Improved interframe registration based nonuniformity correction for focal plane arrays

In this paper, an improved interframe registration based nonuniformity correction algorithm for focal plane arrays is proposed. The method simultaneously estimates detector parameters and carries out the nonuniformity correction by minimizing the mean square error between the two properly registered image frames. A new masked phase correlation algorithm is introduced to obtain reliable shift estimates in the presence of fixed pattern noise. The use of an outliers exclusion scheme, together with a variable step size strategy, could not only promote the correction precision considerably, but also eliminate ghosting artifacts effectively. The performance of the proposed algorithm is evaluated with clean infrared image sequences with simulated nonuniformity and real pattern noise. We also apply the method to a real-time imaging system to show how effective it is in reducing noise and the ghosting artifacts.     

Facile Synthesis of Alkylidene Phthalides by Rhodium-Catalyzed Domino C−H Acylation/Annulation of Benzamides with Aliphatic Carboxylic Acids

The Rh-catalyzed ortho-C(sp²)−H functionalization of 8-aminoquinoline-derived benzamides with aliphatic acyl fluorides generated in situ from the corresponding acids has been developed. This reaction initiated with 8-aminoquinoline-directed ortho-C(sp²)−H acylation, which was accompanied by subsequent intramolecular nucleophilic acyl substitution of amide group to produce alkylidene phthalides This approach exhibits high stereo-selectivity for Z-isomer products, and tolerates a variety of functional groups as well as aliphatic carboxylic acids with diverse structural scaffolds.     

Polynomial solutions of a nonlinear difference equation

A class of nonlinear difference equations is considered. We show how their polynomial solutions can be computed in a systematic manner.     

Evaluation of approximations for concentration-dependent micropore diffusion in sorbent with bidisperse pore structure

Average diffusivity linear driving force (AD-LDF) and concentration-dependent diffusivity linear driving force (CDD-LDF) approximations are introduced to simplify the precise model describing the concentration-dependent micropore diffusion in bidisperse sorbents, and are compared with the precise model in predicting the dynamics of a sorption process under two different perturbations (i.e., step change perturbations and sinusoidal wave perturbation) with different concentrations imposed at the exterior surface of the bidisperse sorbent. The performance of the two approximations is validated by the precise model and experiments. The AD-LDF performs better in step adsorption and CDD-LDF does better in step desorption. Under sinusoidal wave perturbation, the CDD-LDF performs better. The different levels of consistency of the two approximations with the precise model are attributed to the different definitions of the diffusivities.     

The invariant of the stiffness filter function with the weight filter function of the power function form

Based on the independent, continuous and mapping (ICM) method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter function and the corresponding stiffness filter function of the form of power function. The efficiency in searching for optimum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization.     

Undersampled Windowed Exponentials and Their Applications

We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form

$$ {\mathcal{F}}(g): =\bigl\{ e^{2\pi i n x}: n\ge 0\bigr\} \cup \bigl\{ g(x)e^{2\pi i nx}: n< 0\bigr\} $$

for \(L^{2}[-1/2,1/2]\) by the spectra of the Toeplitz operators with the symbol \(g\). Using this characterization, we classify all real-valued functions \(g\) such that \({\mathcal{F}}(g)\) is complete or forms a frame/basis. Conversely, we use the classical non-harmonic Fourier series theory to determine all \(\xi \) such that the Toeplitz operators with the symbol \(e^{2\pi i \xi x}\) is injective or invertible. These results demonstrate an elegant interaction between frame theory of windowed exponentials and Toeplitz operators. Finally, we use our results to answer some open questions in dynamical sampling, and derivative samplings on Paley-Wiener spaces of bandlimited functions.