In this paper, the Lie symmetries and similarity Reduction of a class of wave equations are investigated. First, Lie algorithm is used to get the determining equations of symmetry for the given equations which are complicated and difficult to be solved. Next, differential form of Wu’ s method is used to solve this problem. Moreover, a special case of differential invariant method is used to get similarity Reduction of the given equations.

Purpose: The purpose of this paper is to research the solution of the perturbed coupled Korteweg-de Vries (KdV) equations.Methods: The results are obtained through researching a system of corresponding partial differential equations which approximates the perturbed coupled KdV equations and the symmetry method.Results: The symmetry structure and the corresponding general approximate symmetry Reduction are derived. Then, using the symmetry Reduction, the infinite series solutions are obtained.Conclusions: The approximate symmetry Reduction approach can be used to search for similar results of other perturbed nonlinear differential equations with small parameters.

Inertial Navigation System (INS) is one of the navigation systems widely used in various land-based, aerial, and marine applications. Among all types of INS, Microelectromechanical System (MEMS)-based INS can be widely utilized, owing to their low cost, lightweight, and small size. However, due to the manufacturing technology, MEMS-based INS suffers from deterministic and stochastic errors, which increase positioning errors over time. In this paper, a new effective noise Reduction method is proposed that can provide more accurate outputs of MEMS-based inertial sensors. The intelligent method in this paper is a combined denoising method that combines Wavelet Transform (WT), Permutation Entropy (PE), Support Vector Regression (SVR), and Genetic Algorithm (GA). Firstly, WT is employed to obtain a time-frequency representation of raw data. Secondly, a four-element feature vector is formed. These four features are (1) amplitude of frequency, (2) its ratio to mean of amplitudes of all frequencies, (3) location of frequency in time-frequency representation, and (4) judgment on behaviors of frequency that is obtained by utilizing PE. Thirdly, based on the feature vector, the GA-SVR algorithm predicts amplitudes of all frequencies in the time-frequency representation of the denoised signal. Finally, by employing inverse WT the denoised signal is obtained. In this work, the outputs of the Inertial Measurement Unit (IMU) in ADIS16407 sensor, as a low-cost and MEMS-based INS, have been utilized for data collection. The proposed method has been compared with other noise Reduction methods and the achieved results verify superior improvement than other methods.

A pair of rogue wave solutions of the Davey-Stewartson (DS) equations are obtained by using the exp-function method and Reduction transformations. Firstly, the Davey-Stewartson equations are transformed into two easy-to-solve equations, one of which is the deformed nonlinear Schrö dinger (NLS) equation and the other is a polynomial equation. Secondly, based on the existing known solutions of the deformed NLS equation constructed by the exp-function method, rogue wave solutions of the DS equations are obtained. Finally, some spatial and spatiotemporal structures and dynamical evolutionary plots of the obtained rogue wave solutions are shown.

Background & Aims: supracondylar humerus fracture is one of the most common pediatric elbow fractures accounting for about 16% of the pediatric fractures. Loss of Reduction is one of the complications after closed and percutaneous fixation. This research is aimed to investigate the factors involved in the loss of Reduction. Method: In this descriptive study, the children with supracondylar humerus fractures were examined. 175 children under the age of 10 with type 3 and 4 supracondylar humerus fracture fractures who underwent closed fixation and pinning were entered into the study. The studied factors were analyzed by a logistic regression method. Results: in this study 175 children under the age of 10 including 71 girls and 104 boys (59. 4%) with the average age of 5. 4± 2. 4 were investigated. In 153 cases, (87. 4%) the fixation was anatomical and stable during the follow-up; while 22 cases (12. 6%) had the loss of fixation. The most important anatomical disorder was internal rotation displacement in the medial distal part of fracture in these 22 cases. Pinning technique and obesity were among the effective factors in the failure of the anatomical Reduction. In a way that obese children (above 85 percentile or IBM>25) and the lateral pinning location were divergent but they crossed in the fracture site and were effective with odd ratios of 1. 3 (CI 95% 0. 8-2. 3) and 1. 8 (CI 95% 0. 9-2. 3), respectively. In 14 cases (63. 6%) the failure was due to the place of fracture cross and in 8 cases (36. 6%) the complication occurred in the obese children. The fracture type had no effect on the loss of Reduction as no difference was observed. Conclusions: Obesity and fixation technique are among the effective factors in the loss of Reduction in pediatric supracondylar humerus fractures. In obese children, cross-suitable fixation should be considered to prevent complications.

Over the past few decades, computed tomography (CT) imaging has been one of the leading cross-sectional imaging techniques in a wide range of clinical applications in diagnostic radiology, oncology, and multimodal molecular imaging. Despite the recognized value of this imaging modality, the quality and accuracy of CT images can be compromised by a number of implants. The presence of metal objects such as dental fillings, hip or knee prostheses, heart pacemakers, war fragments, and spinal cages can cause severe image artifacts. These types of artifacts appear as black and white streaks in the CT images, obscuring the structures and tissues around the metal implant, decreasing the images' diagnostic values. Metal artifacts also affect the accuracy of radiation therapy treatment planning, which relies on X-ray images to determine electron density and estimate the relative stopping power of particles. Different algorithms for the Metal Artifact Reduction (MAR) have been proposed over the decades to address this issue. This study evaluated five commonly used MAR algorithms in clinical practice using simulated and clinical datasets. These algorithms include linear interpolation (LI_MAR) of the degraded data in the sinogram space, Reduction of metal artifacts by normalization method (NMAR), metal deletion technique (MDT), and Orthopedic metal artifact Reduction (OMAR), and a method based on iteration algorithms (MAP). Clinical CT images in different anatomical regions of the body, with different dimensions and types of metal implants, have been studied to evaluate the performance of the MAR algorithms. In order to quantitatively evaluate the quality of CT images corrected by the different MAR algorithms, the Normalized Root Mean Square Error (NRMSE) metric was employed. The quantitative analysis demonstrated the overall superior performance of the NMAR algorithm in effective metal artifact Reduction compared to the other algorithms. The NMAR method exhibited relatively less signal distortion and reasonable processing time, making it a dependable solution in clinical practice.