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This paper deals with Lasota-Wazewska red blood cell model with perturbation on time scales. By applying the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by means of Gronwall inequality. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers a class of stochastic systems referred to as stochastic switched systems of neutral type with time-varying delay, which combines switched systems with neutral stochastic systems. The systems consist of subsystems of two forms: (i) only stable subsystems and (ii) both stable subsystems and unstable subsystems. By establishing an integral inequality, the exponential stability in p t h( p≥1)-moment for such systems with only stable subsystems is first considered. Then, by using an average dwell time approach, the exponential stability in p t h( p≥1)-moment for the second form is addressed. An important finding of this study is that when the average dwell time is chosen to be sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of stable subsystems, the exponential stability in p t h( p≥1)-moment for such systems can be guaranteed. Two major advantages of these new results are that the differentiability or continuity of the delay function is not required compared with the existing results in the literature, and the proposed approaches can be used to consider the case when the neutral item and the stochastic perturbation are simultaneously presented. An example is provided to verify the effectiveness and potential of the theoretic results obtained. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses a survey where some respondents were asked sensitive questions directly and others were asked the same questions using randomized response. The use of randomized response was a factor in a 2 × 2 factorial design and dice were used to perform the randomization. First, the paper shows that the perturbation due to the dice can be described using the concept of misclassification and known conditional misclassification probabilities. Second, the paper formulates the likelihood for loglinear models and shows that latent class software can be used to analyse the data. An example including a power analysis is discussed. [ABSTRACT FROM AUTHOR]

Raman spectroscopy is a powerful and nondestructive probe that demonstrates its efficiency in revealing the physical properties of low‐dimensional sp2 carbon systems. It gives access to the number of layers, the quality and the nature of defects of all carbon allotropes, but also to the understanding of the influence of perturbations such as strain and/or doping. In this paper, we review the state of the art regarding the effect of external perturbations on the optical phonons of graphene. We describe how doping can tune the unusual electron–phonon coupling in graphene and thus modify not only the resonance conditions but also the phonon intensities thanks to quantum interferences. We also review the impact of strain on optical phonons and how one can disentangle strain and doping thanks to optical phonons. Last, implementations of this field to strain engineering or to graphene‐based mechanical resonators will be presented. Copyright © 2018 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The installed capacity of non-synchronous devices (NSD), including renewable energy generation and other converter-interfaced equipment is expected to increase and contribute a large proportion of total generation capacity in future power systems. Concerns have been expressed relating to operability and stability of such systems, since NSD are typically decoupled from the grid via power electronic devices and consequently reduce the 'natural' inertia, short-circuit levels and damping which are inherently provided by synchronous machines. This study establishes the instantaneous penetration level (IPL) limits of NSD connected to a model power system in terms of steady-state stability beyond which the system condition becomes unstable. The NSD used in this example will be a conventional dq-axis current injection (DQCI) convertor model. The study introduces a set of system 'viability' criteria relating to locking signal in converter phase-locked loop, frequency, rate of change of frequency and voltage magnitude, which are used to determine the IPL limits. Among many factors which can affect the IPL limits, the impact of frequency and voltage droop slopes and filter time-constants of DQCI converter is quantified. Finally, a frequency domain visualisation method referred here as 'network frequency perturbation' is introduced to provide additional insight into contributions of individual generators. [ABSTRACT FROM AUTHOR]

