In this paper, we show that the smoothing Newton method is also superlinearly convergent if F is semismooth at the solution and f satisfies a Jacobian consistency property. We show that most common smooth functions, such as the Gabriel-Moré function, have this property. As an application, we show that for box constrained variational inequalities if the involved function is P -uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).
a b s t r a c tThis paper overviews recent development in gas detection with micro-and nano-engineered optical fibers, including hollow-core fibers, suspended-core fibers, tapered optical micro/nano fibers, and fiber-tip micro-cavities. Both direct absorption and photoacoustic spectroscopy based detection schemes are discussed. Emphasis is placed on post-processing stock optical fibers to achieve better system performance. Our recent demonstration of distributed methane detection with a $75-m long of hollow-core photonic bandgap fiber is also reported.
Multiplex detection of tumor markers
in blood with high specificity
and high sensitivity is critical to cancer diagnosis, treatment, and
prognosis. Herein, we demonstrate a strategy for simultaneous detection
of multiple tumor markers in blood by functional liquid crystal (LC)
sensors assisted with target-induced dissociation (TID) of an aptamer
for the first time. Magnetic beads (MBs) coated with an aptamer (apt1)
are employed to specifically capture target proteins in blood. After
incubation of the obtained protein-coated MBs with duplexes of another
aptamer (apt2) and signal DNA, sandwich complexes of apt1/protein/apt2
are formed on the MBs due to specific recognition of target proteins
by apt2, which induces release of signal DNA into the aqueous solution.
Subsequently, signal DNA is specifically recognized by highly sensitive
DNA-laden LC sensors. Using this strategy, a 3D printed optical cell
was employed to enable simultaneous detection of multiple tumor markers
such as carcinoembryonic antigen (CEA), alpha-fetoprotein (AFP), and
prostate specific antigen (PSA) with high specificity and high sensitivity.
Overall, this effective and low-cost multiplex approach takes advantage
of the easy separation of MBs, high specificity of aptamer-based recognition,
and high sensitivity of functional LC sensors. Plus, it offers a performance
that is competitive to that of commercial ELISA kits without potential
interference from hemolysis, which makes it very promising in multiplex
detection of tumor markers in clinical applications.
The prospects for realization of all-fiber gas sensors with hollow-core photonic bandgap fibers and tapered micro/nano optical fibers are investigated. Issues such as high background level and slow response time are discussed.
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