Transform-based algorithms have wide applications in applied probability, but rarely provide computable error bounds to guarantee the accuracy. We propose an inversion algorithm for two-sided Laplace transforms with computable error bounds. The algorithm involves a discretization parameter C and a truncation parameter N. By choosing C and N using the error bounds, the algorithm can achieve any desired accuracy. In many cases, the bounds decay exponentially, leading to fast computation. Therefore, the algorithm is especially suitable to provide benchmarks. Examples from financial engineering, including valuation of cumulative distribution functions of asset returns and pricing of European and exotic options, show that our algorithm is fast and easy to implement.

This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

We report here the growth of ultra thin ZnSe nanowires at low temperatures by Au-catalyzed molecule beam epitaxy and structural characterization of the nanowires. ZnSe nanowires may contain a high density of stacking faults and twins from low temperature growth and show a phase change from cubic to hexagonal structures. Ultra thin ZnSe nanowires can grow at a temperature below the eutectic point, and the relationship between the growth rates and nanowire diameters is V = 1/dn + C0 (C0 is a constant and n is a fitting parameter). The growth rate of the ultra thin nanowires at low temperatures can be elucidated based on the model involving interface incorporation and diffusion, in which the catalyst is solidified, and the nanowire growth is controlled through the diffusion of atoms into the interface between catalyst and the nanowire. The growth rate of ZnSe ultra-thin nanowires has been simulated.

A broadband GaN-based semiconductor saturable absorber mirror (SESAM) with a dielectric SiO2/Si3N4 distributed Bragg reflector (DBR) operating at wavelength around 415 nm was fabricated. Serious oscillation fringes due to the light interference were observed in the SESAM's reflectance spectrum. Such oscillation in reflectivity can impede the function of the saturable absorber. Simulations showed that by removing the sapphire substrate and thinning the GaN buffer layer, oscillation fringes could be significantly reduced. Experiments were carried out and the results agreed well with the simulation prediction.

Ferromagnetic nanoclusters are very useful for a magnetic recording. However, the application of ferromagnetic nanoclusters is limited due to air-oxidation. One way to solve air- oxidation is to encapsulate ferromagnetic nanoclusters with inert materials such as carbon when they are produced. This allows us to keep excellent magnetic properties for a long time. In this work, we report a very simple synthetic method of carbon nanotubes (CNTs) encapsulated ferromagnetic cobalt nanoclusters by catalytic decomposing benzene over Co/silica-gel nano- scale catalysts. Unlike previous reports, the catalysts do not need to be pre-reduced prior to the forming of CNTs encapsulated cobalt nanoclusters, thus, the advantage of this method is that CNTs encapsulated ferromagnetic nanoclusters can be produced in one step, at a relatively low cost. High-resolution Transmission electron microscopy (HRTEM), selected area electron diffraction (SAED) patterns and energy dispersive X-ray spectroscopy (EDS) were used to characterize the microstructures and compositions of the products. Experimental results revealed that the encapsulated Co was always presented as high temperature alpha-Co phase with fee structure, which frequently consists of twinned boundaries and stacking faults. Based on the experimental results, a possible growth mechanism of the CNTs encapsulated Co nanoclusters was proposed. Magnetic property measurements showed that the CNTs encapsulated cobalt nanoclusters possessed excellent magnetic properties.

High-quality cobalt-filled carbon nanotubes (CNTs) were prepared in situ in the decomposition of benzene over Co/silica-gel nano-scale catalysts. Unlike the previous reports, the catalysts needn't be pre-reduced prior to the forming of Co-filled CNTs, thus the advantage of this method is that Co-filled CNTs can be produced in one step, at a relatively low cost. Transmission electron microscopy (TEM) investigation showed that the products contained abundance of CNTs and most of them were filled with metallic nanoparticles or nanorods. High-resolution TEM (HRTEM), selected area electron diffraction (SAED) patterns and energy dispersive X-ray spectroscopy (EDS) confirmed the presence of Co inside the nanotubes. The encapsulated Co was further identified always as high temperature alpha-Co phase with fcc structure, which frequently consists of twinned boundaries and stacking faults. Based on the experimental results, a possible growth mechanism of the Co-filled CNTs was proposed.

In this presentation, we described a study on preparation and microstructure of Au (Ru) nano-particles embedded in SiO2 matrices, which were prepared as advanced display materials by using Sol-gel method. Both microstructure and composition of these micro/nano-particles composites were characterized by HRTEM (high resolution transmission electron microscope), EMP (electron microprobe) and nano-probe EDS (energy dispersive X-ray spectroscopy). Experimental results showed that the products have multi-levels in structure like nebulae. The aggregation of Au/Ru nano-particles can be extremely diminished by using SiO2 micro-particles as matrices. Distortions of the atomic lattices of Au and Ru nano-crystallites were often observed in the surface of these nano-particles. Moreover, nano-EDS measurements revealed that Au and Ru nano-particles are always separately embedded in SiO2 matrices, no alloy of them is observed.

Kleitman's conjecture concerning the ‘Kleitman–West problem’ is false for 3-element subsets.

In [1] we introduced and studied for product hypergraphs where ℋi = (i,ℰi), the minimal size π(ℋn) of a partition of into sets that are elements of . The main result was that

if the ℋis are graphs with all loops included. A key step in the proof concerns the special case of complete graphs. Here we show that (1) also holds when the ℋi are complete d-uniform hypergraphs with all loops included, subject to a condition on the sizes of the i. We also present an upper bound on packing numbers.

The partition number of a product hypergraph is introduced as the minimal size of a partition of its vertex set into sets that are edges. This number is shown to be multiplicative if all factors are graphs with all loops included.