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The paper addresses the problem of determining the field of a reflected wave in a multiscale inhomogeneous medium, which consists of a background deterministic large-scale irregularity and multiscale random irregularities with scales both larger and smaller than the wavelength. A layer with a linear permittivity profile is taken as the background irregularity. The small-scale irregularities are responsible for wide-angle scattering including backscattering. The first approximation of the perturbation theory is used to account for scattering from these irregularities. As the zero approximation and Green's function in determining the field backscattered by small-scale irregularities, we utilize the integral representation of the field, obtained in our earlier work by combining the method of double weighted Fourier transform (DWFT) and the Fock proper-time method. Asymptotic methods are used to reduce the sevenfold integral representation of a field to lower-order integrals. Conditions for validity of such representations are obtained. Formulas of the frequency coherence functions of waves reflected and backscattered from the turbulent plasma layer are given. The paper presents the results of the simulation of pulse sounding of a randomly inhomogeneous reflecting plasma layer demonstrating the effect of large-scale irregularities on backscattering by small-scale irregularities. [ABSTRACT FROM AUTHOR]

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series. [ABSTRACT FROM AUTHOR]

In this paper, an IVP for a system of two singularly perturbed delay differential equations with Robin initial conditions is considered. A Shishkin piecewise uniform mesh is implemented and combined with a classical finite difference method to create a numerical method for solving this problem. The numerical approximations obtained are essentially first order convergence uniformly with respect to the singular perturbation parameters. Numerical result is provided in support of the theory. [ABSTRACT FROM AUTHOR]

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT. [ABSTRACT FROM AUTHOR]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, the fractal variational theory is used to show the basic property of the fractal oscillator, and a new form of the Toda oscillator is obtained free of the exponential nonlinear term, which is similar to the form of the Jerk oscillator. The homotopy perturbation method is used to solve the fractal Toda oscillator, and the analytical solution is examined using the numerical solution which shows excellent agreement. Furthermore, the effect of the order of the fractal derivative on the vibration property is elucidated graphically. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonlinear stability of traveling wave solutions for a conserved system of parabolic equations derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. When the initial datum is a continuous small perturbation with zero integral from the spatially shifted traveling wave, the asymptotic stability of the large-amplitude (strong) traveling waves has been established in a series of works [29,34,35] by the second author with his collaborators. In this paper, we shall show that similar stability results indeed hold true for large and discontinuous initial data (i.e. the initial perturbation from the traveling wave could be discontinuous and has large oscillations) such as Riemann data with large jumps. To the best of our knowledge, this paper provides a first result on the asymptotic stability of large-amplitude traveling waves with large initial perturbation for a system of conservation laws, although similar results have been available for the scalar equations (cf. [8,42] ). We also extend existing results to the initial data with lower regularity. [ABSTRACT FROM AUTHOR]

This paper studies soliton perturbation in optical metamaterials, with anti-cubic nonlinearity, by implementing an integration approach, namely, the generalized G ′/ G -expansion method (GGEM). Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also demonstrated. All solutions have been verified back into its corresponding equation with the aid of maple package program. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in optical metamaterials. [ABSTRACT FROM AUTHOR]

This paper retrieves soliton solutions to the perturbed resonant nonlinear Schrödinger's equation with time-dependent coefficients using the modified simple equation method. The four types of exotic non-Kerr laws studied in this paper are quadratic–cubic law, anti-cubic law, cubic–quintic–septic law and triple-power law. These soliton solutions appear with constraint conditions that guarantee their existence. [ABSTRACT FROM AUTHOR]

This paper presents a method for an online real-time electrochemical impedance spectroscopy (EIS) measurement of batteries using closed-loop control of power converter. Unlike the previously proposed method which allows the measurement of the ac impedance for a single frequency, the presented method in this paper allows for obtaining the EIS for a spectrum of frequencies by using the information included in a single perturbation cycle, or a few cycles of perturbation to obtain a more accurate EIS with a very wide frequency range. This will result in faster EIS measurement for a spectrum of frequencies and under the same battery operating conditions. The presented method utilizes closed-loop control operation for the EIS measurement functionality, which allows for better control of the output voltage and for upgrading the concept to be able to achieve no added perturbation ripple at the output of the system. The presented online real-time EIS measurement method utilizes a power converter with closed-loop control in order to create an output voltage step-function perturbation at a given frequency to generate battery voltage and current responses. By applying Fourier analysis to these responses, an EIS can be obtained for a range of frequencies equal or higher than the perturbation frequency of the step function. In addition, this paper presents a method to eliminate the added perturbation ripple when two or more power converters are used. The theoretical basis and experimental prototype results are provided to illustrate and validate the presented method. [ABSTRACT FROM PUBLISHER]

