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After witnessing the implementations of Banach fixed point theory which is stated that a mapping T: X→X has always a unique fixed point in X in giving the existence and uniqueness solutions for many integral and differential equations, various extensions of Banach fixed point theory were established. Consequently, the theory has evolved to encompass diverse extensions and is fruitful in many fields. One of the most significant advances in pure and applied mathematics is the discovery of solutions for linear and nonlinear systems as well fractal graphics, optimization theory, approximation theory, discrete dynamics, and numerous other areas. Our main outcomes in this manuscript represent one of the most important of these extensions. Vital concepts are needed in the sequels which are playing a major role in verifying our major outcomes have been presented. Throughout this manuscript, indicates to a partially ordered set with the partially ordered . In this study, our main objective is to investigate and verify various new enhanced results of coupled fixed point theorems for continuous maps having the property of mixed monotone under the influence of extended contraction circumstances in the context of partially ordered -complete metric spaces. Numerous characterizations of these types of coupled fixed point theorems have been verified. Additionally, an appropriate example that supports the major outcomes was prepared. Our main results in this manuscript have been explored novel various outcomes related to the uniqueness of various coupled fixed point theorems for continuous maps having the property of mixed monotone under the influence of extended contraction circumstances in the context of partially ordered -complete metric spaces. We predict that the discoveries in this study will aid scientists in enhancing the research on popularized partially ordered metric spaces to elevate a universal framework for their practical implementations.

In this paper we consider a class of structured nonsmooth difference-of-convex (DC) minimization in which the first convex component is the sum of a smooth and nonsmooth functions while the second convex component is the supremum of possibly infinitely many convex smooth functions. We first propose an inexact enhanced DC algorithm for solving this problem in which the second convex component is the supremum of finitely many convex smooth functions, and show that every accumulation point of the generated sequence is an (α,η)-D-stationary point of the problem, which is generally stronger than an ordinary D-stationary point. In addition, inspired by the recent work (Pang et al. in Math Oper Res 42(1):95–118, 2017; Wen et al. in Comput Optim Appl 69(2):297–324, 2018), we propose two proximal DC algorithms with extrapolation for solving this problem. We show that every accumulation point of the solution sequence generated by them is an (α,η)-D-stationary point of the problem, and establish the convergence of the entire sequence under some suitable assumption. We also introduce a concept of approximate (α,η)-D-stationary point and derive iteration complexity of the proposed algorithms for finding an approximate (α,η)-D-stationary point. In contrast with the DC algorithm (Pang et al. 2017), our proximal DC algorithms have much simpler subproblems and also incorporate the extrapolation for possible acceleration. Moreover, one of our proximal DC algorithms is potentially applicable to the DC problem in which the second convex component is the supremum of infinitely many convex smooth functions. In addition, our algorithms have stronger convergence results than the proximal DC algorithm in Wen et al. (2018).

A light detection and ranging (LiDAR) sensor can obtain richer and more detailed traffic flow information than traditional traffic detectors, which could be valuable data input for various novel intelligent transportation applications. However, the point cloud generated by LiDAR scanning not only includes road user points but also other surrounding object points. It is necessary to remove the worthless points from the point cloud by using a suitable background filtering algorithm to accelerate the micro-level traffic data extraction. This paper presents a background point filtering algorithm using a slice-based projection filtering (SPF) method. First, a 3-D point cloud is projected to 2-D polar coordinates to reduce the point data dimensions and improve the processing efficiency. Then, the point cloud is classified into four categories in a slice unit: Valuable object points (VOPs), worthless object points (WOPs), abnormal ground points (AGPs), and normal ground points (NGPs). Based on the point cloud classification results, the traffic objects (pedestrians and vehicles) and their surrounding information can be easily identified from an individual frame of the point cloud. We proposed an artificial neuron network (ANN)-based model to improve the adaptability of the algorithm in dealing with the road gradient and LiDAR-employing inclination. The experimental results showed that the algorithm of this paper successfully extracted the valuable points, such as road users and curbstones. Compared to the random sample consensus (RANSAC) algorithm and 3-D density-statistic-filtering (3-D-DSF) algorithm, the proposed algorithm in this paper demonstrated better performance in terms of the run-time and background filtering accuracy.

Introduction and hypothesisThe objective was to determine the relationship between the preoperative D-point and apical outcomes at 24 months, using the Operations and Pelvic Muscle Training in the Management of Apical Support Loss (OPTIMAL) dataset.MethodsThis was a secondary analysis of the OPTIMAL trial, a randomized multi-centered study comparing outcomes of sacrospinous ligament fixation and transvaginal uterosacral ligament suspension (USLS). The 2-year dataset utilized included women undergoing USLS with concomitant hysterectomy. The primary outcome was the relationship between preoperative D-point and apical outcomes at 24 months. Secondary objectives were to determine the relationship between preoperative D-point and anatomical, composite and subjective outcomes, and to determine a D-point cut-off that could be used to predict success in each of these categories.ResultsOf the 186 women in the USLS arm, 120 were available for analysis of anatomical failure at 24 months. A higher preoperative D-point correlated with improved apical outcome (C-point) at 24 months (r = 0.34; p value = 0.0002). Using ROC curves, a moderate association was found between the preoperative D-point and apical and anatomical success, (AUC 0.689 and 0.662). There was no relationship between preoperative D-point and composite or subjective success (AUC 0.577 and 0.458). Based on the ROC curves, a “cut-off” D-point value of −4.25 cm (sensitivity = 0.58, specificity = 0.67) was determined to be a predictor of postoperative anatomical success at 2 years.ConclusionsPreoperative D-point correlates with postoperative anatomical and apical support, but is less successful at predicting subjective outcomes. The strongest predictive D-point cut-off for anatomical and apical success at 24 months was −4.25 cm.

