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Kraft paper is the most popular raw material for based-paper packaging containers. Poisson’s ratio is an important index to indicate the inherent property of materials. There were many difficulties to measure Poisson’s ratio of kraft paper using the traditional contract methods, because of its micro deformation and anisotropy. A simple and efficient non-contract method had been proposed to solve this problem using DIC(Digital Image Correlation) method in this paper. Obtained the relative deformation of samples by calibrated CCD images, Poisson’s ratio could be computed. The test results indicated that Poisson’s ratios of corrugating medium in the MD(Machine Direction) and CD (Cross-machine Direction) were 0.275 and 0.119, and ones of linerboard were 0.275 and 0.119 in MD and CD, respectively. This study showed that DIC was a new approach to measure Poisson’s ratio of kraft paper.

We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

An analytical approach for contact bodies of heavy-manipulator is presented in this paper based on the derivation of an entirety motion equation in the contact region and an entirety analysis method for 3D contact/impact problem is proposed. Using this method, contact force is derived and solved under the common motion status and is used to be the criteria for evaluating contact conditions. This method is used to simulate the collision of two bodies and its validity is verified.

The paper presents a brief mathematical investigation of the continuity properties of the Somigliana displacement and stress identities. It is shown that the regularity conditions for the boundary-integral equation are fully consistent with the continuity requirements for the interior displacements and stresses in elasticity. A new stress-based BIE is obtained. The implications of the new stress-based BIE on the continuity of BEM formulations will be discussed in the full paper.

This paper extracts the period of GPS elevation time series based on HHT algorithm. Firstly, the signal is decomposed by EMD. Taking the PBO fiducial stations, P061, P359, P059, P123, P067, P042 as the examples, the time series in elevation direction from 2008 to 2013 were decomposed into a finite number of intrinsic mode function, whose frequency was decreasing. Through the statistics, the result shows there are half of the month periodic oscillation graph, month periodic oscillation graph, double months periodic oscillation graph, annual periodic oscillation graph half of the annual periodic oscillation graph and annual periodic oscillation graph. Secondly, every component is transformed with Hilbert algorithm. Through the three-dimensional Hilbert spectrum in time-frequency energy space, the offshore stations’ energy on the whole month and bi-monthly periodic oscillation is greater than the inland stations’. Finally, according to the different physical reasons to the elevation, this paper explores the causes of the different periodic oscillation.

In this paper, we try to extend human eyes’ contrast sensitivities characteristics (CSF) to three-dimensional space, but the experimental results show that the traditional characteristics of CSF has limitations in three-dimensional space. In order to investigate the characteristics of human eyes’ CSF in three-dimensional space, the traditional CSF test method is developed to measure the corresponding values of CSF in different inclined planes in three-dimensional space. Human visual contrast sensitivity characteristics with different inclined angles \(\theta \) are analyzed, and the mathematical expression of \(\theta -CSF\) is built up based on the experimental results. The proposed \(\theta -CSF\) model of three-dimensional space in this paper can well reflects human visual contrast sensitivity characteristics in 3D space and has significant effect on three-dimensional image processing.

Frequently alluded in the foregoing chapters, we will now deal in more detail with the problem of Rayleigh’s hypothesis. In 1907, Lord Rayleigh published a paper on the dynamic theory of gratings, as mentioned earlier in Chap. 1. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces in Cartesian coordinates (see Fig. 6.1). Those gratings are of importance in many different fields of physics and in engineering. They are used as dispersive elements in grating spectrographs, for example. In his paper, Rayleigh used a series expansion of the scattered wave in terms of outgoing plane waves only, i.e., in terms of waves which move only away from the grating. He determined the unknown expansion coefficients later by application of the boundary conditions at the periodic surface appropriately, as discussed in Chap. 1. For the special case of a perpendicularly incident plane wave on a sinusoidal but perfectly conducting surface, he derived an equation system which is at first independent of the groove depth. But Rayleigh approximated this system later to allow for an iterative solution for shallow grooves.

In Euclidean vector spaces, dimensionality reduction can be centered at the data mean. In contrast, distances do not split into orthogonal components and centered analysis distorts inter-point distances in the presence of curvature. In this paper, we define a dimensionality reduction procedure for data in Riemannian manifolds that moves the analysis from a center point to local distance measurements. Horizontal component analysis measures distances relative to lower-order horizontal components providing a natural view of data generated by multimodal distributions and stochastic processes. We parametrize the non-local, low-dimensional subspaces by iterated horizontal development, a constructive procedure that generalizes both geodesic subspaces and polynomial subspaces to Riemannian manifolds. The paper gives examples of how low-dimensional horizontal components successfully approximate multimodal distributions.

