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In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.

The authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.

The authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated.

The research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections.

Surface curvature is needed to analyze the range data of real objects and is widely applied in object recognition and segmentation, robotics, and computer vision. Therefore, it is not easy to estimate the curvature of the scanned data. In recent years, machine learning classification methods have gained importance in various fields such as finance, health, engineering, etc. The purpose of this study is to classify surface points based on principal curvatures to find the best method for determining surface point types.

A feature selection method is presented to find the best feature vector that achieves the highest accuracy. For this reason, ten different feature selections are used and six sample datasets of different sizes are classified using these feature vectors.

The author examined the surface examples based on the feature vector using the machine learning classification methods. Also, the author compared the results for each experiment.

To the best of the author's knowledge, this is the first study to examine surface points according to principal curvatures using machine learning classification methods.

The goal of this research is to develop a dynamic step path planning algorithm based on the rapidly exploring random tree (RRT) algorithm that combines Q-learning with the Gaussian distribution of obstacles. A route for autonomous vehicles may be swiftly created using this algorithm.

The path planning issue is divided into three key steps by the authors. First, the tree expansion is sped up by the dynamic step size using a combination of Q-learning and the Gaussian distribution of obstacles. The invalid nodes are then removed from the initially created pathways using bidirectional pruning. B-splines are then employed to smooth the predicted pathways.

The algorithm is validated using simulations on straight and curved highways, respectively. The results show that the approach can provide a smooth, safe route that complies with vehicle motion laws.

An improved RRT algorithm based on Q-learning and obstacle Gaussian distribution (QGD-RRT) is proposed for the path planning of self-driving vehicles. Unlike previous methods, the authors use Q-learning to steer the tree's development direction. After that, the step size is dynamically altered following the density of the obstacle distribution to produce the initial path rapidly and cut down on planning time even further. In the aim to provide a smooth and secure path that complies with the vehicle kinematic and dynamical restrictions, the path is lastly optimized using an enhanced bidirectional pruning technique.

We evaluate the hypothesis of temporal stability in risk preferences using two recent data sets from longitudinal lab experiments. Both experiments included a combination of decision tasks that allows one to identify a full set of structural parameters characterizing risk preferences under Cumulative Prospect Theory (CPT), including loss aversion. We consider temporal stability in those structural parameters at both population and individual levels. The population-level stability pertains to whether the distribution of risk preferences across individuals in the subject population remains stable over time. The individual-level stability pertains to within-individual correlation in risk preferences over time. We embed the CPT structure in a random coefficient model that allows us to evaluate temporal stability at both levels in a coherent manner, without having to switch between different sets of models to draw inferences at a specific level.

The purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.

The methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.

It was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.

To the best of the authors’ knowledge, the application and comparison of several finite difference formulae and corresponding optimal sampling has not been carried out before. With the proposed approach, it is possible to identify multiple damages, which is still a great challenge. The post-processing of shearography measurements with a numerical method, which is inherently a multidisciplinary approach, is also a substantial improvement upon other type of approaches found in the literature.

The purpose of this paper is to study the effect of curvature on the magnetic field distribution and no-load rotor eddy current losses in electric machines, particularly in high-speed permanent magnet (PM) machines.

The magnetic field distribution is obtained using conformal mapping, and the eddy current losses are obtained using a cylindrical multilayer model. The analytical results are validated using a two-dimensional finite element analysis. The analytical method is based on a proportional-logarithmic conformal transformation that maps the cylindrical geometry of a rotating electric machine into a rectangular configuration without modifying the length scale. In addition, the appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. Based on this conformal transformation, a coefficient to quantify the effect of curvature is proposed.

Neglecting the effect of curvature can produce significant errors in the calculation of no-load rotor losses when the ratio between the air-gap length and the rotor diameter is large.

The appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. The proportional-logarithmic transformation proposed provides an insight into the effect of curvature on the magnetic field distribution in the air-gap and no-load rotor losses. Furthermore, the proposed curvature coefficient gives a notion of the effect of curvature for any particular geometry without the necessity of any complicated calculation. The case study shows that neglecting the effect of curvature underestimates the rotor eddy-current losses significantly in machines with large gap-to-rotor diameter ratios.

This study aims to research the prediction performance of the bifurcation approach with different base models in different kinds of turbulent flows with rotation and curvature.

The k−ω and Shear-Stress Transport (SST) k−ω models are modified by using the complete eddy viscosity coefficient expression, and the latter is modified by using two sets of model coefficients. The two bifurcation models were tested in three cases: rotating channel flow with system rotation, Taylor–Couette flow with wall rotation and curvature effect and swirling flow through an abrupt axisymmetric expansion with inlet swirling flow.

In these flows, the bifurcation approach can significantly improve the prediction performance of the base model in the fluctuation velocity. The deviation of the BSkO model is slightly superior to the BkO model by about 2% in the Taylor–Couette flow. The prediction effect of the root-mean-square (RMS) velocity of the BSkO model increases by about 4–5% as the number of grids increases about 2.37 times, and the best is the Large Eddy Simulation (LES) grid used. Finally, compared with the SST k−ω model, the average iteration time of the SST with curvature correction (SST-CC), bifurcation k−ω (BkO) and bifurcation SST k−ω (BSkO) models increased by 27.7%, 86.9% and 62.3%, respectively.

This study is helpful to understand further the application of the bifurcation method in the turbulence model.

This study has focussed on three main areas. First, an evaluation of the physical attributes of cashmere tops available to commercial spinners; second, the influence of processing variables on the efficiency of producing cashmere tops from raw Australian cashmere; and third, the influence of design of cashmere ultrafine wool blends on the fibre curvature of tops. Testing the physical attributes of cashmere tops from traditional and new sources of supply, was followed by statistical analyses based on factors of origin, processor and other determinants. The analyses demonstrated important processor effects and also that cashmere from different origins shows commercially important variations in fibre attributes. It was possible to efficiently produce Australian cashmere tops with Hauteur, tenacity, extension, softness and residual guard hairs quality attributes equivalent to those observed in the best cashmere tops. The blending of cashmere with wool resulted in a reduction of the mean fibre curvature of the blend compared with the unblended wool. The present work demonstrated that the fibre curvature properties of blended low crimp ultrafine wool tops were closer to the properties of pure cashmere tops than were tops made from blended standard high crimp ultrafine wool. The attributes of textiles made from the relatively rare Australian low curvature cashmere could enhance the marketability of both Australian cashmere and low curvature wool.

The purpose of this paper is to develop an effective and reliable corner detection algorithm so as to extract all the desired corners successfully. In addition, the influences of edge detection method as well as smoothing technique on the overall performance of corner detection techniques are investigated.

In this paper, an effective corner detection algorithm based on subpixel edge detector and Gaussian filter is presented. First, a subpixel accuracy edge detector is used rather than a pixel accuracy edge detector to detect edges. Second, B‐splines approximation technique is used to eliminate the staircase effect of a digital curve. Third, curvature curve derived from the edges is smoothed by a Gaussian filter. Finally, statistical process control technique is applied to detect vertices.

The results show that spatial‐moment outperforms chain code as an edge detector. Furthermore, the Gaussian filter should be used to smooth curvature curve instead of smoothing the profile of an object, because the former provides greater impact on the corner detection results.

In addition to object recognition, motion tracking and obstacle avoidance, the proposed method also has many important engineering and manufacturing applications such as dimensional measuring, reverse engineering, and machine vision‐based computer numerical control (CNC) machining of polygonal sheet metal parts.