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In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

A new algorithm is developed for computing ..., where A is an n x n matrix and B is ... with ... The algorithm works for any A, its computational cost is dominated by the formation of products of A with ... matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix ... or a sequence ... on an equally spaced grid of points ... It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. Numerical experiments show that the algorithm performs in a numerically stable fashion across a wide range of problems, and analysis of rounding errors and of the conditioning of the problem provides theoretical support. Experimental comparisons with MATLAB codes based on Krylov subspace, Chebyshev polynomial, and Laguerre polynomial methods show the new algorithm to be sometimes much superior in terms of computational cost and accuracy.(ProQuest: ... denotes formulae/symbols omitted.)

This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank–Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in d-dimensional space, d = 2, 3. In our analysis, we split the error function into two parts, one from the spatial discretization and one from the temporal discretization, by introducing a corresponding time-discrete (elliptic) system. We present a rigorous analysis for the regularity of the solution of the time-discrete system and error estimates of the time discretization. With these estimates and the proved regularity, optimal error estimates of the fully discrete Crank–Nicolson Galerkin method are obtained unconditionally. Numerical results confirm our analysis and show the efficiency of the method.

The objective of this study was to use a prospective error analysis method to examine the process of dispensing medication in community pharmacy settings and identify remedial solutions to avoid potential errors, categorising them as strong, intermediate, or weak based on an established patient safety action hierarchy tool. Focus group discussions and non-participant observations were undertaken to develop a Hierarchical Task Analysis (HTA), and subsequent focus group discussions applied the Systematic Human Error Reduction and Prediction Approach (SHERPA) focusing on the task of dispensing medication in community pharmacies. Remedial measures identified through the SHERPA analysis were then categorised as strong, intermediate, or weak based on the Veteran Affairs National Centre for Patient Safety action hierarchy. Non-participant observations were conducted at 3 pharmacies, totalling 12 hours, based in England. Additionally, 7 community pharmacists, with experience ranging from 8 to 38 years, participated in a total of 4 focus groups, each lasting between 57 to 85 minutes, with one focus group discussing the HTA and three applying SHERPA. A HTA was produced consisting of 10 sub-tasks, with further levels of sub-tasks within each of them. Overall, 88 potential errors were identified, with a total of 35 remedial solutions proposed to avoid these errors in practice. Sixteen (46%) of these remedial measures were categorised as weak, 14 (40%) as intermediate and 5 (14%) as strong according to the Veteran Affairs National Centre for Patient Safety action hierarchy. Sub-tasks with the most potential errors were identified, which included 'producing medication labels' and 'final checking of medicines'. The most common type of error determined from the SHERPA analysis related to omitting a check during the dispensing process which accounted for 19 potential errors. This work applies both HTA and SHERPA for the first time to the task of dispensing medication in community pharmacies, detailing the complexity of the task and highlighting potential errors and remedial measures specific to this task. Future research should examine the effectiveness of the proposed remedial solutions to improve patient safety.

We propose and analyze a time-stepping discontinuous Petrov–Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence, uniqueness, and stability of approximate solutions and derive error estimates. To achieve high order convergence rates from the time discretizations, the time mesh is graded appropriately near t = 0 to compensate for the singular (temporal) behavior of the exact solution near t = 0 caused by the weakly singular kernel, but the spatial mesh is quasi uniform. In the L∞((0, T); L2(Ω))-norm, ((0, T) is the time domain and Ω is the spatial domain); for sufficiently graded time meshes, a global convergence of order km+α/2 + hr+1 is shown, where 0 < α < 1 is the fractional exponent, k is the maximum time step, h is the maximum diameter of the elements of the spatial mesh, and m and r are the degrees of approximate solutions in time and spatial variables, respectively. Numerical experiments indicate that our theoretical error bound is pessimistic. We observe that the error is of order km+1 + hr+1, that is, optimal in both variables.