The purpose of this paper is to introduce and study Ishikawa iterative algorithms for solving the SFP in the setting of infinite-dimensional Hilbert spaces. The main results presented in this paper improve and extend some recent results done by Xu [Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problems 26 (2010) 105018]. At the end we prove that the accumulation of errors in Ishikawa iterative CQ algorithm is bounded in certain range.

In this paper, we apply the solution of the Schrodinger equation, i.e. the Schrodinger operator, to the graph characterization problem. The motivation behind this approach is two-fold. Firstly, the mathematically similar heat kernel has been used in the past for this same problem. And secondly, due to the quantum nature of the Schrodinger equation, our hypothesis is that it may be capable of providing richer sources of information. The two main features of the Schrodinger operator that we exploit in this paper are its non-ergodicity and the presence of quantum interferences due to the existence of complex amplitudes with both positive and negative components. Our proposed graph characterization approach is based on the Fourier analysis of the quantum equivalent of the heat flow trace, thus relating frequency to structure. Our experiments, performed both on synthetic and real-world data, demonstrate that this new method can be successfully applied to the characterization of different types of graph structures.

In this paper we present a new approach for characterizing graphs using the solution of the wave equation. The wave equation provides a richer and potentially more expressive means of characterizing graphs than the more widely studied heat equation. Unfortunately the wave equation whose solution gives the kernel is less easily solved than the corresponding heat equation. There are two reasons for this. First, the wave equation can not be expressed in terms of the familiar node-based Laplacian, and must instead be expressed in terms of the edge-based Laplacian. Second, the eigenfunctions of the edge-based Laplacian are more complex than that of the node-based Laplacian. In this paper we present a solution to the wave equation, where the initial condition is Gaussian wave packets on the edges of the graph. We propose a global signature of the graph which is based on the amplitudes of the waves at different edges of the graph over time. We apply the proposed method to both synthetic and real world datasets and show that it can be used to characterize graphs with higher accuracy.

This paper is presenting a new and efficient method for computing the charge and current distribution on a circular disk type surface. Integral equation is formulated for the circular loop geometry (taking into the account of Moment Method) to cast the equation for charge and current distribution. The technique involves extension of the conventional Pocklington’s integral equation and the uses of antenna’s effective parameters. Paper consist of a transformation into a single integral equation, and then into a linear system of algebraic equation. Plot of the current distribution along the antenna are finally given and compared with conventional thin wire antenna using matrix inversion technique.

In the paper, we present a two-dimensional problem that is obtained by sampling in time and linearising a problem regarding two-phase flow of a viscous fluid without mixing. The fluid satisfies the incompressible Navier-Stokes equations, and it is assumed that there is a time-varying curved interface Γ between liquid phases of different densities and viscosities. The primary result of this paper is an estimate of the convergence rate of an approximate solution to the exact solution of a problem regarding special norms. The results of numerical experiments agree with theoretical estimates of the convergence rate of the approximate solution to the exact solution in the special norms of grid spaces.

In this paper, the influence of the resolution of fractal interfaces to the contact area is investigated by taking into account shear displacements. The paper is based on fractal approaches for the modeling of the multiscale self-affine topography of these interfaces where unilateral contact conditions are assumed to hold. More specifically for every value of the shear displacement a solution is taken in terms of normal forces and displacements at the interface, for different values of the resolution δ and for different values of normal forces. At each scale a classical Euclidean problem is solved. This procedure is applied for the simulation of a unilateral contact problem between two elastic bodies and between two bodies with elastoplastic behavior with hardening. In both cases the same fractal interface is adopted and the same multi-resolution analysis has been performed.

Part 6: Shape and Structural Optimization; International audience; The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ωs in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of Min-Max of a convex-concave Lagrangian with saddle point, and (ii) using a new regularity result on the solution of the wave problem (where the Dirichlet condition on the fixed part of the boundary is essential) to analyze the strong derivative.

In this paper, the authors present a numerical approach to study Defect detection through Stochastic Wave Finite Element Method. The uncertain material properties are modeled as a set of random fields. The structure is presented considering two waveguides connected through a stochastic coupling element, simulated as the defect (crack). Diffusion matrix for uncertain media through stochastic wave finite element method is studied in this paper. The forced response following a vibratory excitation is computed to investigate the defect detection. The computational efficiency of the method is demonstrated by comparison with MC simulation.

