Aliasing Error of Sampling Series in Wavelet Subspaces

Alising error arises whenever a sampling formula, valid for a prescribed space, is applied to a function in a bigger space. In this work, we estimate the aliasing error of classic and average sampling expansions in wavelet subspaces of a multiresolution analysis.     

Molecular dynamics study on the effects of stamp shape, adhesive energy, and temperature on the nanoimprint lithography process

Molecular dynamics simulations of nanoimprint lithography (NIL) were performed to investigate the effects of three critical process parameters in NIL: stamp shape, adhesive energy between the stamp and polymer film, and imprint temperature. The proposed simulation model of the NIL process consists of an amorphous SiO₂ stamp with a line pattern, an amorphous poly(methylmethacrylate) film, and a Si substrate under the periodic boundary condition in the horizontal direction to simulate a real NIL process imprinting periodical line patterns. The behavior of polymer deformation and the effects of adhesion on pattern transfer were investigated by observing the deformation process, calculating the imprint and separation forces, and analyzing the density and stress distribution inside the polymer film. In addition, their dependency on the process parameters is also discussed with reference to the changes in pattern shape, adhesive energy between the stamp and polymer atoms, and imprint temperature of the polymer film. During the imprint process, the rectangular pattern shows inferior cavity filling and higher stress concentration compared to trapezoidal and triangular patterns because it requires much larger flow and deformation of the polymer film. Low imprint temperature also produces high stress concentration and large imprint force due to the lower fluidity of polymer film. In the separation process, the rectangular pattern generates the largest separation force and causes the most serious defects of the transferred pattern and even the polymer film, while the triangular pattern shows the most satisfactory pattern transfer. In addition, the adhesive energy between the stamp and the polymer film also strongly influences the adhesion between the stamp and the polymer film. Low adhesive energy reduces the separation force of the stamp and transferred pattern defects, and therefore enhances the quality of pattern transfer.     

Synthesis of nano-size BaMgAl10O17:Eu blue phosphor by a rapid exothermic reaction

Ultrafine particles of BaMgAl₁₀O₁₇:Eu²⁺ (BAM) phosphor were synthesized by a solid-state combustion reaction in a powder bed of 0.9BaCO₃+MgO+5Al₂O₃+0.05Eu₂O₃+k(KClO₃+1.5C) composition. A large exothermic reaction of the mixture (KClO₃+1.5C) leads to a self-sustaining combustion mode. Under optimized combustion conditions, the product consisted of BAM powder and KCl was obtained. BAM ultrafine particles resulting from the combustion process were easily obtained by simply washing the salt by-product with water. Combustion-processed BAM phosphor shows a homogeneous grain size of 100-500 nm, good dispersity, regular morphology, and improved luminescence properties.     

Efficient compression of motion-compensated sub-images with Karhunen-Loeve transform in three-dimensional integral imaging

An approach to highly enhance the compression efficiency of the integral images by applying the Karhunen-Loeve transform (KLT) algorithm to the motion-compensated sub-images is proposed. The sub-images transformed from the elemental images picked-up from the three-dimensional (3D) object might represent the different perspectives of the object. Thus, the similarity among the sub-images gets better than that among the elemental images, so that an improvement of compression efficiency of the sub-images could be obtained. However, motion vectors occurred among the sub-images might result in an additional increase of image data to be compressed. Accordingly, in this paper, motion vectors have been estimated and compensated in all sub-image in advance. Then the KLT algorithm was applied to these motion-compensated sub-images for compression. It is shown from some experimental results that compression efficiency of the proposed method has been improved up to 24.44%, 40.62%, respectively, on the average compared to that of the conventional KLT compression method and that of the JPEG.     

Characterization of structural irregularities in highly birefringent photonic crystal fiber using torsional acoustic polarization coupling

We demonstrate a novel method to characterize structural irregularities in a highly birefringent photonic crystal fiber (HB PCF) with high accuracy based on polarization coupling by torsional acoustic wave. Birefringence variation induced by the irregularities of air-hole structure in the fiber cross-section is analyzed via the transmission spectra of the acousto-optic coupling between two orthogonal polarization modes propagating along the fiber. The estimated maximum birefringence variation of two sections in the same batch of the HB PCF is 3 × 10^− 6 and 10^− 5, respectively, from nominal birefringence value of 4.86 × 10^− 4. The comparison between the experimental results and the numerical simulation resulted in the estimation of few tens of nm variation in the air-hole structure in the PCF.     

Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.     

Exchangeable claim sizes in a compound Poisson‐type process

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson‐type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel‐type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.     

Hadwiger number and chromatic number for near regular degree sequences

We consider a problem related to Hadwiger's Conjecture. Let D=(d₁, d₂, …, d_n) be a graphic sequence with 0?d₁?d₂?···?d_n?n?1. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. Define h(D)=max{h(G): G∈R[D]} and χ(D)=max{χ(G): G∈R[D]}, where h(G) and χ(G) are Hadwiger number and chromatic number of a graph G, respectively. Hadwiger's Conjecture implies that h(D)?χ(D). In this paper, we establish the above inequality for near regular degree sequences. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 175–183, 2010     

Young measure solutions of some nonlinear mixed‐type equations

This contribution deals with measure‐valued solutions to two types of nonlinear partial differential equations for which, in general, the results on the existence of classical or weak solutions fail. These are the potential equation for transonic flow and the associated unsteady problem (forward–backward diffusion equation). The solutions are constructed by an iteration scheme (Katchanov method) and additional time discretization (Rothe method) in the second case. The existence is proved in the sense of spatial gradient Young measures. Copyright © 2010 John Wiley & Sons, Ltd.     

The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings

Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth‐order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r → 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz‐type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010