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This article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced‐order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single‐degree‐of‐freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non‐intrusive methods. Specifically, a non‐intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element‐wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two‐ and three‐dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods. [ABSTRACT FROM AUTHOR]

The unrestricted Hartree‐Fock method is extended to correlation calculation within the density‐matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin‐orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi‐Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2. [ABSTRACT FROM AUTHOR]

In this work, we investigate complete stability behaviors of the Rosenzweig–MacArthur predator–prey model with delayed harvesting of the prey. The unharvested system exhibits either a steady‐state or an oscillatory dynamics for the coexistence of the species. We explore how the delayed harvesting affects the dynamics of these two modes by analyzing the system stability in effort‐delay bi‐parameter plane. Some novel dynamical scenarios and intricate dynamics are obtained. Analytical conditions for different stability scenarios are derived by examining the associated quasi‐polynomial eigenvalue equation. For invariant harvesting effort, the time delay induces four stability scenarios: stability invariance, instability invariance, stability change, and stability switching. On the other hand, the effort instigates five stability scenarios: stability invariance, instability invariance, stability change, instability change, and instability switching, when the delay strength is fixed. Majority of literatures on harvesting reported that harvesting stabilizes predator–prey interactions. However, we will show that the delayed harvesting can destabilize the system. One of the novelties of the study is to unveil the occurrence of effort‐induced chaos via period‐doubling mechanism. Interestingly, the effort‐induced switching phenomena and chaos do not occur for non‐delayed harvesting. [ABSTRACT FROM AUTHOR]

An analytical method for free vibration of functionally graded (FG) plates with arbitrary boundary conditions in thermal environments is developed based on 3D elasticity theory. Material properties of the FG plate are assumed to be temperature dependent but graded along with its thickness. At the edges of the plate, three different sets of linear springs are introduced, so that its boundary condition can be altered by changing the spring stiffness. Each displacement component of the plate is expanded as a standard Fourier cosine series, supplemented with closed‐form auxiliary functions. With thermal environment effects duly accounted for, the energy method is used to derive eigenvalue equations, whereas the Rayleigh−Ritz procedure is utilized to calculate the natural frequencies of the FG plate. Numerical examples show that the present method converges quickly and gives satisfactory results. The method is then utilized to calculate the natural frequencies of FG plates having different aspect ratios, volume fractions, and elastic boundaries. [ABSTRACT FROM AUTHOR]

Mode matching is a widely used method in various electromagnetic problems due to its dimensional advantages. However, the numerical implementation of mode matching is challenged by its high computational complexity in solving eigenvalue problems. The Lanczos method approximates the original eigenvalue problem in an efficient way and transforms the mode matching into an implicit form. The price of efficiency enhancement is the loss of eigenmode accuracy and behaviour interpretation. Its numerical efficiency is also influenced by block matrix dimensions while solving multi‐junctional waveguide structures. This work proposes a novel structure eigenmode restoration algorithm based on the Krylov subspace method. The method takes the conventional explicit mode matching strategy, but the efficiency enhancement for solving eigenmodes is prominent. The overall computational complexity is reduced from the original O(N3) to O(N1.5) without the cost of eigenmode accuracy loss. Numerical benchmark cases verify the proposed method's accuracy and efficiency. The efficiency advantage is outstanding especially in computational time. Extra discussions about eigenmode selection strategies based on accuracy controlling indicate that the proposed method possesses better flexibility in solving complicated waveguide problems. [ABSTRACT FROM AUTHOR]