In this paper, we propose a numerical scheme to solve a kind of the nonlinear telegraph equation by using the Kansa’s method with Radial Basis Functions (RBFs). From the numerical results of experiments presented in this paper, we can get that the accuracy between the numerical solutions and the analytical solutions are valid. In this paper, we also give the analysis of the parameter c in IMQ radical basis function for the results.

Lyapunov exponents of a dynamical system give information about its long-term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In a previous paper, the authors proposed an algorithm for Lyapunov exponents estimation in piecewise linear systems that strongly reduces the computational time. In this paper, the algorithm is applied also to chaotic systems with polynomial nonlinearity. Firstly, a suitable piecewise linear approximation for the polynomial nonlinear function is evaluated by means of a Multi-Layer Perceptron neural network with linear and saturating linear transfer functions. Then, the linearity of the new state equation and of the variational equation, obtained resorting to the piecewise linear approximation of the nonlinear function, are exploited to accurately evaluate Lyapunov exponents of the approximated system with a reduced execution time.

In this paper, a fourth-order non-homogeneous parabolic partial differential equation with initial and separated boundary conditions is solved by using a non-polynomial spline method. In the solution of the problem, finite difference discretization in time, and parametric quintic spline along the spatial coordinate have been carried out. The result shows that the applied method in this paper is an applicable technique and approximates the exact solution very well.

The second author of this paper has designed a conservative front-tracking method. The method tracks discontinuities by using the conservation property of the hyperbolic conservation laws rather than the Hugoniot condition. We compute the numerical solution on each side of a discontinuity using information only from the same side. In this paper, we develop the method for one-dimensional scalar conservation laws with nonconvex flux. Numerical examples are presented to show the robustness and accuracy of the method.

Propagating waves in a binary gas mixture from a boundary of variable temperatures and velocities are discussed on the basis of two Boltzmann equations. Variable temperatures on the boundary could be gotten by using a thin thermal absorbent with fine holes heated by laser lights of variable powers, and variable velocities on a boundary could be gotten by moving gases through a porous media. In this paper, the Hermite expansion method (Grad [1]) of the distribution function would be extended to a binary gas-mixture, i.e. the Herimite expansion method is used to solve two distribution functions for both gases. We have two Boltzmann equations expanded by Hermite functions. The Galerkin method is applied to solve two Boltzmann equations, i.e. the scalar products of Hermite functions and two expanded Boltzmann equations are executed. Thus, a system of partial differential equations for the expansion coefficients, which are functions of position and time, is obtained. The Hermite expansion is taken up to the third order, so that we have twenty coefficients and a system of twenty partial differential equations. Here, the one dimensional flow in space is considered, so that the number of expansion coefficients and differential equations would reduce from twenty to eight. The intermolecular force consisting of an inverse fifth- and inverse third- order power of intermolecular distance. We have applied this method to the relaxation phenomena of the binary gas mixture with different temperatures and velocities, which are both uniform in space ([2]and [3]). In this paper, we are going to discuss propagating waves in the gas mixture. Temperatures, number densities and velocities at x = 0 could be given. We calculate numerically the time developments of velocity, temperature and number density. The initial conditions of \( v_1^{(i)}(x,0), T^{(i)}(x,0), n^{(i)}(x,0) \) etc. are taken as uniform in 0 ≤ x ≤ ∞ . The boundary conditions at x = 0 are taken as \( T^{(i)}(0,t)=T_b^{(i)}(t),\> v_1^{(i)}(0,t)=u_b^{(i)}(t), \> n^{(i)}(0,t)=n_b^{(i)}(t) \). Time developments of temperatures, mass velocities and number densities etc. have been calculated.

This paper is concerned with an iterative functional equation from the problem of invariant curves. By reducing the equation with the Schroder transformation to another functional equation without iteration of the unknown function f. For technical reasons, in previous work the constant λ given in the Schroder transformation is required to fulfil that λ is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we obtain analytic solutions in the case of λ at resonance, i.e., at a root of the unity and the case of λ near resonance under the Brjuno condition.

This paper presents a method for generation iterated function systems fractal attractor images based on hidden Markov model. The method can draw the shape and color of fractal images by using probability matrix. Furthermore, the paper also gives a method to show how to draw the local shape and color with multi-level by resolving the affine transformations of IFS into many affine transformations of sub-images. Finally, the effect of the method is showed by computer experiments in the simulation of the trees etc.

This paper is concerned with a functional differential equation with state dependent delay. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtain. For technical reasons, in previous work the constant α given in the Schroder transformation, is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.