The integrodifferential equations of mathematical physics are objects of research, and construction of interpolating polynomials to obtain approximate solutions of such equations is the subject of investigation. This paper lays out a technique for constructing approximate expressions for functionals on solutions of integrodifferential equations which are an analog of the Hermite polynomial used to interpolate functions. In the example of the diffusion equation, it is shown that the use of such basis solutions allows a substantial increase in the accuracy of the approximate representation of the functionals in comparison to the first approximation of perturbation theory with practically the same computational costs. [ABSTRACT FROM AUTHOR]

In this paper, input-to-state stability (ISS) properties of perturbed systems with event-triggered receding horizon control (RHC) schemes are studied. Two event-triggered control schemes, which are the event-triggered quasi-infinite RHC (EQRHC) and the event-triggered dual-mode RHC (EDRHC) strategies, respectively, are considered. In the EQRHC scheme, an optimal control problem (OCP) should be considered at triggering time and the event is triggered if the error between the actual system state and the optimal system state violating a threshold. While in the EDRHC strategy, an OCP is only solved outside the terminal region and a local control law will be used inside the terminal region. The corresponding event condition is redesigned based on if the system state enters the terminal region or not. The event-triggering condition outside the terminal region is the same with that of the EQRHC scheme and the event-triggering condition inside the terminal region is proposed based on the difference between the actual system state and the predictive system state. Sufficient conditions of feasibility are proposed and ISS properties of both event-triggered control schemes are studied, respectively. At last, numerical simulations show the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

The recently proposed universal state-selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011)] to approximate multi-reference coupled-cluster (MRCC) energies can be commonly applied to any type of MRCC theory based on the Jeziorski-Monkhorst [B. Jeziorski and H. J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] exponential ansatz. In this paper we report on the performance of a simple USS correction to the Brillouin-Wigner and Mukherjee's MRCC approaches employing single and double excitations (USS-BW-MRCCSD and USS-Mk-MRCCSD). It is shown that the USS-BW-MRCCSD correction, which employs the manifold of single and double excitations, can be related to a posteriori corrections utilized in routine BW-MRCCSD calculations. In several benchmark calculations we compare the USS-BW-MRCCSD and USS-Mk-MRCCSD results with the results obtained with the full configuration interaction method. [ABSTRACT FROM AUTHOR]

In this paper the effect of bias and geometric symmetry breaking on the electronic spectrum of a model molecular system is studied. Geometric symmetry breaking can either enhance the dissipative effect of the bias, where spectral peaks are disabled, or enable new excitations that are absent under zero bias conditions. The spectral analysis is performed on a simple model system by solving for the electronic response to an instantaneously impulsive perturbation in the dipole approximation. The dynamical response is extracted from the electronic equations of motion as expressed by the Keldysh formalism. This expression provides for the accurate treatment of the electronic structure of a bulk-coupled system at the chosen model Hamiltonian electronic structure level. [ABSTRACT FROM AUTHOR]

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method. [ABSTRACT FROM AUTHOR]

We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh–Schrödinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Mo\ller–Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH2, and CH3. The spectroscopic constants of 3Σ- state of NH and OH+ molecular systems and the ground 1Σg+ as well as excited 3Σu+ states of N2 have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries. [ABSTRACT FROM AUTHOR]

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Mo\ller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods. [ABSTRACT FROM AUTHOR]