In this article, characteristic modes for metallic‐dielectric composite structures (MDCS) are explored for fast and accurate analysis of scattering from large antenna arrays. Specifically, a generalized eigenvalue equation is formulated from a method of moments (MoM) impedance matrix of the electric field integral equation and Poggio, Miller, Chang, Harrington, Wu, and Tsai formulation. Modal currents for an antenna element with MDCS are then used as entire domain basis functions in the MoM for expanding equivalent currents over a large antenna array with MDCS. Only a small number of the modal currents are required to approximate the induced current over the antenna array with sufficient accuracy. Thus, the number of the unknowns and the corresponding CPU time in the MoM are significantly reduced in the proposed method. Furthermore, as the periodicity and intrinsic relationship of the matrix elements are considered when using the modal currents as entire domain basis functions, the computational efficiency of the proposed method is further improved. Numerical results of typical antenna arrays with MDCS are presented to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Reservoir computing (RC) is a machine‐learning paradigm that is capable to process empirical time series data. This paradigm is based on a neural network with a fixed hidden layer having a high‐dimensional state space, called a reservoir. Reservoirs including time delays are considered to be good candidates for practical applications because they make hardware realization of the high‐dimensional reservoirs simple. Performance of the well‐trained RCs depends both on dynamical properties of attractors of the reservoirs and tasks they solve. Therefore, in the conventional monostable RCs, there arise task‐wise optimization problems of the reservoirs, which have been solved based on trial and error approaches. In this study, we analyzed the relationship between the dynamical properties of the time‐delay reservoir and the performance in terms of the spectra of the delayed dynamical systems, which might facilitate the development of the unified systematic optimization techniques for the time‐delay reservoirs. In addition, we propose a novel RC framework that performs well on distinct tasks without the task‐wise optimization using bistable reservoir dynamics, which can reduce complicated hardware management of the reservoirs. [ABSTRACT FROM AUTHOR]

We put forward an algorithm for the issue on the partial eigenstructure assignment in a high‐order system, in which some certain eigenpairs, in a given system, can be assigned without changing others. Then a differential equation could be used to model the given systems, so that a multi‐input state feedback control deal with this assignment. Moreover, the algorithm requests the information of a few of the eigenpairs merely. As well some numerical cases are shown to prove the effect of our algorithm. [ABSTRACT FROM AUTHOR]

Summary: In variational data assimilation a least‐squares objective function is minimised to obtain the most likely state of a dynamical system. This objective function combines observation and prior (or background) data weighted by their respective error statistics. In numerical weather prediction, data assimilation is used to estimate the current atmospheric state, which then serves as an initial condition for a forecast. New developments in the treatment of observation uncertainties have recently been shown to cause convergence problems for this least‐squares minimisation. This is important for operational numerical weather prediction centres due to the time constraints of producing regular forecasts. The condition number of the Hessian of the objective function can be used as a proxy to investigate the speed of convergence of the least‐squares minimisation. In this paper we develop novel theoretical bounds on the condition number of the Hessian. These new bounds depend on the minimum eigenvalue of the observation error covariance matrix and the ratio of background error variance to observation error variance. Numerical tests in a linear setting show that the location of observation measurements has an important effect on the condition number of the Hessian. We identify that the conditioning of the problem is related to the complex interactions between observation error covariance and background error covariance matrices. Increased understanding of the role of each constituent matrix in the conditioning of the Hessian will prove useful for informing the choice of correlated observation error covariance matrix and observation location, particularly for practical applications. [ABSTRACT FROM AUTHOR]

Summary: This paper discusses techniques for computing a few selected eigenvalue–eigenvector pairs of large and sparse symmetric matrices. A recently developed class of techniques to solve this type of problems is based on integrating the matrix resolvent operator along a complex contour that encloses the interval containing the eigenvalues of interest. This paper considers such contour integration techniques from a domain decomposition viewpoint and proposes two schemes. The first scheme can be seen as an extension of domain decomposition linear system solvers in the framework of contour integration methods for eigenvalue problems, such as FEAST. The second scheme focuses on integrating the resolvent operator primarily along the interface region defined by adjacent subdomains. A parallel implementation of the proposed schemes is described, and results on distributed computing environments are reported. These results show that domain decomposition approaches can lead to reduced run times and improved scalability. [ABSTRACT FROM AUTHOR]

In this note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators div and curl. We also use this formula to deal with Maxwell and Stokes eigenvalue problems. [ABSTRACT FROM AUTHOR]

