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This article explains that in the Grundrisse Marx considered that the discontinuity in his transformation procedure was no logical inconsistency, but a necessary feature of the disproportionate tra...

Dense stereo matching based on two viewpoint images is an important step in 3D reconstruction. In this study, a new disparity estimation algorithm for depth discontinuity areas is proposed. Dense s...

Filled function methods have been considered as an effective approach for solving global optimization problems. However, most filled functions have the drawbacks of discontinuity, non-differentiabi...

Different numerical schemes are introduced to formulate and solve nonlinear vibration analysis of elastically supported multilayer composite plate problems. The type of elastic foundation is Winkle...

This paper presents a material relative permittivity extraction technique based on three measurements of two identical coaxial lines, terminated by a short-circuit configuration. The test cells hav...

Based on embedded analysis, an accurate pin power reconstruction (PPR) method is proposed for conventional nodal analysis. Unlike the common form function (FF) method, the new PPR method, named the...

In beginning textbooks, bounded real valued functions with domain R and one point of discontinuity are usually defined piecewise with each piece being given by a formula. When I first took calculus...

The G01 tool path, which consisted of linear segments, is commonly used in NC machining. There is the tangential and curvature discontinuity at the junctions of adjacent linear segments, which can ...

The present work is concerned with a novel generalized thermoelasticity theory introduced by Yu et al. [A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Me...

In this paper, we study weighted singular p-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied...

Sample size determination in multilevel randomized trials (MRTs) and multilevel regression discontinuity designs (MRDDs) can be complicated due to multilevel structure, monetary restrictions, diffe...

The Discontinuity Model (DM) described in this article proposes that adults can learn part of L2 morphosyntax twice, in two different ways. The same item can be learned as the product of generation...

The inverse problem for impulsive Sturm–Liouville operators with discontinuity conditions is considered. We have shown that all parameters used in the boundary conditions as well as q(x) ca...

With the aid of three-dimensional laser scanning (3D-LS), a lot of geometric properties of rock discontinuities can be derived from the point cloud data. Due to the complexity of registration and g...

Modeling the propagation of radiative heat-waves in optically thick material using a diffusive approximation is a well-known problem. In optically thin material, classic methods, such as classic diffusion or classic $P_1$, yield the wrong heat wave propagation behavior, and higher order approximation might be required, making the solution harder to obtain. The asymptotic $P_1$ approximation [Heizler, {\em NSE} 166, 17 (2010)] yields the correct particle velocity but fails to model the correct behavior in highly anisotropic media, such as problems that involve sharp boundary between media or strong sources. However, the solution for the two-region Milne problem of two adjacent half-spaces divided by a sharp boundary, yields a discontinuity in the asymptotic solutions, that makes it possible to solve steady-state problems, especially in neutronics. In this work we expand the time-dependent asymptotic $P_1$ approximation to a highly anisotropic media, using the discontinuity jump conditions of the energy density, yielding a modified discontinuous $P_1$ equations in general geometry. We introduce numerical solutions for two fundamental benchmarks in plane symmetry. The results thus obtained are more accurate than those attained by other methods, such as Flux-Limiters or Variable Eddington Factor., Comment: 18 pages, 13 figures

We introduce a new stochastic partial differential equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space–time whi...

The uncoupled thermoelasticity problem of a homogenous isotropic layer containing a line of temperature discontinuity and a Volterra edge dislocation is solved. The analysis is performed for discon...

Seam-line-based image fusion technology is widely used in unmanned aerial vehicle (UAV) image mosaicking for its superiority to effectively avoid the ghosting phenomenon. Existing algorithms typically determine a seam-line by minimizing the sum of the mismatching values on the line. However, the strategy of directly summing the mismatch scores is inadequate because a seam-line segment with significant mismatches, even if it is short, is more visible than a lengthy one with small differences. Seeking the minimal solution also results in these methods having large computation cost. To this end, we propose a novel seam-line determination method based on minimal connected area searching and minimum spanning tree to eliminate observable visual discontinuity and improve the time efficiency. The proposed method first finds the minimal connected area by eliminating occlusions across the overlapping area. It then applies the minimum spanning tree algorithm to find the optimal seam-line. Finally, it searche...