We consider a single-server system with service stations in each point of the circle. Customers arrive after exponential times at uniformly distributed locations. The server moves at finite speed and adopts a greedy routing mechanism. It was conjectured by Coffman and Gilbert in 1987 that the service rate exceeding the arrival rate is a sufficient condition for the system to be positive recurrent, for any value of the speed. In this paper we show that the conjecture holds true.© 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In this paper, we discuss basic properties, a least-squares problem for row extended matrices and the associated approximation problem. First, we obtain their basic properties by applying their particular structure. Then we derive a general representation of the solutions to the least-squares problem, and we obtain an expression for the solution to the associated approximation problem. Finally, we provide a perturbation analysis and a perturbation bound for the best approximate solution. The results are illustrated by numerical examples. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, by generalizing the ideas of the (generalized) polar decomposition to the weighted polar decomposition and the unitarily invariant norm to the weighted unitarily invariant norm, we present some perturbation bounds for the generalized positive polar factor, generalized nonnegative polar factor, and weighted unitary polar factor of the weighted polar decomposition in the weighted unitarily invariant norm. These bounds extend the corresponding recent results for the (generalized) polar decomposition. In addition, we also give the comparison between the two perturbation bounds for the generalized positive polar factor obtained from two different methods. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider the non-Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non-Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT Full-waveform inversion suffers from local minima, due to a lack of low frequencies in data. A reflector below the zone of interest may, however, help in recovering the long-wavelength components of a velocity perturbation, as demonstrated in a paper by Mora. With the Born approximation for a perturbation in a reference model consisting in two homogeneous isotropic acoustic half-spaces and the assumption of infinitely large apertures available in the data, analytic expressions can be found that describe the spatial spectrum of the recorded seismic signal as a function of the spatial spectrum of the inhomogeneity. Diving waves can be included if the deeper part of the homogeneous model is replaced by one that has a vertical velocity gradient. We study this spectrum in more detail by separately considering scattering of direct, reflected and head waves, as well as singly and multiply reflected diving waves for a gradient model. Taking the reflection coefficient of the deeper reflector into account, we obtain sensitivity estimates for each wavetype. Although the head waves have a relatively small contribution to the reconstruction of the velocity perturbation, compared to the other waves, they contain reliable long-wavelength information that can be beneficial for full-waveform inversion. If the deeper part has a constant positive velocity gradient with depth, all the energy eventually returns to the source-receiver line, given a sufficiently large acquisition aperture. This will improve the sensitivity of the scattered reflected and refracted wavefields to perturbations in the background model. The same happens for a zero velocity gradient but with a very high impedance contrast between the two half-spaces, which results in a large reflection coefficient. [ABSTRACT FROM AUTHOR]

Spectral points of positive and negative type, and type π+ and type π− for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-self-adjoint case under various kinds of perturbations, for example, compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded self-adjoint operators in Krein spaces. [ABSTRACT FROM AUTHOR]

This paper is devoted to the perturbation analysis for the matrix sign functions of the regular matrix pair. The first-order perturbation bounds and the global perturbation bounds are obtained. The results are illustrated by some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application. Rebuilding the whole triangulation from scratch is surprisingly a very viable option compared to relocating the vertices. This can be explained by several recent advances in efficient construction of Delaunay triangulations. However, when all points move with a small magnitude, or when only a fraction of the vertices move, rebuilding is no longer the best option. This paper considers the problem of efficiently updating a Delaunay triangulation when its vertices are moving under small perturbations. The main contribution is a set of filters based upon the concept of vertex tolerances. Experiments show that filtering relocations is faster than rebuilding the whole triangulation from scratch under certain conditions. [ABSTRACT FROM AUTHOR]

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In this survey we illustrate how the matching distance between reduced size functions can be applied for shape comparison. We assume that each shape can be thought of as a compact connected manifold with a real continuous function defined on it, that is a pair (ℳ,ϕ : ℳ → ℝ), called size pair. In some sense, the function ϕ focuses on the properties and the invariance of the problem at hand. In this context, matching two size pairs (ℳ, ϕ) and (𝒩, ψ) means looking for a homeomorphism between ℳ and 𝒩 that minimizes the difference of values taken by ϕ and ψ on the two manifolds. Measuring the dissimilarity between two shapes amounts to the difficult task of computing the value δ = inff maxP∈ℳ |ϕ(P) - ψ(f(P))|, where f varies among all the homeomorphisms from ℳ to 𝒩. From another point of view, shapes can be described by reduced size functions associated with size pairs. The matching distance between reduced size functions allows for a robust to perturbations comparison of shapes. The link between reduced size functions and the dissimilarity measure δ is established by a theorem, stating that the matching distance provides an easily computable lower bound for δ. Throughout this paper we illustrate this approach to shape comparison by means of examples and experiments. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 154–161, 2006 [ABSTRACT FROM AUTHOR]

This paper gives simple approximations for the distribution function and quantiles of the sum X + Y when X is a continuous variable and Y is an independent variable with variance small compared to that of X . The approximations are based around the distribution function or quantiles of X and require only the first two or three moments of Y to be known. Example evaluations with X having a normal, Student’s t or chi-squared distribution suggest that the approximations are good in unbounded tail regions when the ratio of variances is less than 0.2. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fractal dynamics of a reaction-diffusion system, - the forced Brusselator model. The Julia set of the discrete version of the model is established. Then, the control of the Julia set is realized by combining the parameter perturbation control method and feedback control method. The box-counting dimensions of the Julia sets of the controlled system for different control parameters are computed, which is used to describe the complexity and irregularity of the Julia sets. Finally, nonlinear coupling items are designed to make one Julia change to be another. The simulations illustrate the efficacy of these methods. [ABSTRACT FROM AUTHOR]