Medication errors can endanger the health and safety of patients and need to be managed appropriately. This study aimed at developing a new and comprehensive method for estimating the probability of medication errors in hospitals. An extensive literature review was conducted to identify factors affecting medication errors. Success Likelihood Index Methodology was employed for calculating the probability of medication errors. For weighting and rating of factors, the Fuzzy multiple attributive group decision making methodology and Fuzzy analytical hierarchical process were used, respectively. A case study in an emergency department was conducted using the framework. A total number of 17 factors affecting medication error were identified. Workload, patient safety climate, and fatigue were the most important ones. The case study showed that subtasks requiring nurses to read the handwritten of other nurses and physicians are more prone to human error. As there is no specific method for assessing the risk of medication errors, the framework developed in this study can be very useful in this regard. The developed technique was very easy to administer.

Interferometric synthetic aperture radar (InSAR) processing techniques have been widely used to derive surface deformation or retrieve terrain elevation. Over the development of the past few decades, most research has mainly focused on its application, new techniques for improved accuracy, or the investigation of a particular error source and its correction method. Therefore, a thorough discussion about each error source and its influence on InSAR-derived products is rarely addressed. Additionally, InSAR is a challenging topic for beginners to learn due to the intricate mathematics and the necessary signal processing knowledge required to grasp the core concepts. This results in the fact that existing papers about InSAR are easy to understand for those with a technical background but difficult for those without. To cope with the two issues, this paper aims to provide an organized, comprehensive, and easily understandable review of the InSAR error budget. In order to assist readers of various backgrounds in comprehending the concepts, we describe the error sources in plain language, use the most fundamental math, offer clear examples, and exhibit numerical and visual comparisons. In this paper, InSAR-related errors are categorized as intrinsic height errors or location-induced errors. Intrinsic height errors are further divided into two subcategories (i.e., systematic and random error). These errors can result in an incorrect number of phase fringes and introduce unwanted phase noise into the output interferograms, respectively. Location-induced errors are the projection errors caused by the slant-ranging attribute of the SAR systems and include foreshortening, layover, and shadow effects. The main focus of this work is on systematic and random error, as well as their effects on InSAR-derived topographic and deformation products. Furthermore, because the effects of systematic and random errors are greatly dependent on radar wavelengths, different bands are utilized for comparison, including L-band, S-band, C-band, and X-band scenarios. As examples, we used the parameters of the upcoming NISAR operation to represent L-band and S-band, ERS-1 and Sentinel-1 to represent C-band, and TerraSAR-X to represent X-band. This paper seeks to bridge this knowledge gap by presenting an approachable exploration of InSAR error sources and their implications. This robust and accessible analysis of the InSAR error budget is especially pertinent as more SAR data products are made available (e.g., NISAR, ICEYE, Capella, Umbra, etc.) and the SAR user-base continues to expand. Finally, a commentary is offered to explore the error sources that were not included in this work, as well as to present our thoughts and conclusions.

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The Euclidean distance error of calibration results cannot be calculated during the hand–eye calibration process of a manipulator because the true values of the hand–eye conversion matrix cannot be obtained. In this study, a new method for error analysis and algorithm optimization is presented. An error analysis of the method is carried out using a priori knowledge that the location of the augmented reality markers is fixed during the calibration process. The coordinates of the AR marker center point are reprojected onto the pixel coordinate system and then compared with the true pixel coordinates of the AR marker center point obtained by corner detection or manual labeling to obtain the Euclidean distance between the two coordinates as the basis for the error analysis. We then fine-tune the results of the hand–eye calibration algorithm to obtain the smallest reprojection error, thereby obtaining higher-precision calibration results. The experimental results show that, compared with the Tsai–Lenz algorithm, the optimized algorithm in this study reduces the average reprojection error by 44.43% and the average visual positioning error by 50.63%. Therefore, the proposed optimization method can significantly improve the accuracy of hand–eye calibration results.