In this paper we present a local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments. This way, controllable accuracy and smooth convergence towards the exact result are obtained in the framework of an a posteriori approximation scheme. For the representation of the occupied space a new set of local orbitals is presented with the size of a minimal basis set. This set is atom centered, is nonorthogonal, and has shapes which are fairly independent of the details of the molecular system of interest. Two slightly different versions of combined local coupled cluster and perturbation theory equations are considered. In the limit both converge to the untruncated CCSD result. Benchmark calculations for four systems (heptane, serine, water hexamer, and oxadiazole-2-oxide) are carried out, and decay of the amplitudes, truncation error, and convergence towards the exact CCSD result are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for constructing simple state-dependent many-body potentials for quantum vibrations in a classical bath. The approach is based on an adiabatic separation between high-frequency quantum vibrational modes of the solute and the lower frequency classical motion of the solvent, and on a first-order perturbation theory description of the dependence of the quantum energies on bath configuration. In the simplest realization of the method, the delocalized quantum probability density of the vibrational mode is approximated by a sum of two δ functions, with positions and weights chosen to represent the lowest three moments of the exact distribution. Thus, in the many-body description of the system, each atom describing the quantum vibration is represented by a pair of particles. These quantum particles are held in rigid relative position and interact with the bath via potentials the magnitudes of which are modified by the δ-function weights. The resulting approach allows the classical molecular dynamics of molecules in arbitrary quantum vibrational states to be simulated with a little more effort than a purely classical description. The applicability of the method is illustrated in many-body simulations of the dephasing of vibrational superposition states of I2 in a cryogenic krypton matrix, yielding results in good agreement with experiment. [ABSTRACT FROM AUTHOR]

The Griddy Gibbs sampling was proposed by Ritter and Tanner [Facilitating the Gibbs Sampler: the Gibbs Stopper and the Griddy–Gibbs Sampler. J Am Stat Assoc. 1992;87(419):861—868] as a computationally efficient approximation of the well-known Gibbs sampling method. The algorithm is simple and effective and has been used successfully to address problems in various fields of applied science. However, the approximate nature of the algorithm has prevented it from being widely used: the Markov chains generated by the Griddy Gibbs sampling method are not reversible in general, so the existence and uniqueness of its invariant measure is not guaranteed. Even when such an invariant measure uniquely exists, there was no estimate of the distance between it and the probability distribution of interest, hence no means to ensure the validity of the algorithm as a means to sample from the true distribution. In this paper, we show, subject to some fairly natural conditions, that the Griddy Gibbs method has a unique, invariant measure. Moreover, we provideestimates on the distance between this invariant measure and the corresponding measure obtained from Gibbs sampling. These results provide a theoretical foundation for the use of the Griddy Gibbs sampling method. We also address a more general result about the sensitivity of invariant measures under small perturbations on the transition probability. That is, if we replace the transition probabilityPof any Monte Carlo Markov chain by another transition probabilityQwhereQis close toP, we can still estimate the distance between the two invariant measures. The distinguishing feature between our approach and previous work on convergence of perturbed Markov chain is that by considering the invariant measures as fixed points of linear operators on function spaces, we do not need to impose any further conditions on the rate of convergence of the Markov chain. For example, the results we derived in this paper can address the case when the considered Monte Carlo Markov chains are not uniformly ergodic. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameter perturbation homotopy continuation method for solving fixed point problems on more general nonconvex sets with both inequality and equality constraints. By adopting appropriate techniques, we make the initial points not certainly in the set consisting of the equality constraints. This point can improve the computational efficiency greatly when the equality constraints are complex. In addition, we also weaken the assumptions of the previous results in the literature so that the method proposed in this paper can be applied to solve fixed point problems in more general nonconvex sets. Under suitable conditions, we obtain the global convergence of this homotopy continuation method. Moreover, we provide several numerical examples to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

Relative permeability controls the flow of multiphase fluids in porous media. The estimation of relative permeability is generally solved by Levenberg-Marquardt method with finite difference Jacobian approximation (LM-FD). However, the method can hardly be used in large-scale reservoirs because of unbearably huge computational cost. To eliminate this problem, the paper introduces the idea of simultaneous perturbation to simplify the generation of the Jacobian matrix needed in the Levenberg-Marquardt procedure and denotes the improved method as LM-SP. It is verified by numerical experiments and then applied to laboratory experiments and a real commercial oilfield. Numerical experiment indicates that LM-SP uses only 16.1% computational cost to obtain similar estimation of relative permeability and prediction of production performance compared with LM-FD. Laboratory experiment also shows the LM-SP has a 60.4% decrease in simulation cost while a 68.5% increase in estimation accuracy compared with the earlier published results. This is mainly because LM-FD needs 2 n ( n is the number of controlling knots) simulations to approximate Jacobian in each iteration, while only 2 simulations are enough in basic LM-SP. The convergence rate and estimation accuracy of LM-SP can be improved by averaging several simultaneous perturbation Jacobian approximations but the computational cost of each iteration may be increased. Considering the estimation accuracy and computational cost, averaging two Jacobian approximations is recommended in this paper. As the number of unknown controlling knots increases from 7 to 15, the saved simulation runs by LM-SP than LM-FD increases from 114 to 1164. This indicates LM-SP is more suitable than LM-FD for multivariate problems. Field application further proves the applicability of LM-SP on large real field as well as small laboratory problems. [ABSTRACT FROM AUTHOR]