Abstract: We present the basic results and conjectures regarding possibility of approximating finite‐energy sequences of Müller's functional (which was for the first time, and in its simplest form, studied in paper S. Müller: Singular perturbations as a selection criterion for periodic minimizing sequences, Calc. Var. Partial Differential Equations 1(2), 169–204 (1993)) by 1‐Lipschitz and 1‐periodic finite‐energy sequences. Our results extend known results in the case of simplest pinning term concerning the actual minimizers as small parameter epsilon tends to zero, whereby standard assumption on growth of 2‐well potential at infinity (which immediately yields equi‐coercivity) is replaced by non‐standard one. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

It is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined. When the motion thus examined are compared with the one obtained by the general relativity theory in post‐Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession. [ABSTRACT FROM AUTHOR]

A double hybrid approximation using the Coulomb-attenuating method (CAM-DH) is derived within range-separated density-functional perturbation theory, in the spirit of a recent work by Cornaton et al. (Phys. Rev. A 2013, 88, 022516). The energy expression recovered through second order is linear in the parameters α and β that control the Coulomb attenuation. The method has been tested within the local density approximation on a small test set consisting of rare-gas and alkaline-earth-metal dimers as well as diatomics with single, double, and triple bonds. In this context, the semiempirical α = 0.19 and β = 0.46 parameters, which were optimized for the hybrid CAM-B3LYP functional, do not provide accurate interaction and total energies. Using semilocal functionals with density scaling, which was neglected in this work, may lead to different conclusions. Calibration studies on a larger test set would be necessary at this point. This is left for future work. Finally, we propose as a perspective, an alternative CAM-DH approach that relies on the perturbation expansion of a partially long-range-interacting wavefunction. In this case, the energy is not linear anymore in α and β. Work is in progress in this direction. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In this study, the authors study the finite-time cluster synchronisation problem for a class of Markovian switching complex networks with stochastic noise perturbations. By constructing the suitable stochastic Lyapunov-Krasovskii functional, using finite-time stability theorem, inequality techniques and the properties of Weiner process, sufficient conditions are obtained to ensure finite-time cluster synchronisation for the complex networks with or without time delays. The effects of control parameters on cluster synchronisation speed and time delays are also analysed. Since finite-time cluster synchronisation means the optimality in convergence time and has better robustness and disturbance rejection properties, this study has important theory significance and practical application value. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of assessing local influence of small perturbations in GARCH processes. First, we examine the local influence on the Lagrange multiplier (LM) statistic. Second, we assess the local influence on the pseudo-likelihood of the GARCH model. We find that short patches of high volatility observations that have a strong influence on the LM statistic may not necessarily be influential on the pseudo-likelihood. This is mainly due to the fact that the effects of high volatility could be incorporated through GARCH modeling. An empirical example is presented to illustrate the effectiveness of the proposed methods. It is interesting to note that observations which have a very strong influence on the LM statistic are far less influential on the GARCH pseudo-likelihood, suggesting that under the GARCH model they should not be regarded as outliers. [ABSTRACT FROM AUTHOR]

Based on the usual perturbation and Padé approximation, a new static displacement reanalysis method for structures is developed in this paper. By this method, the accuracy of the static displacements for moderate- to-large modifications of the parameters of structures is improved. As an application of the method, a numerical example is given, and the third-order perturbation method, Kirsch's combined method and the proposed method are compared in the computational accuracy. The results show that the presented method is effective. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

“Trimpi” events observed at night during a reception of the very low frequency (VLF) wave propagating in the earth-ionosphere waveguide is used as a diagnostic tool for the lower ionosphere. A three-dimensional analysis is needed to understand this event. Theoretically, an analysis has been carried out for a three-dimensional model. In such an analysis, a WKB approximation is applied to an approximate solution based on the perturbation method in which single-mode propagation is assumed. However, the present authors considered that mode conversion needs to be included in the analysis of the scattered electromagnetic field near the ionospheric perturbation. Hence, although a two-dimensional model was used, the scattering problem was analyzed by applying the finite-element method in the case where there is a perturbation along the propagation path. In this paper, the results of the scattering by a perturbation given by a Gaussian function at f = 5 ∼ 20 kHz are presented. From the distribution of the scattered electromagnetic field obtained, it is found that the incident mode is converted to multimodes at the perturbation location. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(3): 78–88, 1997 [ABSTRACT FROM AUTHOR]

This paper, based on the boundary-element technique, presents a perturbation method which can be applied to reanalysis of the eigenvalues and eigenvectors in an elastic structure. Regarding the shape changes of a structure as the perturbation of its surface nodes within the neighbourhood of the given values, this method uses the perturbation formula to obtain the eigensolutions of the modified system without solving the generalized eigenvalue problem. Finally, the authors give some sample examples to demonstrate the validity of the method. [ABSTRACT FROM AUTHOR]