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\\mathbb F_p(t)$, when $p$ is prime and $r\\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\\mathbb F_q(t^1/d)$.

We suggest a new method for constructing an efficient point predictor for the future order statistics when the sample size is a random variable. The suggested point predictor is based on some characterization properties of the distributions of order statistics. For several distributions, including the mixture distribution, the performance of the suggested predictor is evaluated by means of a comprehensive simulation study. Three examples of real lifetime data-sets are analyzed by using this method and compared with an efficient recent method given by Barakat et al. [1], that deals with non-random sample sizes. One of these examples predicts the accumulative new cases per million for infection of the new Coronavirus (COVID-19).

The extraction of relevant features from the photoplethysmography signal for estimating certain physiological parameters is a challenging task. Various feature extraction methods have been proposed in the literature. In this study, we present a novel fiducial point extraction algorithm to detect c and d points from the acceleration photoplethysmogram (APG), namely “CnD”. The algorithm allows for the application of various pre-processing techniques, such as filtering, smoothing, and removing baseline drift; the possibility of calculating first, second, and third photoplethysmography derivatives; and the implementation of algorithms for detecting and highlighting APG fiducial points. An evaluation of the CnD indicated a high level of accuracy in the algorithm’s ability to identify fiducial points. Out of 438 APG fiducial c and d points, the algorithm accurately identified 434 points, resulting in an accuracy rate of 99%. This level of accuracy was consistent across all the test cases, with low error rates. These findings indicate that the algorithm has a high potential for use in practical applications as a reliable method for detecting fiducial points. Thereby, it provides a valuable new resource for researchers and healthcare professionals working in the analysis of photoplethysmography signals.

In this work, weinvestigate conditions for summability of the Fourier-Laplace series of integrable functions by Riesz means. The kernel of Riesz means is estimated through comparison with the Cesaro means. Properties of D and D* points are required in obtaining this estimation.

Background After witnessing the implementations of Banach fixed point theory which is stated that a mapping T: X→X has always a unique fixed point in X in giving the existence and uniqueness solutions for many integral and differential equations, various extensions of Banach fixed point theory were established. Consequently, the theory has evolved to encompass diverse extensions and is fruitful in many fields. One of the most significant advances in pure and applied mathematics is the discovery of solutions for linear and nonlinear systems as well fractal graphics, optimization theory, approximation theory, discrete dynamics and numerous other areas. Our main outcomes in this manuscript represent one of the most important of these extensions. Methods and Results Vital concepts such as D d ∗ -Symmetric spaces and weakly compatible maps are reviewed to establish the framework for our main results. The major objective of the present study is to investigate and verify the uniqueness of some common fixed point theorems for three pairs of self-maps under the influence of other enhanced categories of extended contractive conditions in the context of D d ∗ -Symmetric spaces. Our first main outcomes were established by applying the concepts of weak compatibility and common limit in the range property, whereas we obtained our second major results by utilizing the notion of occasionally weakly compatible mapping. Additionally, various common fixed point outcomes for the two pairs of self-maps were determined. Conclusion This manuscript explores novel outcomes regarding the uniqueness of various common fixed point theorems for three pairs of self-maps under the influence of other enhanced types of extended contractive conditions in the context of D d ∗ -Symmetric spaces. We anticipate that the discoveries in this manuscript will aid scientists in enhancing the authors on popularized extended symmetric-spaces to elevate a universal framework for their practical implementations in each advanced branches of science.

New relations between the Banach algebras of absolutely convergent Fourier integrals of complex-valued measures of Wiener and various issues of trigonometric Fourier series (see classical monographs by A. Zygmund [1] and N. K. Bary [2]) are described. Those bilateral interrelations allow one to derive new properties of the Fourier series from the known properties of the Wiener algebras, as well as new results to be obtained for those algebras from the known properties of Fourier series. For example, criteria, i.e. simultaneously necessary and sufficient conditions, are obtained for any trigonometric series to be a Fourier series, or the Fourier series of a function of bounded variation, and so forth. Approximation properties of various linear summability methods of Fourier series (comparison, approximation of function classes and single functions) and summability almost everywhere (often with the set indication) are considered.The presented material was reported by the author on 12.02.2021 at the Zoom-seminar on the theory of real variable functions at the Moscow State University.