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This paper aims to address the importance of behavioural finance issues among real investors. It analyses whether private investors are susceptible to extrapolation bias and whether this bias affects market prices.

A qualitative coding of message board posts facilitates the construction of sentiment proxies. Using linear techniques, it is tested whether after-hours sentiment is positively predicted by daily share return and whether daily share return exhibits positive autocorrelation.

Private investors are impaired by extrapolation bias, while market prices remain unaffected. Probably, sophisticated professional investors benefit by offsetting the irrational private investor transactions.

As the sample of German blue-chip banks is small and covers a period during the Eurozone crisis, the findings should be generalised with caution. Future research might use a different sample and explore whether non-crisis periods provide comparable results.

Investors should not take for granted the neoclassical assumption that all market participants always act rationally and according to self-interest.

Irrespective of whether market prices are efficient, a level playing field between private and professional investors is necessary. Otherwise, confidence in the financial marketplace is not guaranteed and society may incur welfare losses.

The approach of extracting sentiment from a German share message board through qualitative content analysis (QCA) is unique for analysing extrapolation bias. This paper is valuable in drawing attention to the importance of rational investment behaviour among private investors.

Extrapolation is a process used to accelerate the convergence of a sequence of approximations to the true value. Different stepsizes are used to obtain approximate solutions, which are combined to increase the order of the approximation by eliminating leading error terms. The smoothing technique is also applied to suppress order reduction and to dampen the oscillatory component in the numerical solution when solving stiff problems. The extrapolation and smoothing technique can be applied in either active, passive or the combination of both active and passive modes. In this paper, the authors investigate the best strategy of implementing extrapolation and smoothing technique and use this strategy to solve stiff ordinary differential equations. Based on the experiment, the authors suggest using passive smoothing in order to reduce the computation time.

The two-step smoothing is a composition of four steps of the symmetric method with different weights. It is used as the final two steps when combined with many steps of the symmetric method. The aim is to preserve symmetry and provide damping for stiff problem and to be more robust than the one-step smoothing. The two-step smoothing is L-stable. The new method is then applied with extrapolation process in passive and active modes to investigate the most efficient and accurate method of implementation.

In this paper, the authors constructed the two-step smoothing to be more robust than the one-step smoothing. The two-step smoothing is constructed to achieve as high order as possible and able to restore the classical order of particular method compared to the one-step active smoothing that is only able to achieve order-1 condition. The two-step smoothing for ITR is also superior in solving stiff case since it has the super-convergent order-4 behavior. In our experiments with extrapolation, it is proven that the two-step smoothing is more accurate and more efficient than the one-step smoothing, namely 1ASAX. It is also observed that the method with smoothing is comparable if not superior to the existing base method in certain cases. Based on the experiment, the authors would suggest using passive smoothing if the aim is to reduce computation time. It is of interest to conduct more experiment to validate the accuracy and efficiency of the smoothing formula with and without extrapolation.

The implementation of extrapolation on two-step symmetric Runge–Kutta method has not been tested on variety of other test problems yet. The two-step symmetrization is an extension of the one-step symmetrization and has not been constructed by other researchers yet. The method is constructed such that it preserves the asymptotic error expansion in even powers of stepsize, and when used with extrapolation the order might increase by 2 at a time. The method is also L-stable and eliminates the order reduction phenomenon when solving stiff ODEs. It is also of interest to observe other ways of implementing extrapolation using other sequences or with interpolation.

The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains.

Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed.

Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner.

Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

The purpose of this paper is to present a study on methods for load spectrum (LS) determination and extrapolation, basing on data obtained from experiments.

A sequence of loads registered in flight becomes an object of analysis aimed to calculate full cycles of loads, and on this basis two possible types of LS are determined, i.e. as the transfer array, or in classic form (as the plot presenting appearances of load increments, called “incremental load spectrum”). While the use of incremental LS enables just application of deterministic extrapolation methods, the transfer array enables application of the stochastic method of extrapolation that consists of random redistribution of the transfer array cell values.

The paper presents a comparison between the results of application of deterministic or stochastic extrapolation methods. Attention was focused on the LS registered during thermal flights. The stochastic extrapolation method is less conservative than the deterministic ones, and enables better adjustment of estimated LS to the reality.

The novel extrapolation method consists of cumulation of the results of stochastic redistribution of the values in transfer array obtained from the experiment.

This paper aims to provide a new method of generating relatively accurate and smooth saturated B-H curves based on reliable measurement data to improve the accuracy and efficiency of electromagnetic simulation.

The characteristics of different B-H curve extrapolation models are summarized, and an improved method is proposed. The fitting procedure in low fields and extrapolation procedure in high fields are presented in detail. The saturated B-H curves generated by various methods are compared and discussed. Finally, a simulation case study proved the advantages of the new method in terms of simulation accuracy and efficiency.

The B-H curve created by the new method avoids extrapolation from a single point and simultaneously smoothens the entire B-H curve, thereby improving the simulation accuracy and efficiency. The low magnetic potential requirements for closed measurements and the small deviation with open measurements indicate that this method is well-suited for implementation.