In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko (Sov Phys JETP 27:851-857, 1968) and studied by Treschev (Physica D 116(1-2):21-43, 1998; J Nonlinear Sci 12(1):27-58, 2002), Piftankin (Nonlinearity (19):2617-2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3-108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at , 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at , 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior. [ABSTRACT FROM AUTHOR]

In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force. We obtain the upper bound and Lundberg-Cramér approximation for the infinite-time ruin probability, and consider the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed. We show that the model in our paper has similar results to the classical risk process and some existing generalized models. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of an approximately controllable system perturbed by a certain Lipschitz-continuous nonlinearity. By assuming that the intensity of the nonlinear influence is 'weak', we prove that the perturbed system is still approximately controllable. Using this perturbation theory, we prove that a third-order semilinear dispersion equation on a finite interval is approximately controllable whenever the nonlinearity effect is 'weak'. The result in the paper is a complement of the results obtained in (Zhou in SIAM J. Control Optim. 21:551-565, 1983), in which the control operator (resp. infinitesimal generator of the dynamics) of the unperturbed linear system is assumed to be bounded (resp. generated a differentiable semigroup on the state space). [ABSTRACT FROM AUTHOR]

Let (), let with closed range. In this paper, utilizing the gap between closed subspaces and the perturbation bounds of metric projections, we present some new perturbation results of the Moore-Penrose metric generalized inverse. As applications of our results, we also investigate the best approximate solution problem for the ill-posed operator equation Tx=y under some conditions. The main results have three parts, part one covers the null space preserving case, part two covers the range preserving case, and part three covers the general case. Examples in connection with the theoretical results will be also presented. [ABSTRACT FROM AUTHOR]

Abstract In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the determination of pseudospectra of matrix polynomials is very demanding computationally. This paper describes a new approach to computing approximations of pseudospectra of matrix polynomials by using rank-one or projected rank-one perturbations. These perturbations are inspired by Wilkinson's analysis of eigenvalue sensitivity. This approach allows the approximation of both structured and unstructured pseudospectra. Computed examples show the method to perform much better than a method based on random rank-one perturbations both for the approximation of structured and unstructured (i.e., standard) polynomial pseudospectra. [ABSTRACT FROM AUTHOR]

In this paper, in order to solve a class of nonlinear bilevel programming problems, we equivalently transform the nonlinear bilevel programming problems into corresponding single level nonlinear programming problems by using the Karush-Kuhn-Tucker optimality condition. Then, based on penalty function theory, we construct a smooth approximation method for obtaining optimal solutions of classic l1-exact penalty function optimality problems, which is equivalent to the single level nonlinear programming problems. Furthermore, using ∈-approximate optimal solution theory, we prove convergence of a simple ∈-approximate optimal algorithm. Finally, through adding parameters in the constraint set of objective function, we prove some perturbation convergence results for solving the nonlinear bilevel programming problems. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the problem of whether the best approximation to any x in a real Hilbert space X from the closed convex set K ≔ C ∩ D can be characterized by the best approximation to a perturbation x − l of x from the set C for some l in a certain cone in X. The set C is a closed convex subset of X and D ≔ { x ∈ X : g j (x) ≤ 0 , ∀ j = 1 , 2 , ... , m } , where the functions g j : X ⟶ R (j = 1 , 2 , ... , m) are continuously Fréchet differentiable that are not necessarily convex. We show under suitable conditions that this "perturbation property" is characterized by the strong conical hull intersection property of C and D at the point x 0 ∈ K. We prove this by first establishing a dual cone characterization of a nearly convex set. Our result shows that the convex geometry of K is critical for the characterization rather than the representation of D by convex inequalities, which is commonly assumed for the problems of best approximation from a convex set. In the special case where the set D is convex, we show that the Lagrange multiplier characterization of best approximation holds under the standard Slater's constraint qualification together with a non-degeneracy condition. The lack of representation of D by convex inequalities is supplemented by the non-degeneracy condition, but the characterization, even in this special case, allows applications to problems with quasi-convex functions g j , j = 1 , 2 , ... , m , as they guarantee the convexity of D. Simple numerical examples illustrate the nature of our assumptions. [ABSTRACT FROM AUTHOR]