The concept of Nash equilibrium is widely used to analyse non-cooperative games. However, one of the problems with that concept is that many games have multiple equilibria. Recent work has concentrated on reducing or refining the set of Nash equilibria in some games. In this paper, we survey some equilibrium concepts based on perturbations of strategies that refine the set of Nash equilibria. We discuss the pros and cons of each concept and its relationship to the others by the use of numerous examples and intuition. It is hoped that this survey will enable the economist to consider the relevance of a particular equilibrium concept to a given economic model of interest. [ABSTRACT FROM AUTHOR]

We consider a 2 time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ϵ of the time scales. We search for an approximation involving only the slow time unknowns and valid uniformly for all times at order O(ϵ2). A classical approach to study these problems is Tikhonov's singular perturbation theorem. We develop an approach leading to a higher order approximation using the renormalization group (RG) method. We apply it in 2 steps. In the first step, we show that the RG method allows for approximation of the fast time variables by their RG expansion taken at the slow time unknowns. Next, we study the slow time equations, where the fast time unknowns are replaced by their RG expansion. This allows to rigorously show the second order uniform error estimate. Our result is a higher order extension of Hoppensteadt's work on the Tikhonov singular perturbation theorem for infinite times. The proposed procedure is suitable for problems from applications, and it is computationally less demanding than the classical Vasil'eva‐O'Malley expansion. We apply the developed method to a mathematical model of stem cell dynamics. [ABSTRACT FROM AUTHOR]

The formation of vacuum state and delta shock wave in the solutions to the Riemann problem for the simplified pressureless Euler system is considered under the linear approximations of flux functions. The method is to perturb the non‐strictly hyperbolic system into a nearby strictly hyperbolic system by introducing appropriately the linear approximations of flux functions. The solutions to the Riemann problem for the approximated system can be constructed explicitly and then the formation of vacuum state and delta shock wave can be observed by taking the perturbation parameter tend to zero in the solutions. [ABSTRACT FROM AUTHOR]

Abstract: We study how the stationary measure associated to analytic contractions on the unit interval behaves under changes in the contractions and the weights. Firstly we give a simple proof of the fact that the integrals of analytic functions with respect to the stationary measure vary analytically if we perturb the contractions and the weights analytically. Secondly, we consider the special case of affine contractions and we prove a conjecture of J. Fraser in on the Kantorovich–Wasserstein distance between two stationary measures associated to affine contractions on the unit interval with different rates of contraction. [ABSTRACT FROM AUTHOR]

Efficient implementations of analytic gradients for the orbital‐optimized MP3 and MP2.5 and their standard versions with the density‐fitting approximation, which are denoted as DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5, are presented. The DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density‐fitted perturbation theory (DF‐MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF‐MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z‐vector equation, back‐transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc‐pCVQZ basis set, is 0.0001–0.0002 Å. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We present a new method of resumming the Brillouin‐Wigner perturbation series with Epstein‐Nesbet partitioning. Both the nondegenerate and quasi‐degenerate cases are considered. We illustrate the accuracy of the proposed resummed Brillouin‐Wigner perturbation theory for selected atoms and small molecules, as well as a simple model system like the quartic anharmonic oscillator. For the electronic structure problems, it is found that the present theory provides essentially the same results as the corresponding configuration‐interaction calculations at the level of the fourth‐order calculations. [ABSTRACT FROM AUTHOR]

A brief review of asymptotic methods to deal with frictionless unilateral contact problems for an elastic layer of finite thickness is presented. Under the assumption that the contact radius is small with respect to the layer thickness, an effective asymptotic method is suggested for solving the unilateral contact problem with a priori unknown contact radius. A specific feature of the method is that the construction of an asymptotic approximation is reduced to a linear algebraic system with respect to integral characteristics (polymoments) of the contact pressure. As an example, the sixth-order asymptotic model has been written out. [ABSTRACT FROM AUTHOR]

We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2)TQ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In this study, zero-forcing matrix decomposition polynomial expansion update (ZF-MDPE-update) and zero-forcing successive over relaxation update (ZF-SOR-update) algorithms are proposed to update a zero-forcing detector quickly without requiring complicated matrix inversion recomputations when massive multiple-input multi-output systems channel estimates contain a small perturbation. To further accelerate the convergence rate and to maximise date throughput, a new method of calculating the optimal coefficients for the matrix polynomial that can significantly improve the accuracy of the initial input inverse matrix approximation is considered by the ZF-MDPE-update algorithm. On the other hand, the ZF-SOR-update algorithm with an optimal iterative initial solution and an optimal relaxation parameter is devised, which achieves excellent detection performance. Results demonstrate that when the ratio of base station (BS) antennas to user terminal (UT) antennas, β, is small, the proposed update detection algorithms, with only a few operations, achieve a significant improvement in the average achievable rate of the UTs compared to the recently proposed update algorithm. Therefore, more UTs can be served in a cell with a fixed number of BS antennas. At the same time, the authors' algorithms are shown to facilitate easy memory transfer and are low cost. [ABSTRACT FROM AUTHOR]

