Weak and point-wise convergence in for filter convergence

We study those filters on for which weak -convergence of bounded sequences in C(K) is equivalent to point-wise -convergence. We show that it is sufficient to require this property only for C[0,1] and that the filter-analogue of the Rainwater extremal test theorem arises from it. There are ultrafilters which do not have this property and under the continuum hypothesis there are ultrafilters which have it. This implies that the validity of the Lebesgue dominated convergence theorem for -convergence is more restrictive than the property which we study.     

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.     

At-line microextraction by packed sorbent-gas chromatography–mass spectrometry for the determination of UV filter and polycyclic musk compounds in water samples

An at-line analysis protocol is presented that allows the determination of four UV filters, two polycyclic musk compounds and caffeine in water at concentration level of ng L⁻¹. The fully automated method includes analytes enrichment by Microextraction by packed sorbent (MEPS) coupled directly to large volume injection-gas chromatography–mass spectrometry. Two common SPE phases, C8 and C18, were examined for their suitability to extract the target substances by MEPS. The analytes were extracted from small sample volumes of 800 μL with recoveries ranging from 46 to 114% for the C8-sorbent and 65–109% for the C18-sorbent. Limits of detection between 34 and 96 ng L⁻¹ enable the determination of the analytes at common environmental concentration levels. Both sorbents showed linear calibration curves for most of the analytes up to a concentration level of 20 ng mL⁻¹. Carryover was minimized by washing the sorbents 10 times with 100 μL methanol. After this thorough cleaning, the MEPS are re-used and up to 70 analyses can be performed with the same sorbent. The fully automated microextraction GC–MS protocol was evaluated for the influence of matrix substances typical for wastewater. Dilution of samples prior to MEPS is recommended when the polar caffeine is present at high concentration. Real water samples were analyzed by the MEPS-GC–MS method and compared to standard SPE.     

光电混合相关识别系统中匹配滤波器缩放比例的确定方法

在光电混合匹配滤波相关识别系统中,由于输入图像的频谱与匹配滤波器的形成方式不同,不能直接实现对应频率成份的准确对准。这个问题需要通过对匹配滤波器进行缩放来解决。根据透镜的傅里叶变换性质和计算全息理论,分别推导出输入图像的频谱的表达式和滤波空间光调制器加载了匹配滤波器后的透射函数的表达式,并根据这两个表达式得到匹配滤波器的缩放比例的公式,然后在实际的光学识别系统中对根据该公式计算的缩放比例进行了验证。实验结果表明,在该缩放比例下,相关峰的质量有较大改善,这说明此时输入图像的频谱与匹配滤波器对应频率成份实现了较好地对准。     

Suppressing the charged coupled device noise in univariate thin-layer videoscans: A comparison of several algorithms

The digital processing of chromatographic thin-layer plate images has increasing popularity among last years. When using a camera instead of flatbed scanner, the charged coupled device (CCD) noise is a well-known problem—especially when scanning dark plates with weakly fluorescing spots. Various techniques are proposed to denoise (smooth) univariate signals in chemometric processing, but the choice could be difficult. In the current paper the classical filters (Savitzky–Golay, adaptive degree polynomial filter, Fourier denoising, Butterworth and Chebyshev infinite impulse response filters) were compared with the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 8 decomposition levels). The signal obtained from 256 averaged videoscans was treated as the reference signal (with noise naturally suppressed, which was found to be almost white one). The best choice for denoising was the Haar mother wavelet with soft denoising and any decomposition level larger than 1. Satisfying similarity to reference signal was also observed in the case of Butterworth filter, Savitzky–Golay smoothing, ADPF filter, Fourier denoising and soft-thresholded wavelet shrinkage with any mother wavelet and middle to high decomposition level. The Chebyshev filters, Whittaker smoother and wavelet shrinkage with hard thresholding were found to be less efficient. The results obtained can be used as general recommendations for univariate denoising of such signals.     

三区振幅型三维超分辨光瞳滤波器的优化设计

光瞳滤波器是光学成像系统实现超分辨的基本元件之一，多数三维超分辨滤波器因结构复杂而难于实现。用MATLAB优化工具箱，采用非线性规划，对三区振幅型（1-0—1型）光瞳滤波器进行了三维超分辨优化设计。建立了优化模型，并给出了优化实例。结果表明所设计的滤波器较好地实现了横向和轴向三维超分辨，且轴向超分辨能力优于横向。该滤波器结构简单，容易实现。     

A conditionally almost linear filtering problem with non-gaussian initial condition ∗

We derive a formula for computing explicitly the optimal non-linear filter for a class of problems which admit finite dimensional filters. The result includes all known results of this kind as special cases     

A study of uniformity of elements deposition on glass fiber filters after collection of airborne particulate matter (PM-10), using a high-volume sampler

A study was conducted to evaluate the homogeneity of the distribution of metals and metalloids deposited on glass fiber filters collected using a high-volume sampler equipped with a PM-10 sampling head. The airborne particulate matter (APM)-loaded glass fiber filters (with an active surface of about 500 cm²) were weighed and then each filter was cut in five small discs of 6.5 cm of diameter. Each disk was mineralized by acid-assisted microwave (MW) digestion using a mixture of nitric, perchloric and hydrofluoric acids. Analysis was performed by axial view inductively coupled plasma optical emission spectrometry (ICP OES) and the elements considered were: Al, As, Cd, Cr, Cu, Fe, Mn, Ni, Pb, Sb, Ti and V. The validation of the procedure was performed by the analysis of the standard reference material NIST 1648, urban particulate matter. As a way of comparing the possible variability in trace elements distribution in a particular filter, the mean concentration for each element over the five positions (discs) was calculated and each element concentration was normalized to this mean value. Scatter plots of the normalized concentrations were examined for all elements and all sub-samples. We considered that an element was homogeneously distributed if its normalized concentrations in the 45 sub-samples were within ±15% of the mean value ranging between 0.85 and 1.15. The study demonstrated that the 12 elements tested showed different distribution pattern. Aluminium, Cu and V showed the most homogeneous pattern while Cd and Ni exhibited the largest departures from the mean value in 13 out of the 45 discs analyzed. No preferential deposition was noticed in any sub-sample.