The results are applicable for materials subject to such excitation levels that saturation has to be taken into account.

While some extrapolation models of B-H curves have been investigated in reference papers, there is still room for improvement in accuracy and smoothness. The new method processes low fields and high fields magnetization data and then connects them based on third-order boundary equations for the first time. This method can generate saturated B-H curves with good accuracy and smoothness while retaining outstanding operability.

Motivated with the ever growing number of bibliometric trend extrapolation studies, the purpose of this paper is to demonstrate through two technologies how the selection of an upper limit of growth affects the correlation and causality of technology development measured with bibliometric data.

The paper uses Gompertz and Fisher-Pry curves to model the technological development of white light emitting diodes and flash memory, and show with extrapolation results from several bibliometric sources how a typical bias is caused in trend extrapolations.

The paper shows how drastic an effect the decision to set an upper bound has on trend extrapolations, to be used as a reference for applications. The paper recommends carefully examining the interconnection of actual development and bibliometric activity.

Despite increasing interest in modelling technological data using this method, reports rarely discuss basic assumptions and their effects on outcomes. Since trend extrapolations are applied more widely in different disciplines, the basic limitations of methods should be explicitly expressed.

The purpose of this paper is to present the author’s method of conservative load spectrum (LS) derivation and close-proximity LS extrapolation applying a correction for measurement uncertainty caused by too low sampling frequency or signal noise, which may affect the load histories collected during the flying session and cause some recorded load increments to be lower than the actual values.

Having in mind that the recorded load signal is burdened with some measurement error, a conservative approach was applied during qualification of the recorded values into 32 discrete load-level intervals and derivation of 32 × 32 half-cycle arrays. A part of each cell value of the half-cycle array was dispersed into the neighboring cells placed above by using a random number generator. It resulted in an increase in the number of load increments, which were one or two intervals higher than those resulting from direct data processing. Such an array was termed a conservative clone of the actual LS. The close-proximity approximation consisted of multiplication of the LSs clones and their aggregation. This way, the LS for extended time of operation was obtained. The whole process was conducted in the MS Excel environment.

Fatigue life calculated for a chosen element of aircraft structure using conservative LS is about 20%–60% lower than for the actual LS (depending on the applied value of dispersion coefficients used in the procedure of LSs clones generation). It means that such a result gives a bigger safety margin when operational life of the aircraft is estimated or when the fatigue test for an extended operational period is programed based on a limited quantity of data from a flying session.

This paper presents a proposal for a novel, conservative approach to fatigue life estimation based on the short-term LS derived from the load signal recorded during the flying session.

Cutting force prediction is pretty important for manufacture management. Thus, the purpose of this paper is to obtain the cutting force of the machining process with high efficiency and low cost. A method based on the improved auto regressive moving average (ARMA) model is proposed for cutting force predictions in milling process.

First, classification and normalization are made for initial cutting force. Second, the cutting force sequences are compressed followed singular and valid value removed. At last, the improved ARMA model is used for cutting force fit and extrapolation considered the time domain characteristics.

A series of cutting force with the spindle speed 595r/min is carried out in the research. It is showed that the mean absolute percentage error value of cutting force extrapolation results which is based on the improved model is smaller. The percentage value is approximately 5.80%. Then the root mean square error test value is only 72.49, which is smaller than that with other traditional method, such as hidden Markov model. The extrapolation results with the proposed model performed good consistency and accuracy in terms of peaks, valleys and volatility compared with the experiment results.

The proposed method that is based on the improved ARMA model can be used for cutting force predictions conveniently. And the predictions can be used for improving the qualities in milling process.

Under the development trend of intelligent manufacturing, the unstructured environment requires the robot to have a good generalization performance to adapt to the scene changes. The purpose of this paper aims to present a learning from demonstration (LfD) method (task parameterized [TP]-dynamic movement primitives [DMP]-GMR) that combines DMPs and TP-LfD to improve generalization performance and solve object manipulation tasks.

The dynamic time warping algorithm is applied to processing demonstration data to obtain a more standard learning model in the proposed method. The DMPs are used to model the basic trajectory learning model. The Gaussian mixture model is introduced to learn the force term of DMPs and solve the problem of learning from multiple demonstration trajectories. The robot can learn more local geometric features and generalize the learned model to unknown situations by adding task parameters.

An evaluation criterion based on curve similarity calculated by the Frechet distance was constructed to evaluate the model’s interpolation and extrapolation performance. The model’s generalization performance was assessed on 2D virtual data sets, and first, the results show that the proposed method has better interpolation and extrapolation performance than other methods.

The proposed model was applied to the axle-hole assembly task on real robots, and the robot’s posture in grasping and placing the axle part was taken as the task parameter of the model. The experiment results show that The proposed model is competitive with other models.

The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method.

This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces.

The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10⁻⁵ ≤ Da ≤ 5 × 10⁻¹) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces.

No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.