In the paper an interval method for solving the one-dimensio-nal heat conduction equation with mixed boundary conditions is considered. The idea of the interval method is based on the finite difference scheme of the conventional Crank-Nicolson method adapted to the mixed boundary conditions. The interval method given in the form presented in the paper includes the error term of the conventional method.

The paper deals with the interval backward finite difference method for solving the one-dimensional diffusion equation with the position dependent diffusion coefficient and the boundary conditions of the first type. The interval method considered is based on the conventional backward finite difference method. Moreover, it takes into account a formula of a local truncation error of the method. Such local truncation error of the conventional method is bounded by the appropriate interval values. In most scientific applications we cannot find the endpoints of such intervals exactly and it is of great importance to approximate them in the most accurate way. The paper presents a method of such approximation.

The Barcelona Basic Model (Alonso et al. 1990) yield locus has been proven to be non-convex for certain set of parameters (see Wheeler at al. 2002). This paper shows that as this model is formulated in the semi-logarithmic space, the elastic stress path corresponding to a given strain increment is not a straight line. Therefore, the simple assumption that the stress increment is elastic when the stress state is elastic at the beginning and the end of the stress path is no longer correct. The paper examines some strain increments leading to elasto-plastic stress paths which may be easily mistaken for being fully elastic. Some of the stress paths described in the paper can only occur when certain sets of parameters of the Barcelona Basic Model are selected, but others are not dependent on the model parameter set. In the latter case the described mechanism may be relevant to great many other constitutive models which assume a constant shear modulus G and are formulated in the semi-logarithmic space.

Being the only imaging modality capable of delineating the anatomical structure of the white matter, diffusion magnetic resonance imaging (dMRI) is currently believed to provide a long-awaited means for early diagnosis of various neurological conditions as well as for interrogating the brain connectivity. Despite substantial advances in practical use of dMRI, a solid mathematical platform for modelling and treating dMRI signals still seems to be missing. Accordingly, in this paper, we show how a Hilbert space of $\mathbb{L}^2$-valued mappings $u: X \to \mathbb{L}^2({\mathbb{S}^2})$, with X being a subset of ℝ3 and $\mathbb{L}^2({\mathbb{S}^2})$ being the set of squared-integrable functions supported on the unit sphere ${\mathbb{S}^2}$, provides a natural setting for a specific example of dMRI, known as high-angular resolution diffusion imaging. The proposed formalism is also shown to provide a basis for image processing schemes such as total variation minimization. Finally, we discuss a way to amalgamate the proposed models with the tools of compressed sensing to achieve a close-to-perfect recovery of diffusion signals from a minimal number of their discrete measurements. The main outcomes of this paper are supported by a series of experimental results.

We consider left-invariant diffusion processes on DTI data by embedding the data into the space $\mathbb{R}^3\rtimes S^2$ of 3D positions and orientations. We then define and solve the diffusion equation in a moving frame of reference defined using left-invariant derivatives. The diffusion process is made adaptive to the data in order to do Perona-Malik-like edge preserving smoothing, which is necessary to handle fiber structures near regions of large isotropic diffusion such as the ventricles of the brain. The corresponding partial differential systems are solved using finite difference stencils. We include experiments both on synthetic data and on DTI-images of the brain.

In this paper, a new modal parameters identification method is presented based on NExT (natural excitation technique) and the response data of the structure under non-stationary ambient excitation the white noise excitation assumption for NExT is extended to a MA (q) model assumption to establish an extended NExT method. Then the assumption that the non-stationary excitation is composed of a (d-1)-th order polynomial and a MA(q) model is proposed. Taking d-th order difference of the non-stationary excitation yields a MA(q+d) model, which satisfies the assumption of the extended NExT method mentioned above. Thus, the extended NExT method can be used in the condition of non-stationary excitation. In order to reduce the error of difference calculation during identification implementation, the difference computation is performed in frequency-domain instead of time-domain. The identification results from the proposed method are compared with the standard NExT for a three DOFs (degrees of freedom) vibration system and the finite element (FE) model of Longtanhe Bridge. The results show that the method proposed in this paper can obtain better modal parameters of the system under non-stationary ambient excitation than the standard NExT.

In this paper existence of local analytic solutions of an iterative functional differential equation is studied. As well as in previous works, we reduce this problem with the Schrodƒtƒt er transformation to finding analytic solutions of a functional equation without iteration of the unknown function x. For technical reasons, in previous works the constant ƒN given in the Schroƒtƒtder transformation is required to fulfil that ƒN is off the unite circle s1 or lies on the circle with the Diophantine condition. In this paper, we obtain analytic solutions in the case of ƒN at resonance, i.e., at a root of the unity and the case of near resonance under the Brjuno condition.