A numerical scheme for simulating multi-species shock accelerated flows using lattice Boltzmann approach has been proposed. It uses the moment conservation approach of Yang, Shu, and Wu and extends it to multi-species fluid problems. The multi-species method of Wang et al. has been modified by use of a predictor–corrector approach. This has helped in preventing the pressure oscillations while handling multi-species. Simulation of 2D shock cylinder interaction with this solver has shown good agreement with the experimental data and could capture material discontinuity and unsteady shocks. The simulation of a single mode Richtmyer–Meshkov instability showed that the solver is able to capture the development of spike and bubble as per the experimental findings of Aure and Jacobs. The dissipation in the proposed scheme was further reduced by the use of fifth-order weighted essentially non-oscillatory (WENO). Validated with multiple problems, this method has been found to capture shock instability with...

We study inverse problems of spectral analysis for second-order differential operators on a finite interval with complex-valued weights and with discontinuity conditions inside the interval. Proper...

This paper is about conceptual engineering (CE). Specifically, it discusses a common objection to CE, which I call the Discontinuity Objection. According to the Discontinuity Objection, CE leads to problematic discontinuities in subject and/or inquiry – making it philosophically uninteresting or irrelevant. I argue that a conceptual engineer can dismiss the Discontinuity Objection by showing that the pre-engineering concept persists through the proposed changes. In other words, the Discontinuity Objection does not apply if the proposal involves identity-preserving changes. Two existing views on identity-preserving changes are considered and rejected. I then argue that an identity-preserving conceptual change is one that allows the concept to continue to perform its function. A concept’s function is its job, its point and purpose, its role in a conceptual repertoire. In a slogan: Preserve a concept’s function, and you preserve the concept itself; preserve the concept, and you preserve the subject. ...

In this paper, a completely new integral equation for the price of an American put option as well as its optimal exercise price is successfully derived. Compared to existing integral equations for pricing American options, the new integral formulation has two distinguishable advantages: (i) it is in a form of one-dimensional integral, and (ii) it is in a form that is free from any discontinuity and singularities associated with the optimal exercise boundary at the expiry time. These rather unique features have led to a significant enhancement of the computational accuracy and efficiency as shown in the examples.

International audience; In this paper, an enthalpic lattice Boltzmann method formulation for 3D unsteady convection-diffusion heat transfer problems is used to overcome discontinuity issues in heterogeneous media. The new formulation is based on the appearance of a source term added to the collision step. The major achievement of the proposed enthalpic LB formulation is avoiding any interface treatments or geometry considerations even when dealing with complex geometries. The performance of the present method is tested for several three-dimensional convection-diffusion problems. Comparisons are made with the control volume method, and numerical results show excellent agreements.

Analogue maps, such as illustrated paper maps, historical maps and map signboards, are detailed, thematic and attractive for local traveling. When integrated with mobile mapping on mobile devices s...

The main idea of the paper is to introduce a robust regression estimation method under an α-mixing dependence assumption, staying free of any parametric model restrictions while also allowing for some sudden changes in the unknown regression function. The sudden changes in the model may correspond to discontinuity points (jumps) or higher order breaks (jumps in corresponding derivatives) as well. We firstly derive some important statistical properties for local polynomial M-smoother estimates and we will propose a statistical test to decide whether some given point of interest is significantly important for a change to occur or not. As the asymptotic distribution of the test statistic depends on quantities which are left unknown we also introduce a bootstrap algorithm which can be used to mimic the target distribution of interest. All necessary proofs are provided together with some experimental results from a simulation study and a real data example.

In the current work, an advanced computational technique is formulated and performed to investigate the wave scattering problem from an infinitely transversally large anisotropic cylinder with arbitrary cross section. A meshless local Petrov–Galerkin method is used to discretize the anisotropic interior (inside the scatterer) and isotropic exterior (outside the scatterer) problems. The total electric fields inside and outside the scatterer are approximated by linear combinations of the generalized multiquadric radial basis functions. The local Heavisde step function is employed as the test function in weak formulation. Moreover, a simple collocation scheme is used to impose the interface and radiation boundary conditions directly. The proposed numerical technique is an efficient instrument to deal with practical complex scatterers and also has a good advantage in treating the material discontinuity at the interface between two different media. The performance and efficiency of the method are demonstrated ...

The extended displacement discontinuity boundary integral–differential equation method is developed for the analysis of an interface crack of arbitrary shape in a three-dimensional (3D), transverse...

The legal regulations require the minimum wage in Germany to be adjusted biennially which gives rise to a policy discontinuity. From the perspective of rational expectations models, such policy features render standard local approximation techniques infeasible. The article presents a stylized model in which negotiated wages and corporate profits are the outcome of an optimization problem, while changes to the minimum wage are modelled by a discontinuous policy rule. Using the simple example of minimum wage setting in Germany, the article illustrates how such models can be solved using the method of undetermined coefficients and presents selected simulation results.