Abstract The Harten–Lax–van Leer with contact (HLLC) approximate Riemann solver is known to be plagued by various forms of numerical shock instability. In this paper, we propose a new framework for developing shock stable versions of the HLLC scheme for the Euler system of equations without compromising on its contact and shear preserving ability. The proposed framework, termed as S elective W ave M odification (SWM), identifies and enhances the magnitude of the inherent HLL-type diffusive component within the HLLC scheme in the vicinity of a normal shock front. This is achieved by suitably increasing the magnitudes of the nonlinear wave speed estimates appearing in them through a dissipation parameter ϵ. A linear perturbation analysis is performed to gauge the effectiveness of the proposed framework in damping unwanted perturbations in physical quantities and is also used to estimate a von-Neumann-type stability bound on the CFL number associated with its use. Two distinct methods to estimate ϵ , which results in HLLC-SWM-E (Eigenvalue based) and HLLC-SWM-P (Pressure based) schemes, are proposed and compared. Further, a matrix based stability analysis is used to show that the proposed schemes can be configured to remain shock stable over a wide range of free stream Mach numbers. Numerical results confirm that the proposed schemes are capable of computing shock stable solutions for a wide variety of problems. On viscous flows, the HLLC-SWM-P variant is found to be the most accurate. Performance of these schemes suggests that it is possible to construct shock stable upwind schemes that simultaneously retains accuracy on the linearly degenerate wavefields. Highlights • A simple strategy to cure shock instability in the HLLC Riemann solver proposed. • Cure achieved by enhancing the inherent HLL-type diffusive component. • Two shock stable variants namely HLLC-SWM-E and HLLC-SWM-P are developed. • Robustness and accuracy of the scheme are demonstrated on several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the relative perturbation bounds for joint eigenvalues of commuting tuples of normal $n\times n$ matrices. Some Hoffman–Wielandt-type relative perturbation bounds are proved using the Clifford algebra technique. We also extend a result for diagonalisable matrices which improves a relative perturbation bound for single matrices. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study woven approximate Schauder g-frames. We show that for any two approximate Schauder g-frames, each weaving is an approximate Schauder g-frame if and only if there is a uniform constant C ≥ 1 such that every weaving is a C-approximate Schauder g-frame, and we obtain some perturbation results for approximate Schauder g-frames. Finally, some results have been found for weaving approximate Schauder g-frames. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions of the pressureless type system with flux approximation. First, the Riemann problem of the pressureless type system with a flux perturbation is considered. A parameterized delta-shock and generalized constant density solution are obtained. Then we rigorously prove that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state of the pressureless type system, respectively. Secondly, by adding an artificial pressure term in the pressureless type system, we solve the Riemann problem of the system with a double parameter flux approximation including pressure. It is shown that, as the flux perturbations vanish, any two-shock Riemann solution tends to a delta-shock solution to the pressureless type system; any two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution to the pressureless type system and the intermediate nonvacuum state in between tends to a vacuum state. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Camassa–Holm equation, which is a model for shallow water waves. We first establish the existence of solitary wave solutions for the equation without delay. And then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system, especially the geometric singular perturbation theory and invariant manifold theory. According to the relationship between solitary wave and homoclinic orbit, the Camassa–Holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution. It is proved that the equation with disturbance also possesses homoclinic orbit, and there exists solitary wave solution of the delayed Camassa–Holm equation. [ABSTRACT FROM AUTHOR]

