On Global Convergence of Third-Order Chebyshev-Type Method under General Continuity Conditions

There are very few papers that talk about the global convergence of iterative methods with the help of Banach spaces. The main purpose of this paper is to discuss the global convergence of third order iterative method. The convergence analysis of this method is proposed under the assumptions that Fréchet derivative of first order satisfies continuity condition of the Hölder. Finally, we consider some integral equation and boundary value problem (BVP) in order to illustrate the suitability of theoretical results.

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.

Mathematical Model for Metal Transfer Study in Additive Manufacturing with Electron Beam Oscillation

A computer model has been developed to investigate the processes of heat and mass transfer under the influence of concentrated energy sources on materials with specified thermophysical characteristics, including temperature-dependent ones. The model is based on the application of the volume of fluid (VOF) method and finite-difference approximation of the Navier–Stokes differential equations formulated for a viscous incompressible medium. The “predictor-corrector” method has been used for the coordinated determination of the pressure field which corresponds to the continuity condition and the velocity field. The modeling technique of the free liquid surface and boundary conditions has been described. The method of calculating surface tension forces and vapor recoil pressure has been presented. The algorithm structure is given, the individual modules of which are currently implemented in the Microsoft Visual Studio environment. The model can be applied for studying the metal transfer during the deposition processes, including the processes with electron beam spatial oscillation. The model was validated by comparing the results of computational experiments and images obtained by a high-speed camera.

Typical transient effects in a piezoelectric semiconductor nanofiber under a suddenly applied axial time-dependent force

Based on the mechanical motion equation, Gauss’s law, and the current continuity condition, we study a few typical transient effects in a piezoelectric semiconductor (PS) fiber to realize the startup and turning-off functions of common piezotronic devices. In this study, the transient extensional vibration induced by a suddenly applied axial time-dependent force is examined in a cantilevered n-type ZnO nanofiber. Neither the magnitude of the loadings nor the doping concentration significantly affects the propagation caused by disturbance of the axial displacement. However, both of the factors play an important role in the propagation caused by disturbance of the electron concentrations. This indicates that the electromechanical coupling effect can be expected to directly determine the electronic performance of the devices. In addition, the assumption of previous simplified models which neglect the charge carriers in Gauss’s law is discussed, showing that this assumption has a little influence on the startup state when the doping concentration is smaller than 1021 m−3. This suggests that the screening effect of the carriers on the polarized electric field is much reduced in this situation, and that the state is gradually transforming into a pure piezoelectric state. Nevertheless, the carriers can provide a damping effect, which means that the previous simplified models do not sufficiently describe the turning-off state. The numerical results show that the present study has referential value with respect to the design of newly multifunctional PS devices.

Free and Forced Vibration Characteristics Analysis of a Multispan Timoshenko Beam Based on the Ritz Method

The uniform formulation of dynamic vibration analysis of multispan beams is presented by using an efficient domain decomposition method in this paper. Firstly, the structure is divided into several equal sections based on domain decomposition method. Next, the artificial spring is used to simulate complex boundaries and continuity condition of multispan beam. Finally, the admissible displacement functions are expanded through Jacobi orthogonal polynomials, and the free and forced vibration characteristics of multispan beam structures can be obtained by using Rayleigh–Ritz method. Results for various boundary conditions, ratios of thickness to length (h/L), numbers, and stiffness of supporting springs are presented. It is clearly shown that accurate solutions can be obtained by using the proposed method, and this study extends the application range of the Jacobi polynomials-Ritz method. In addition, the research results of this paper can provide data support for engineers such as bridge designers to design multispan bridges.

Continuity and catastrophic risk

Suppose that a decision-maker’s aim, under certainty, is to maximize some continuous value, such as lifetime income or continuous social welfare. Can such a decision-maker rationally satisfy what has been called ‘continuity for easy cases’ while at the same time satisfying what seems to be a widespread intuition against the full-blown continuity axiom of expected utility theory? In this note I argue that the answer is ‘no’: given transitivity and a weak trade-off principle, continuity for easy cases violates the anti-continuity intuition. I end the note by exploring an even weaker continuity condition that is consistent with the aforementioned intuition.

LANCET

Cutting-edge machine learning techniques often require millions of labeled data objects to train a robust model. Because relying on humans to supply such a huge number of labels is rarely practical, automated methods for label generation are needed. Unfortunately, critical challenges in auto-labeling remain unsolved, including the following research questions: (1) which objects to ask humans to label, (2) how to automatically propagate labels to other objects, and (3) when to stop labeling. These three questions are not only each challenging in their own right, but they also correspond to tightly interdependent problems. Yet existing techniques provide at best isolated solutions to a subset of these challenges. In this work, we propose the first approach, called LANCET, that successfully addresses all three challenges in an integrated framework. LANCET is based on a theoretical foundation characterizing the properties that the labeled dataset must satisfy to train an effective prediction model, namely the Covariate-shift and the Continuity conditions. First, guided by the Covariate-shift condition, LANCET maps raw input data into a semantic feature space, where an unlabeled object is expected to share the same label with its near-by labeled neighbor. Next, guided by the Continuity condition, LANCET selects objects for labeling, aiming to ensure that unlabeled objects always have some sufficiently close labeled neighbors. These two strategies jointly maximize the accuracy of the automatically produced labels and the prediction accuracy of the machine learning models trained on these labels. Lastly, LANCET uses a distribution matching network to verify whether both the Covariate-shift and Continuity conditions hold, in which case it would be safe to terminate the labeling process. Our experiments on diverse public data sets demonstrate that LANCET consistently outperforms the state-of-the-art methods from Snuba to GOGGLES and other baselines by a large margin - up to 30 percentage points increase in accuracy.