This article presents a new flow continuity model by modifying the traditional Elrod-Adams model. Both fully flooded lubrication and starved lubrication can be predicted using the universal model. In particular, for the starved lubrication problem, the inlet and outlet boundaries of oil film can be automatically determined. The discontinuity of the convection flow (or lubricant transport velocity) at the interface between the full lubricant film region and the partial lubricant film region is overcome by introducing a transition region. In addition, the two-dimensional version of the presented model is deduced. Furthermore, using the presented model, the results are presented to gain insight on the influence of starvation on the friction for the textured ring–liner system.

This paper is devoted to study the well-known Razumikhin-type theorem for a class of stochastic functional differential equations with Levy noise and Markov switching. In comparison to the standard Gaussian noise, Levy noise and Markov switching make the analysis more difficult owing to the discontinuity of its sample paths. In this paper, we attempt to overcome this difficulty. By using the Razumikhin method and Lyapunov functions, we obtain several Razumikhin-type theorems to prove the pth moment exponential stability of the suggested system. Based on these results, we further discuss the pth moment exponential stability of stochastic delay differential equations with Levy noise and Markov switching. In particular, the results obtained in this paper improve and generalise some previous works given in the literature. Finally, an example is provided to illustrate the effectiveness of the theoretical results.

In most applications of computational fluid dynamics (CFD), it is very important to correctly project the interaction phenomena when we compute the typical discontinuous structure. Numerical methods for the conservation law are usually divided into two kinds: One is the “single stepping method”; another is the “semidiscrete scheme”. When the semidiscrete scheme handles the issues of high accuracy and operational process without oscillations, it is a very successful method. In this article, we consider the one-dimensional Euler equations for the Riemann problem of a typical shock tube without external active force to improve the nonphysical numerical oscillation problem near the contact discontinuity interface and shock wave. We try to improve the computational accuracy of numerical resolution of the Riemann problem and reduce nonphysical numerical oscillations through the AUSMDV numerical flux scheme with implementing distinct flux limiters and time-stepping methods. Using the conditions of single...

New discontinuity factors (DFs), i.e., individual and common DFs, for the simplified P3 (SP3) theory are proposed. In the individual DFs, two DFs are used for zeroth- and second-order angular momen...

It is well known that functionally graded materials can be used to eliminate the stress discontinuity that is often encountered in multilayer composites. In this article, the stress analysis for the coating-functionally graded interfacial layer-substrate structure under a rigid spherical punch is investigated. A linear multi-layer model is used to model the graded interfacial layer with arbitrary varying materials properties along the thickness direction. The spherical indentation problem is formulated in terms of a singular integrate equation with the method of transfer matrix and Hankel integral transform technique. The stress components in the coating-graded interfacial layer-substrate structure are calculated by solving the equation numerically. The results show that stiffens ratio and the gradient index of the graded interfacial layer has a significant effect on the distribution of stress components.

High-order finite difference discontinuity detectors are essential for the location of discontinuities on discretized functions, especially in the application of high-order numerical method...

The Lamb wave dispersion in a PZT/Metal/PZT sandwich plate is investigated by employing the exact linear equations of electro-elastic waves in piezoelectric materials within the scope of the plane-strain state. It is assumed that at the interfaces between the piezoelectric face layers and metal core layer, shear-spring and normal-spring type imperfect conditions are satisfied. The degree of this imperfectness is estimated through the corresponding shear-spring and normal-spring type parameters which appear in the contact condition characterizing the transverse and normal displacements’ discontinuity. The corresponding dispersion equation is derived, and as a result of the numerical solution to this equation, the dispersion curves are constructed for the first and second lowest modes in the cases where the material of the face layers is PZT and the material of the middle layer is Steel (St). Consequently, for the PZT/St/PZT sandwich plate, the study of the influence of the problem parameters such a...

International audience; We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of different tests when the intensity function of the observed inhomogeneous Poisson process has two different types of singularity: cusp and discontinuity. The asymptotic results are illustrated by numerical simulations.

This paper presents the analysis of scattering characteristics of two radially directed posts in an oversized circular waveguide making an arbitrary angle in the transverse plane using method of moments. Electric-type dyadic Green's function has been used to compute the scattered field in a circular waveguide. Simulated data on return loss and power coupling in the dominant mode and higher order modes have been compared with the data computed using Ansoft HFSS. The data on return loss for the incident TE11 mode have been compared with experimental data for the circular waveguide loaded with two posts.