(1.1) Let M be a two-dimensional C2-manifold endowed with a C2-Riemannian metric. We say that M is a generalized surface if the metric in M is allowed to degenerate at isolated points; such points are called singularities of the metric. In this paper we use the method of Fiala-Bol (cf. [12, 9]) to give a proof of the following general isoperimetric inequality.

Within this paper we consider scattering problems with periodic exterior domains, modeled by the Helmholtz equation. Most current works on this subject make specific assumptions on the geometry of the periodic cell, e.g. special symmetries or shapes, and cannot be generalized to higher space dimensions in an easy way. In contrast our goal is the realization of an easy dimension independent concept which is valid for all kinds of periodic structures with local defects. We will first give a general analytical formulation and then present an algorithmic realization. At the end of the paper we will also depict a 1D and 2D example.

In this paper, first, we provide a resultant-based implicitization method for revolution surfaces, generated by non necessarily rational curves. Secondly, we analyze the offsetting problem for revolution surfaces, proving that the offsetting and the revolution constructions are commutative. Finally, as a consequence of this, the (total and partial) degree formulas for the generic offset to an irreducible plane curve, given in our previous papers, are extended to the case of offsets to surfaces of revolution.

This paper describes the addition law for a new form for elliptic curves over fields of characteristic 2. Specifically, it presents explicit formulae for adding two different points and for doubling points. The case of differential point addition (that is, point addition with a known difference) is also addressed. Finally, this paper presents unified point addition formulae; i.e., point addition formulae that can be used for doublings. Applications to cryptographic implementations are discussed.

The analytical review of the existing dynamic technical theories of thin-walled beams of open profile is carried out, from which it follows that all papers in the field can be divided into three groups. The papers, wherein the governing set of equations is both hyperbolic and correct from the viewpoint of the physically admissible magnitudes of the velocities of the transient waves resulting from these equations, fall into the first category. The second category involves the articles presenting hyperbolic but incorrect equations from the above mentioned viewpoint, i.e. resulting in incorrect magnitudes of the transient waves. The papers providing the governing system of equations which are not hyperbolic fall into the third group. The simple but effective procedure for checking for the category, within which this or that paper falls in, has been proposed and illustrated by several examples. It has been shown that only the theories of the first group, such as the Korbut–Lazarev theory, could be used for solving the problems dealing with transient wave propagation, while the theories belonging to the second and third group could be adopted for static problems only.

3-dimensional scanner is a data acquisition tool in recent years. The scanned datum are 3-dimension discrete points. Veracity of approximation curvature of 3-dimension discrete points is difficulty. In this paper, according to geometrical properties of 3-dimension curve, a method of curvature calculation of 3-dimension discrete points on edge curve is introduced. Concretely, Firstly, feasibility in theory of method in this paper is proved; secondly, virtual arc is used to approximate discrete edge curve, so that curvature and correction-curvature will be calculated; thirdly, method in this paper is contrasted with method dealing with similar question in experiment, and the result of experiment manifests that accuracy of method in this paper is better than method contrasted; finally, an application experiment is made.

Recently, there are increasing attention paid on compressed sensing which is distinct different from traditional signal processing and image reconstructed from indirect or incomplete measurement, especially l 1-norm problem which is transformed from compressive sensing. The idea of l 1_regularization, as the one of l 1-norm, has been receiving a lot of interest in signal processing, image recovery and statistic, etc. This paper will introduces a continuation log-barrier method for solving l 1_regularized least squares problem in the field of compressive sensing, which is a second-order method. Our work is inspired by the work in [4] and continuation idea, and the paper will introduce the continuation technique to increase the convergence rate. Therefore, Our continuation log-barrier method for l 1_regularized least square problem is accurate and fast in the sense.

In this paper, the problems of calculating and solution about axial symmetric electric fields were studied. An accurate theoretic model was established that it can be applied in high-performance numerical calculation. The new calculating method was proposed using Maxwell’s equations and calculus under the conditions of static, axial symmetric, contains charge, finite, differentiable and integrabel. This new calculating method was called alternating iterative method and its expression form was also given here. The electric field outside of axis can be expressed as each order derivative and one-dimensional integration of electric field which on the symmetric axis and also electric charge. By means of this method, the result is progression form, which is the best form for computer approximate calculation. It’s very easy, quick and accurate to carry out numerical calculation by using this method. The calculation method provided in this paper has important theoretical significance and broad prospect of application.