82 research outputs found
Asymptotic Methods applied to an American Option under a CEV Process
We consider an American put option under the Constant Elasticity of Variance (CEV) process. This corresponds to a free boundary problem for a partial differential equation (PDE). We show that this free boundary satisfies a nonlinear integral equation, and analyze it in the limit of small = , where is the interest rate and is the volatility. We find that the free boundary behaves differently for five ranges of time to expiry. We then analyze option price , as a function of the asset price and time to expiry . We obtain the asymptotic expansion of as , first via an integral equation formulation, and then using the PDE satisfied by , and analyzing it by perturbation theory and matched asymptotic expansions
Facile Fabrication of Highly Efficient g‑C<sub>3</sub>N<sub>4</sub>/Ag<sub>2</sub>O Heterostructured Photocatalysts with Enhanced Visible-Light Photocatalytic Activity
Highly
efficient visible-light-driven g-C<sub>3</sub>N<sub>4</sub>/Ag<sub>2</sub>O heterostructured photocatalysts were prepared by a simple
liquid phase synthesis method at room temperature. The composition,
structure, morphology, and optical absorption properties of the as-prepared
g-C<sub>3</sub>N<sub>4</sub>/Ag<sub>2</sub>O composites were characterized
by XRD, FTIR, XPS, TEM, and UV–vis DRS, respectively. We found
interestingly that the photogenerated charge carriers separations
of the as-prepared g-C<sub>3</sub>N<sub>4</sub>/Ag<sub>2</sub>O composites
were closely related to the mass ratio of g-C<sub>3</sub>N<sub>4</sub> and Ag<sub>2</sub>O. When the mass ratio of g-C<sub>3</sub>N<sub>4</sub> and Ag<sub>2</sub>O reached 1:4, the as-prepared composite
exhibited the highest photocatalytic activity, which was almost 11
and 1.2 times as high as that of individual g-C<sub>3</sub>N<sub>4</sub> and Ag<sub>2</sub>O, respectively. The enhancement of photocatalytic
activity could be attributed to the synergetic effects between g-C<sub>3</sub>N<sub>4</sub> and Ag<sub>2</sub>O as well as the improved
dispersibility and the decreased particle size of Ag<sub>2</sub>O.
Moreover, the as-prepared composites showed excellent stability toward
the photodegradation of methyl orange (MO). Finally, a possible photocatalytic
and charge separation mechanism was proposed
Media 3: Electrically actuated liquid iris
Originally published in Optics Letters on 01 March 2015 (ol-40-5-831
Media 1: Electrically actuated liquid iris
Originally published in Optics Letters on 01 March 2015 (ol-40-5-831
Media 2: Electrically actuated liquid iris
Originally published in Optics Letters on 01 March 2015 (ol-40-5-831
Media 2: A polarization converter array using a twisted-azimuthal liquid crystal in cylindrical polymer cavities
Originally published in Optics Express on 01 July 2013 (oe-21-13-16222
Additional file 1 of The serum lipid profiles in immune thrombocytopenia: Mendelian randomization analysis and a retrospective study
Supplementary Material
Media 1: A polarization converter array using a twisted-azimuthal liquid crystal in cylindrical polymer cavities
Originally published in Optics Express on 01 July 2013 (oe-21-13-16222
Media 1: An adaptive liquid lens with a reciprocating movement in a cylindrical hole
Originally published in Optics Express on 15 December 2014 (oe-22-25-31041
Dielectric Liquid Microlens Array with Tunable Focal Length Based on Microdroplet Array Created via Dip-Coating Method
A dielectric liquid microlens array (LMA) with a tunable
focal
length was fabricated by using a microdroplet array generated through
the dip-coating method. The process began with treating the octadecyltrichlorosilane
(OTS) layer with selective UV/O3 irradiation for 20 min
to establish a hydrophilic–hydrophobic patterning surface.
The substrate was subsequently immersed in glycerol and then withdrawn
at a constant rate to create a microdroplet array. Upon filling the
cell with matching oil (SL5267) and placing it within a square array
of a 200 μm diameter glycerol microdroplet array, the LMA was
produced. The focal length ranged from approximately −0.96
to −0.3 mm within a voltage range of 0 to 60 Vrms. The glycerol microdroplets, characterized by their shapes, sizes,
curvatures, and filling factors, can be precisely controlled by designing
an OTS patterning or adjusting the dip-coating speed. This approach
offers a rapid and high-throughput method for preparation. Our approach
to fabricating tunable LMA offers several advantages, including simplicity
of fabrication, uniform structural properties, cost-effectiveness,
polarization independence, and excellent optical performance. These
focus-tunable LMAs hold significant potential for applications in
image processing, 3D displays, medical endoscopy, and military technologies
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