In this paper, a recurrent perturbation fuzzy neural network (RPFNN) is used to online approximate an unknown nonlinear term in the system dynamics. A sine–cosine perturbed membership function is used to handle rule uncertainties when it is hard to exactly determine the grade of the value of fuzzy sets. Unlike type-2 fuzzy sets use an extra type reduction operation to find the output, the proposed RPFNN does not require heavy computational loading. Meanwhile, this paper proposes an intelligent dynamic sliding-mode neural control (IDSNC) system which is composed of a neural controller and an exponential compensator. The neural controller is designed as the main controller via dynamic sliding-mode approach, and the exponential compensator is designed to obtain a faster reaching time and a good robustness. The parameter adaptation laws of the IDSNC system are derived based on the Lyapunov function, so that the system stability can be guaranteed. Finally, the IDSNC system is applied to an inverted pendulum problem and a chaotic synchronization problem. The simulation results demonstrate that the IDSNC system can achieve favorable control performance and is robust against parameter variations and external disturbances. [ABSTRACT FROM AUTHOR]

Inevitable perturbations have a significant impact on collaborative production (CP) cause that the complexity are greatly increased. In order to assess the impact accurately enterprises to make precise decisions, it is prerequisite to master the dynamic behaviour of CP when changes occur. Accordingly, in this paper, an evolution model for simulating CP task state to perturbations is proposed. Regard CP tasks as a directed weighted complex network (DWCPTN) firstly, and statistical properties of DWCPTN are analysed. Two perturbation cases and two modifications policies are defined followed. Based on above mentioned, evolution model based on cellular automaton (CA) and SIS (Susceptible-Infected-Susceptible) is presented to reveal the varying process by three indices (friction of resolved nodes, convergence time and economic behaviour). Finally, analytic results from a case of a chemical product CP network (CPNCP) are used to illustrate the model and method proposed in this paper. Simulation results shows that unplanned perturbations promote a negative role to CP but the improvements of self-healing can decrease the negative effects efficiently. With the analysis, it can provide insight into ways of improving the strategic and operational decision making for enterprises. [ABSTRACT FROM AUTHOR]

This paper discusses a best-practice representation of uncertainty in satellite remote sensing data. An estimate of uncertainty is necessary to make appropriate use of the information conveyed by a measurement. Traditional error propagation quantifies the uncertainty in a measurement due to well-understood perturbations in a measurement and in auxiliary data -- known, quantified "unknowns". The underconstrained nature of most satellite remote sensing observations requires the use of various approximations and assumptions that produce non-linear systematic errors that are not readily assessed -- known, unquantifiable "unknowns". Additional errors result from the inability to resolve all scales of variation in the measured quantity -- unknown "unknowns". The latter two categories of error are dominant in underconstrained remote sensing retrievals, and the difficulty of their quantification limits the utility of existing uncertainty estimates, degrading confidence in such data. This paper proposes the use of ensemble techniques to present multiple self-consistent realisations of a data set as a means of depicting unquantified uncertainties. These are generated using various systems (different algorithms or forward models) believed to be appropriate to the conditions observed. Benefiting from the experience of the climate modelling community, an ensemble provides a user with a more complete representation of the uncertainty as understood by the data producer and greater freedom to consider different realisations of the data. [ABSTRACT FROM AUTHOR]

This paper gives the concepts of finite dimensional irreducible operators ((FDI) operators) and infinite dimensional irreducible operators ((IDI) operators). Discusses the relationships of (FDI) operators, (IDI) operators and strongly irreducible operators ((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an (FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in (ΣFDI)( X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in (ΣFDI)( X) with respect to the norm topology on a Banach space X with a Schauder basis, where (ΣFDI)( X):= { T ∈ B( X): T = Σ ⊕ T, T ∈ (FDI), k ∈ ℕ}. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight w ( x ) = x α e − x − t / x , x ∈ ( 0 , ∞ ) , t > 0 and α > 0 . When the matrix size n → ∞ , we obtain an asymptotic formula for the Hankel determinants, valid uniformly for t ∈ ( 0 , d ] , d > 0 fixed. A particular Painlevé III transcendent is involved in the approximation, as well as in the large- n asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results in an earlier paper of the authors, obtained by using the Deift–Zhou nonlinear steepest descent method. [ABSTRACT FROM AUTHOR]