Vehicle–track interaction at railway crossings is complex due to the discontinuity of the crossings. In this study, the effect of the local crossing geometry, the track alignment, and the wheel profiles on the wheel transition behaviour is investigated using the multi-body system software package VI-Rail. The transition behaviour is evaluated based on the location of the transition point along the crossing (and the location of impact), the contact pressure and the energy dissipation during the wheel–rail contact. A detailed parametric study of the crossing geometry has been performed, through which the most effective parameters for defining the crossing geometry are identified. These parameters are the cross-sectional shape of the nose rail, which can be tuned by one variable, and the vertical distance between the top of the wing rail and the nose rail. Additionally, a parametric study on the interaction influence of the crossing geometry, the track alignment and the wheel profile is performed using the d...

Action change detection in video aims to detect action discontinuity in video. The silhouettes-based features are desirable for action change detection. This paper studies the problem of silhouette-quality assessment. For that, a non-reference approach without the need for ground truth is proposed in this paper to evaluate the quality of silhouettes, by exploiting both the boundary contrast of the silhouettes in the spatial domain and the consistency of the silhouettes in the temporal domain. This is in contrast to that either only spatial information or only temporal information of silhouettes is exploited in conventional approaches. Experiments are conducted using artificially generated degraded silhouettes to show that the proposed approach outperforms conventional approaches to achieve more accurate quality assessment. Furthermore, experiments are performed to show that the proposed approach is able to improve the accuracy performance of conventional action change approaches in two human actio...

A new image segmentation algorithm based on mean shift (MS) is proposed, with an objective to single out croplands in high-resolution remote sensing imagery (HRRSI). The algorithm is composed of two parts. First, in order to improve the discontinuity preserving smoothing of MS filtering for cropland HRRSI, normal and uniform kernels are used to filter inner fields and boundary areas, respectively. A new spectral bandwidth estimation is also developed for better suppressing intra-field variation. Second, a two-stage region-merging technique, with the second stage combining mutual best-fit rule and iterative thresholding, is implemented. An HRRSI scene is used for validation, the results of which indicate good performance of our method.

The two-dimensional problem of scattering of small-amplitude surface water-waves by two symmetric vertical thin porous plates is investigated here assuming the linear theory. The problem is formulated in terms of two hypersingular integral equations of the second kind involving the discontinuities in the unknown symmetric and antisymmetric potential functions describing the motion in the fluid across one of the plates. Exploiting the conditions at the two tips of the plate, the discontinuity is approximated by expanding it in terms of a finite series involving Chebyshev polynomials of the second kind multiplied by an appropriate weight function, and then the integral equations are solved numerically by a collocation method. Using the solutions, the reflection and the transmission coefficient are computed numerically. The numerical results for the reflection and the transmission coefficients, amount of energy dissipation and the hydrodynamic forces are depicted graphically against the wave number. Known re...

The theory of distributions of L. Schwartz is a very useful and convenient way for the analysis of physical problems since physical distributions, especially charge distributions yielding the discontinuity of the potential and boundary conditions, can be correctly described in terms of mathematical distributions. To obtain the charge distributions, the distributional form of the Laplacian is applied to the Poisson's equation; therefore, for the correct representations and interpretations, the distributional forms and their proper applications are very important. In this article, it is shown that the distributional form of the Laplacian has been presented by Schwartz and also others with a missing term, leading to confusing and wrong results mathematically, and as a result electromagnetically; and the revised, correct, and complete distributional representations of the Laplace operator, the Poisson equation, and double layers, defined as the dipole layer and equidensity layer, are obtained and presented with detailed discussions and explanations including boundary conditions. By using the revised form of the Laplacian, Green's theorem is obtained explicitly with special emphases about important points and differences with previous works. The generalized forms of the Laplacian, Poisson's equation, charge densities, boundary conditions, and Greens theorem are also presented when there is a multi-layer on the surface of discontinuity.

Railway local irregularities are a growing source of ground-borne vibration and can cause negative environmental impacts, particularly in urban areas. Therefore, this paper analyses the effect of railway track singular defects (discontinuities) on ground vibration generation and propagation. A vehicle/track/soil numerical railway model is presented, capable of accurately predicting vibration levels. The prediction model is composed of a multibody vehicle model, a flexible track model and a finite/infinite element soil model. Firstly, analysis is undertaken to assess the ability of wheel/rail contact models to accurately simulate the force generation at the wheel/rail contact, in the presence of a singular defect. It is found that, although linear contact models are sufficient for modelling ground vibration on smooth tracks, when singular defects are present higher accuracy wheel/rail models are required. Furthermore, it is found that the variation in wheel/rail force during the singular defect contact depends on the track flexibility, and thus requires a fully coupled vehicle/track/foundation model. Next, a parametric study of ground vibrations generated by singular rail and wheel defects is undertaken. Six shapes of discontinuity are modelled, representing various defect types such as transition zones, switches, crossings, rail joints and wheel flats. The vehicle is modelled as an AM96 train set and it is found that ground vibration levels are highly sensitive to defect height, length and shape.