This work revisits the theory of the mixed Rossby–gravity (MRG) wave on a sphere. Three analytic methods are employed in this study: (a) derivation of a simple ad hoc solution corresponding to the MRG wave that reproduces the solutions of Longuet‐Higgins and Matsuno in the limits of zero and infinite Lamb's parameter, respectively, while remaining accurate for moderate values of Lamb's parameter, (b) demonstration that westward‐propagating waves with phase speed equalling the negative of the gravity‐wave speed exist, unlike the equatorial β‐plane, where the zonal velocity associated with such waves is infinite, and (c) approximation of the governing second‐order system by Schrödinger eigenvalue equations, which show that the MRG wave corresponds to the branch of the ground‐state solutions that connects Rossby waves with zonally symmetric waves. The analytic conclusions are confirmed by comparing them with numerical solutions of the associated second‐order equation for zonally propagating waves of the shallow‐water equations. We find that the asymptotic solutions obtained by Longuet‐Higgins in the limit of infinite Lamb's parameter are not suitable for describing the MRG wave even when Lamb's parameter equals 104. On the other hand, the dispersion relation obtained by Matsuno for the MRG wave on the equatorial β‐plane is accurate for values of Lamb's parameter as small as 16, even though the equatorial β‐plane formally provides an asymptotic limit of the equations on the sphere only in the limit of infinite Lamb's parameter. This article provides explicit expressions for the dispersion relation and meridional structure of the mixed Rossby–gravity (MRG) wave on a sphere and the accuracy of these analytic expressions is confirmed numerically. Unlike the equatorial β‐plane, on a sphere the westward‐propagating gravity wave is not excluded from the MRG spectrum. The approximation of the governing equations by a Schrödinger equation confirms that the MRG wave connects the n = 0 Rossby mode at large zonal wavenumber with the n = 0 zonally symmetric mode. [ABSTRACT FROM AUTHOR]

The purpose of this article is to report on improvements on the interpretation and insights emerging from dynamic decomposition weight analysis (DDWA). These improvements emerged from efforts to further automate and expand the eigenvalue elasticity analysis methods and resolve inconsistencies in assumptions made in published reports of DDWA usage. In addition to making available to the broad system dynamics community an improved toolset to perform eigenvalue elasticity analysis, in this paper we clarify the set of assumptions needed to obtain reliable results and develop a new framework to assess the impact of model parameters on the projections of behavior modes on stock behavior. We illustrate the use of these developments by updating a previously published model analysis. The paper concludes by summarizing our findings and their implications for the further development of structural dominance analysis. © 2018 System Dynamics Society [ABSTRACT FROM AUTHOR]

In this article, stabilization result for the Benjamin‐Bona‐Mahony‐Burgers' (BBM‐B) equation, that is, convergence of unsteady solution to steady state solution is established under the assumption that a linearized steady state eigenvalue problem has a minimal positive eigenvalue. Based on appropriate conditions on the forcing function, exponential decay estimates in L ∞ ( H j ) , j = 0 , 1 , 2 , and W 1 , ∞ ( L 2 ) ‐norms are derived, which are valid uniformly with respect to the coefficient of dispersion as it tends to zero. It is, further, observed that the decay rate for the BBM‐B equation is smaller than that of the decay rate for the Burgers equation. Then, a semidiscrete Galerkin method for spatial direction keeping time variable continuous is considered and stabilization results are discussed for the semidiscrete problem. Moreover, optimal error estimates in L ∞ ( H j ) ,   j = 0 , 1 ‐norms preserving exponential decay property are established using the steady state error estimates. For a complete discrete scheme, a backward Euler method is applied for the time discretization and stabilization results are again proved for the fully discrete problem. Subsequently, numerical experiments are conducted, which verify our theoretical results. The article is finally concluded with a brief discussion on an extension to a multidimensional nonlinear Sobolev equation with Burgers' type nonlinearity. [ABSTRACT FROM AUTHOR]

Summary: This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results. [ABSTRACT FROM AUTHOR]

A novel approach, referred to as the homotopy stochastic finite element method, is proposed to solve the eigenvalue problem of a structure associated with some amount of uncertainty based on the homotopy analysis method. For this approach, an infinite multivariate series of the involved random variables is proposed to express the random eigenvalue or even a random eigenvector. The coefficients of the multivariate series are determined using the homotopy analysis method. The convergence domain of the derived series is greatly expanded compared with the Taylor series due to the use of an approach function of the parameter h. Therefore, the proposed method is not limited to random parameters with small fluctuation. However, in practice, only single-variable and double-variable approximations are employed to simplify the calculation. The numerical examples show that with a suitable choice of the auxiliary parameter h, the suggested approximations can produce very accurate results and require reduced or similar computational efforts compared with the existing methods. [ABSTRACT FROM AUTHOR]

Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. In this paper, we introduce a new class of structured tensors called W-tensors, which not only extends the well-studied nonnegative tensors by allowing negative entries but also covers several important tensors arising naturally from spectral hypergraph theory. We then show that finding the maximum H-eigenvalue of an even-order symmetric W-tensor is equivalent to solving a structured semidefinite program and hence can be validated in polynomial time. This yields a highly efficient semidefinite program algorithm for computing the maximum H-eigenvalue of W-tensors and is based on a new structured sums-of-squares decomposition result for a nonnegative polynomial induced by W-tensors. Numerical experiments illustrate that the proposed algorithm can successfully find the maximum H-eigenvalue of W-tensors with dimension up to 10,000, subject to machine precision. As applications, we provide a polynomial time algorithm for computing the maximum H-eigenvalues of large-size Laplacian tensors of hyperstars and hypertrees, where the algorithm can be up to 13 times faster than the state-of-the-art numerical method introduced by Ng, Qi, and Zhou in 2009. Finally, we also show that the proposed algorithm can be used to test the copositivity of a multivariate form associated with symmetric extended Z-tensors, whose order may be even or odd. [ABSTRACT FROM AUTHOR]

To enhance the convergent rate and robustness of buck-type DC-DC converter system, a new finite-time voltage regulation control algorithm is proposed in this paper. First, an average state space-based model is analyzed, which considers both the parameters uncertainties and the variations of load and input voltage. By using saturation finite-time control theory, at the first step, in the absence of disturbance, a new fast voltage regulation control algorithm is designed, which can guarantee that the output voltage converges to the reference voltage in a finite time. Because the saturation constraint is considered during the controller design, the duty ratio function of the converter satisfies the constraint between 0 and 1. Second, in the presence of disturbance, a finite-time convergent disturbance observer is designed to estimate the unknown disturbances in a finite time. Finally, a disturbance observer-based finite-time voltage regulation control algorithm is developed. Compared with PI (Proportional-Integral) control algorithm, circuit simulations show that the proposed algorithm has a faster regulation performance and stronger robustness performance on disturbance rejection. [ABSTRACT FROM AUTHOR]

Principal component analysis is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations. Theoretically, such extreme high dimensionality will cause biased or inconsistent eigenvector estimates, but in practice, the principal component scores are used for visualization with great success. In this paper, we explore when and why the classical principal component scores can be used to visualize structures in high-dimensional data, even when there are few observations compared with the number of variables. Our argument is twofold: First, we argue that eigenvectors related to pervasive signals will have eigenvalues scaling linearly with the number of variables. Second, we prove that for linearly increasing eigenvalues, the sample component scores will be scaled and rotated versions of the population scores, asymptotically. Thus, the visual information of the sample scores will be unchanged, even though the sample eigenvectors are biased. In the case of pervasive signals, the principal component scores can be used to visualize the population structures, even in extreme high-dimensional situations. [ABSTRACT FROM AUTHOR]

The contour integral-based eigensolvers are the recent efforts for computing the eigenvalues inside a given region in the complex plane. The best-known members are the Sakurai-Sugiura method, its stable version CIRR, and the FEAST algorithm. An attractive computational advantage of these methods is that they are easily parallelizable. The FEAST algorithm was developed for the generalized Hermitian eigenvalue problems. It is stable and accurate. However, it may fail when applied to non-Hermitian problems. Recently, a dual subspace FEAST algorithm was proposed to extend the FEAST algorithm to non-Hermitian problems. In this paper, we instead use the oblique projection technique to extend FEAST to the non-Hermitian problems. Our approach can be summarized as follows: (a) construct a particular contour integral to form a search subspace containing the desired eigenspace and (b) use the oblique projection technique to extract desired eigenpairs with appropriately chosen test subspace. The related mathematical framework is established. Comparing to the dual subspace FEAST algorithm, we can save the computational cost roughly by a half if only the eigenvalues or the eigenvalues together with their right eigenvectors are needed. We also address some implementation issues such as how to choose a suitable starting matrix and design-efficient stopping criteria. Numerical experiments are provided to illustrate that our method is stable and efficient. [ABSTRACT FROM AUTHOR]

For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid-structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE-BE) method is developed for the numerical eigenanalysis of the fluid-structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton-Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE-BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE-BE method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We define Atkinson's semi-definite p-Laplacian eigenvalue problems, which include the regular p-Laplacian eigenvalue problems with L1 coefficient functions. Then we show that the Sturm oscillation theorem also holds for this eigenvalue problem. [ABSTRACT FROM AUTHOR]