The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics or a social network in behavioral sciences. However, computing all the eigenvalues explicitly is prohibitively expensive for real-world applications. This paper presents two types of methods to efficiently estimate the spectral density of a matrix pencil (A,B) where both A and B are sparse Hermitian and B is positive definite. The methods are targeted at the situation when the matrix B scaled by its diagonal is very well conditioned, as is the case when the problem arises from some finite element discretizations of certain partial differential equations. The first method is an adaptation of the kernel polynomial method (KPM) and the second is based on Gaussian quadrature by the Lanczos procedure. By employing Chebyshev polynomial approximation techniques, we can avoid direct factorizations in both methods, making the resulting algorithms suitable for large matrices. Under some assumptions, we prove bounds that suggest that the Lanczos method converges twice as fast as the KPM method. Numerical examples further indicate that the Lanczos method can provide more accurate spectral densities when the eigenvalue distribution is highly nonuniform. As an application, we show how to use the computed spectral density to partition the spectrum into intervals that contain roughly the same number of eigenvalues. This procedure, which makes it possible to compute the spectrum by parts, is a key ingredient in the new breed of eigensolvers that exploit "spectrum slicing." [ABSTRACT FROM AUTHOR]

This paper studies the tracial stability of C*-algebras, which is a general property of stability of relations in a Hilbert-Schmidt-type norm defined by a trace on a C*-algebra. Precise definitions are formulated in terms of tracial ultraproducts. For nuclear C*-algebras, a characterization of matricial tracial stability in terms of approximation of tracial states by traces of finite-dimensional representations is obtained. For the nonnuclear case, new obstructions and counterexamples are constructed in terms of free entropy theory. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of two tubular reactor models, the non-isothermal tubular reactor model and a biochemical reactor model. It is mathematically shown in particular that multiple equilibrium profiles can be exhibited if the diffusion coefficients are large enough by considering regular perturbation arguments. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the structured componentwise perturbation analysis to Hamiltonian eigenvalue problems. The explicit expressions for the relative structured componentwise condition number for Hamiltonian eigenvalue problems are derived. Also, we will compare the relative structured componentwise condition number with the relative unstructured componentwise condition number and the relative structured normwise condition number, respectively. We show the superiority of the relative structured componentwise condition number through numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we construct a piecewise smooth solution for a 2-D supersonic potential flow past a curved wedge, whose boundary is assumed to have large variation. In fact, we originally provide a background solution, which is constructed by assuming the coming flow has limit speed. Its shock coincides with the curved wedge and the flow behind the shock is defined only along the wedge. Then our problem can be treated as a perturbation of this background solution and the solution is obtained by showing specific estimates. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a novel theoretical framework for dynamic identification in a structure occupied by a single human. The framework enables the prediction of the dynamics of the human-structure system from the known properties of the individual system components, the identification of human body dynamics from the known dynamics of the empty structure and the human-structure system and the identification of the properties of the structure from the known dynamics of the human and the human-structure system. The novelty of the proposed framework is the provision of closed-form solutions in terms of frequency response functions obtained by curve fitting measured data. The advantages of the framework over existing methods are that there is neither need for nonlinear optimisation nor need for spatial/modal models of the empty structure and the human-structure system. In addition, the second-order perturbation method is employed to quantify the effect of uncertainties in human body dynamics on the dynamic identification of the empty structure and the human-structure system. The explicit formulation makes the method computationally efficient and straightforward to use. A series of numerical examples and experiments are provided to illustrate the working of the method. [ABSTRACT FROM AUTHOR]

Suppose that d ≥ 1 and 0 < β < α < 2. We establish the existence and uniqueness of the fundamental solution qb(t, x, y) to a class of (typically non-symmetric) non-local operators Lb = Δ α/² + Sb, where and b(x, z) is a bounded measurable function on Rd x Rd with b(x, z) = b(x,-z) for x, z < Rd. Here A(d,-β) is a normalizing constant so that Sb = Δ β/2 when b(x, z) ≡ 1. We show that if b(x, z) ≥ then qb(t, x, y) is a strictly positive continuous function and it uniquely determines a conservative Feller process Xb, which has strong Feller property. The Feller process Xb is the unique solution to the martingale problem of (Lb, S(Rd)), where S(Rd) denotes the space of tempered functions on Rd . Furthermore, sharp two-sided estimates on qb(t, x, y) are derived. In stark contrast with the gradient perturbations, these estimates exhibit different behaviors for different types of b(x, z). The model considered in this paper contains the following as a special case. Let Y and Z be (rotationally) symmetric α-stable process and symmetric β-stable processes on Rd, respectively, that are independent to each other. Solution to stochastic differential equations dXt = dYt + c(Xt-)dZt has infinitesimal generator Lb with b(x, z) = -c(x)β. [ABSTRACT FROM AUTHOR]