In this article, a new, higher-order accurate method, namely higher-order compact-flow field-dependent variation (HOC-FDV) method, has been developed to solve two-dimensional Navier-Stokes equations. The HOC-FDV scheme is of third-order accuracy in time and fourth-order in space. The spatial derivatives in the flow field-dependent variation (FDV) equations proposed by Chung are approximated using higher-order compact (HOC) Hermitian (Pade) scheme. The solution procedure at each time step consists of a system of block tri-diagonal matrices which can be solved efficiently in a standard manner. Several numerical examples are tested to examine the accuracy and capability of the new scheme to capture the shock and to simulate accurately separation and discontinuity.

In this study, an efficient meshless method named mixed radial point interpolation meshless method supplemented by a new (mixed) basis function is proposed. The proposed basis function is the multiplication of two conventional basis functions and possesses some extraordinary properties in comparison with conventional ones. In order to investigate the improvements of this basis function, an important type of electromagnetic problems, i.e. parallel plate waveguide with an internal discontinuity is analyzed. It is seen that the mixed basis function possesses better precision and convergence rate with respect to other basis functions.

We continue research of the new type of options called ‘British’ that was introduced recently by presenting the British lookback option with fixed strike. This article generalizes the work about the British Russian option and provides financial analysis of lookback options with fixed non-zero strike. The British holder enjoys the early exercise feature of American options whereupon his pay-off (deliverable immediately) is the ‘best prediction’ of the European lookback pay-off under the hypothesis that the true drift of the stock price equals a contract drift. We derive a closed-form expression for the arbitrage-free price in terms of the optimal stopping boundary of two-dimensional optimal stopping problem with a scaling strike and show that the rational exercise boundary of the option can be characterized via the unique solution to a nonlinear integral equation. We also show the remarkable numerical example where the rational exercise boundary exhibits a discontinuity. Using these results, we per...

The aim of this work is to delve into the numerical analysis of viscoplastic-type non-Newtonian fluid flows. Specifically, improvements in the spatial discretization schemes and the temporal integration methods have been proposed to overcome the numerical problems introduced by the transpose diffusive term and associated with the velocity field discontinuity, the artificial viscous diffusion, and the transpose viscous coupling. The resulting knowledge may be useful, among many other reasons, to improve the corresponding numerical simulations and gain insight into the underlying physics of this class of non-Newtonian fluid flows. The aim of this work is to delve into the numerical analysis of viscoplastic-type non-Newtonian fluid flows. Specifically, improvements in the spatial discretization schemes and the temporal integration methods have been proposed to overcome the numerical problems introduced by the transpose diffusive term and associated with the velocity field discontinuity, the artificial viscous diffusion, and the transpose viscous coupling. The resulting knowledge may be useful, among many other reasons, to improve the corresponding numerical simulations and gain insight into the underlying physics of this class of non-Newtonian fluid flows.

In this paper, I argue that there is neither valid deductive support nor strong inductive support for Kuhn’s incommensurability thesis. There is no valid deductive support for Kuhn’s incommensurability thesis because, from the fact that the reference of the same kind terms changes or discontinues from one theoretical framework to another, it does not necessarily follow that these two theoretical frameworks are taxonomically incommensurable. There is no strong inductive support for Kuhn’s incommensurability thesis, since there are rebutting defeaters against it in the form of episodes from the history of science that do not exhibit discontinuity and replacement, as Kuhn’s incommensurability thesis predicts, but rather continuity and supplementation. If this is correct, then there are no compelling epistemic reasons to believe that Kuhn’s incommensurability thesis is true or probable.

Word reordering is one of the challengeable problems of machine translation. It is an important factor of quality and efficiency of machine translation systems. In this paper, we introduce a novel reordering model based on an innovative structure, named, phrasal dependency tree. The phrasal dependency tree is a modern syntactic structure which is based on dependency relationships between contiguous non-syntactic phrases. The proposed model integrates syntactical and statistical information in the context of log-linear model aimed at dealing with the reordering problems. It benefits from phrase dependencies, translation directions (orientations) and translation discontinuity between translated phrases. In comparison with well-known and popular reordering models such as distortion, lexicalised and hierarchical models, the experimental study demonstrates the superiority of our model in terms of translation quality. Performance is evaluated for Persian → English and English → German translation tasks using Te...