In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler-DeWitt equation for the Friedmann-Lemaître-Robertson-Walker metric is completely equivalent to a Sturm-Liouville problem provided that the related eigenvalue and the cosmological constant be identified. The explicit calculation is performed with the help of a variational procedure with trial wave functionals related to the Bessel function of the second kind [ABSTRACT FROM AUTHOR]

We study the eigenvalue problem for the Neumann-Laplace operator in conformal regular planar domains [ABSTRACT FROM AUTHOR]

We present numerical methods for model reduction in the numerical simulation of disk brake squeal. Automotive disk brake squeal is a high frequency noise phenomenon based on self excited vibrations. Our method is based on a variation of the proper orthogonal decomposition method and involves the solution of a large scale, parametric eigenvalue problem. Several important challenges arise, some of which can be traced back to the finite element modeling stage. Compared to the current industrial standard our new approach is more accurate in vibration prediction and achieves a better reduction in model size. This comes at the price of an increased computational cost, but it still gives useful results when the classical modal reduction method fails to do so. We illustrate the results with several numerical experiments, some from real industrial models, some from simpler academic models. These results indicate where improvements of the current black box industrial codes are advisable. [ABSTRACT FROM AUTHOR]

Recalculating the subspace basis of a deformable body is a mandatory procedure for subspace simulation, after the body gets modified by interactive applications. However, using linear modal analysis to calculate the basis from scratch is known to be computationally expensive. In the paper, we show that the subspace of a modified body can be efficiently obtained from the subspace of its original version, if mesh changes are small. Our basic idea is to approximate the stiffness matrix by its low-frequency component, so we can calculate new linear deformation modes by solving an incremental eigenvalue decomposition problem. To further handle nonlinear deformations in the subspace, we present a hybrid approach to calculate modal derivatives from both new and original linear modes. Finally, we demonstrate that the cubature samples trained for the original mesh can be reused in fast reduced force and stiffness matrix evaluation, and we explore the use of our techniques in various simulation problems. Our experiment shows that the updated subspace basis still allows a simulator to generate visual plausible deformation effects. The whole system is efficient and it is compatible with other subspace construction approaches. [ABSTRACT FROM AUTHOR]

Here are described four solvers for time-harmonic electromagnetic fields in checkerboard patterns. A pattern is built by four squares with constant permittivity [ABSTRACT FROM AUTHOR]

Dielectric resonator antennas are widely used in wireless communication systems. A theory of characteristic modes (CMs) for modal analysis of dielectric resonators is highly demanded. Although a few earlier studies had proposed CM theory for modelling scattering from dielectric bodies, the physical characteristics of these CMs and their eigenvalues are not as clear as that of those for conducting bodies. This study revisits the CM theory for dielectric resonators. Following the Poynting's theorem and the PMCHWT (Poggio, Miller, Chang, Harrington, Wu, and Tsai) equation, two generalised eigenvalue equations are formulated. The resultant eigenvalues possess clear physical meanings that are the same as those of perfectly electrically conducting problems. In addition, other possible CM formulations based on the PMCHWT equation are also discussed. Mathematical proofs are given in the Appendix to show how to formulate CM theory to physically describe the fundamental resonant modes of dielectric resonators. Numerical results are given to show the proposed CM formulations are effective in solving resonant frequencies and modal fields for dielectric resonators. [ABSTRACT FROM AUTHOR]

Stochastic subspace identification (SSI) methods have been widely employed for oscillatory mode identification on probing and ambient data and are reported to have good performances. This work proposes a novel SSI-based approach for identifying dominant oscillatory mode from measurement data and extends the application of SSI to ringdown condition. The proposed approach first constructs an initial cluster of eigenvalues from SSI with repetitive calculations and then utilises a novel hierarchical clustering method to extract the dominant modes from the initial cluster. The repetitive calculations within the SSI are performed through varying the model order over a range defined by a novel initial order determination process. By doing so the challenge of model order determination for SSI-based methods is resolved. Moreover, benefiting from the repetitive calculations and the clustering process, the proposed approach is highly immune to prevalent noises in the measurements. Finally, the proposed approach is applied and validated on the field-measurement data from the phasor measurement units of China Southern Power Grid (CSG) through comparisons with Prony, ARMAX, and Monte Carlo methods. Test results demonstrate that the proposed approach performs with high accuracy, robustness, and efficiency in CSG. [ABSTRACT FROM AUTHOR]

In this paper, a new multilevel correction scheme is proposed to solve Stokes eigenvalue problems by the finite element method. This new scheme contains a series of correction steps, and the accuracy of eigenpair approximation can be improved after each step. In each correction step, we only need to solve a Stokes problem on the corresponding fine finite element space and a Stokes eigenvalue problem on the coarsest finite element space. This correction scheme can improve the efficiency of solving Stokes eigenvalue problems by the finite element method. As applications of this multilevel correction method, a multigrid method and an adaptive finite element technique are introduced for Stokes eigenvalue problems. Some numerical results are given to validate our schemes. [ABSTRACT FROM AUTHOR]

This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors to do reconstruction. Basic resolution and stability analysis are presented. Least-square norm methods with respect to Generalized Polarization Tensors are used for reconstruction of conductivities. Finally, reconstruction of three different types of conductivities in the plane is demonstrated. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Owing to the vulnerability of synthetic aperture radar (SAR) system to interferences, effective interference suppression has been an urgent task for SAR imaging. In this work, a novel time-varying narrowband interference and wideband interference suppression method is presented based on time-frequency reconstruction and mask technique. This method consists of four key stages. First, the authors present an efficient signal reconstruction method (ESRM) based on eigenvalue decomposition from the Wigner distribution. Next, echoes contaminated by the interference are identified in the frequency domain and the jamming components are obtained by using the mask technique in timefrequency plane. Then, the ESRM is applied to quickly and accurately synthesise interference signals by incorporating the principle of energy minimum without the need of the prior knowledge of the interference. Finally, the interference components are subtracted from the echoes in data domain, and the well-focused SAR image is obtained by conventional imaging algorithm. Results of simulated and measured data prove the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Let ( a, b) be a finite interval and 1/ p, q, r∈ L1[ a, b]. We show that a general solution (in the weak sense) of the equation ( p u′)′+ q u = λ r u on ( a, b) can be constructed in terms of power series of the spectral parameter λ. The series converge uniformly on [ a, b] and the corresponding coefficients are constructed by means of a simple recursive procedure. We use this representation to solve different types of eigenvalue problems. Several numerical tests are discussed. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a design method of finite dimensional robust H ∞ distributed consensus filters (DCFs) for a class of dissipative nonlinear partial differential equation (PDE) systems with a sensor network, for which the eigenvalue spectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement. Initially, the modal decomposition technique is applied to the PDE system to derive a finite dimensional ordinary differential equation system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Then, based on the slow subsystem, a set of finite dimensional robust H ∞ DCFs are developed to enforce the consensus of the slow mode estimates and state estimates of all local filters for all admissible nonlinear dynamics and observation spillover, while attenuating the effect of external disturbances. The Luenberger and consensus gains of the proposed DCFs can be obtained by solving a set of linear matrix inequalities (LMIs). Furthermore, by the existing LMI optimization technique, a suboptimal design of robust H ∞ DCFs is proposed in the sense of minimizing the attenuation level. Finally, the effectiveness of the proposed DCFs is demonstrated on the state estimation of one dimensional Kuramoto-Sivashinsky equation system with a sensor network. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the MDGKN type, where the different n × n matrices have certain characteristic properties. These matrix properties have consequences for the underlying eigenvalue problem. Engineers have developed a good intuitive understanding of such systems, particularly for systems without gyroscopic terms ( G-matrix) and circulatory terms ( N-matrix, which may lead to self-excited vibrations). A number of important engineering problems in the linearized form are described by this type of equations. It has been known for a long time, that damping ( D-matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. Here we present some new results (using a variety of methods of proof) on the influence of the damping terms, which are quite general. Starting from a number of conjectures, they were jointly developed by the authors during recent months. [ABSTRACT FROM AUTHOR]

Given a bounded open set [ABSTRACT FROM AUTHOR]

A new developed approximation is used to obtain the arbitrary l-wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic-type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov-Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Let [ABSTRACT FROM AUTHOR]

It is shown in the Weyl limit-point case that system of root functions of the non-self-adjoint Bessel operator and its perturbation Sturm-Liouville operator form a complete system in the Hilbert space. Furthermore, asymptotic behavior of the eigenvalues of the non-self-adjoint Bessel operators is investigated, and it is proved that system of root functions form a Bari basis in the same Hilbert space. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large-scale linear systems of equations and eigenvalue problems as well as to the construction of blurring matrices. Extensions that allow the matrix A to be rectangular and applications to Lanczos bidiagonalization, as well as to the recently proposed subspace-restricted SVD method for the solution of linear discrete ill-posed problems, also are considered.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we introduce two types of q-deformed Wigner algebras. One is q-deformation of Wigner algebra with q-reflection symmetry and another is q-deformation of Wigner algebra with reflection symmetry. For two types of q-deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q-calculus, we introduce the (q; ν)- numbers, (q; ν)-derivatives and (q; ν)-Hermite polynomials for two algebras. For the deformation parameter q = 1 - ϵ with small ϵ, we discuss the thermodynamics of the particle obeying the q-deformed Wigner algebra. [ABSTRACT FROM AUTHOR]

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a large class of derivative-assets. The payoff of the derivative-assets may be path-dependent. In addition, the process underlying the derivatives may exhibit killing (i.e., jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility may be multiscale, in the sense that it may be driven by one fast-varying and one slow-varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative-assets: a vanilla option on a defaultable stock, a path-dependent option on a nondefaultable stock, and a bond in a short-rate model. [ABSTRACT FROM AUTHOR]

In this work, we review recent extensions of the density functional tight binding (DFTB) methodology and its application to organic and biological molecules. DFTB denotes a class of computational models derived from density functional theory (DFT) using a Taylor expansion around a reference density. The first- and second-order models, DFTB1 and DFTB2, have been reviewed recently ( WIREs Comput Mol Sci 2012, 2:456-465). Here, we discuss the extension to third order, DFTB3, which in combination with a modification of the Coulomb interactions in the second-order formalism and a new parametrization scheme leads to a significant improvement of the overall performance. The performance of DFTB2 and DFTB3 for organic and biological molecules are discussed in detail, as well as problems and limitations of the underlying approximations. WIREs Comput Mol Sci 2014, 4:49-61. doi: 10.1002/wcms.1156 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a second-order resonance anti-periodic boundary value problem [ABSTRACT FROM AUTHOR]

A generalization of the concept of Wigner's symmetrical operator, i.e., of the operator invariant under symmetry transformations forming a group, namely ${\cal G}$, is proposed here. Symmetrical operators in the present general sense do constitute a set whose elements are mutually commuting and equivalent to each other under transformations ${S_i} \in {\cal G}$. A generalization of a well known theorem attributed to Wigner is established: for a given operator  and its equivalent ones Â[ i] = Ŝ [ABSTRACT FROM AUTHOR]

The aim of this note is to give a sharp upper bound on the ratio[formula]where φ is a nonconstant eigenfunction for the Laplace–Beltrami operator on a connected compact Riemannian manifold without boundary. This ratio is always positive, since maxφ>0 and minφ<0 for every nonconstant eigenfunction. We assume that maxφ≥−minφ, in order to simplify the notation. For the case of a two-dimensional manifold with nonnegative Ricci curvature, our theorem implies that the above ratio is less than the ratio of the maximum divided by the absolute value of the minimum of the Bessel function of order zero.The proof is based on a gradient estimate from a previous paper of the author (see [5]), which in turn was proved using the maximum principle technique. In contrast to the standard applications of gradient estimates, which are based on integration along geodesics, we arrive at a contradiction by integrating the gradient estimate over small spheres centred at a point where the absolute value of the eigenfunction attains its maximum.The main motivation for our work is that the ratio of the maximum and the minimum of an eigenfunction plays a role in estimates of the corresponding eigenvalues (see [5] and [7]). More precisely, our theorem implies that there are minimizing sequences of compact manifolds such that the first eigenvalues of the manifolds approach the corresponding lower bound for the first eigenvalue obtained in [5, Theorem 2] for every possible ratio of the maximum and the minimum of the corresponding eigenfunction. 1991 Mathematics Subject Classification 58G25. [ABSTRACT FROM AUTHOR]

The article discusses the approximation of ground state Eigenfunction on the snowflake domain. It reveals that constructing a piecewise smooth homeomorphism with elliptic operators might extend the result to more general snowflake type regions. It also presents the power series representation of the Eigenfunction.