ABSTRACT The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation-based methods and other approximations. [ABSTRACT FROM AUTHOR]

In a series of recent works by Demirkaya et al., stability analysis for the static kink solutions to the one-dimensional continuous and discrete Klein-Gordon equations with a [ABSTRACT FROM AUTHOR]

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and structured pseudospectra, based on determining the spectra of many suitably chosen rank-one or projected rank-one perturbations of the given matrix is proposed. The choice of rank-one or projected rank-one perturbations is inspired by Wilkinson's analysis of eigenvalue sensitivity. Numerical examples illustrate that the proposed approach gives much better insight into the pseudospectra and structured pseudospectra than random or structured random rank-one perturbations with lower computational burden. The latter approach is presently commonly used for the determination of structured pseudospectra. [ABSTRACT FROM AUTHOR]

Self-modeling curve resolution methods have continuously been improved during recent years. Many efforts have been made on curve resolution methods to reduce the rotational ambiguity by means of different types of constraints. Choosing proper constraints and cost functions is critically important for the reduction of the rotational ambiguity because the constraints have a direct influence on the accuracy of the area of feasible solution (AFS). In this work, we introduce a new improved cost function, which serves to apply nonnegativity, unimodality, equality, and closure constraints. We also investigate the reduction of the AFS under hard and soft constraints. Another point of this work is to evaluate the accuracy and precision of the reduced AFS in the presence of noise and perturbations, under hard and soft implementation of nonnegativity, unimodality, equality, and closure constraints. A comparison is given between the reduced AFS with soft constraints (small deviations from constraints are accepted) and the reduced AFS under hard constraints (restrictedly forced constraints). A graphical visualization of this comparison is presented for various model problems. The results show that an AFS computation with soft constraints provides more reliable results, especially in the presence of noise. The test problems substantiate significant advantages of soft constraints over hard constraints because the obtained profiles are closer to the potentially true noisy profiles, which contain small deviations from ideal responses. Using tunable parameters ϵ, γ, ω, δ is one of the advantages of soft constrained cost function that allows the small deviations from ideal responses. Ultimately, soft constraints can help to reduce the lack-of-fit, and they are a proper instrument to handle the effect of noise on the AFS. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This work is focused on the long-time behavior of solutions to the singularly perturbed damped Boussinesq equation in a 3D case [ABSTRACT FROM AUTHOR]

We study the effects of adding a local perturbation in a pattern-forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a periodic pattern, one finds an unbounded linear operator that is not Fredholm due to continuous spectrum in typical translation invariant or weighted spaces. We show that Kondratiev spaces, which encode algebraic localization that increases with each derivative, provide an effective means to circumvent this difficulty. We establish Fredholm properties in such spaces and use the result to construct deformed periodic patterns using the Implicit Function Theorem. We find a logarithmic phase correction, which vanishes for a particular spatial shift only, which we interpret as a phase-selection mechanism through the inhomogeneity. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT The aim of this article is to develop methodology for detecting influential observations in crossover models with random individual effects. Various case-weighted perturbations are performed. We obtain the influence of the perturbations on each parameter estimator and on their dispersion matrices. The obtained results exhibit the possibility to obtain closed-form expressions of the influence using the residuals in mixed linear models. Some graphical tools are also presented. [ABSTRACT FROM AUTHOR]

SUMMARY The problem of symmetric rank-one approximation of symmetric tensors is important in independent components analysis, also known as blind source separation, as well as polynomial optimization. We derive several perturbative results that are relevant to the well-posedness of recovering rank-one structure from approximately-rank-one symmetric tensors. We also specialize the analysis of the shifted symmetric higher-order power method, an algorithm for computing symmetric tensor eigenvectors, to approximately-rank-one symmetric tensors. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Such fifth-rung functionals approach the performance of com-posite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives avail-able. In this article, we provide a critical analysis of the varia-bles and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density func-tional theory (DFT), exact exchange, and perturbative correla-tion in both the same spin and opposite spin terms], and the addition of an ad-hoc dispersion correction; we have termed these parametrizations "DSD-DFT" (Dispersion corrected, Spin-component scaled, Double-hybrid DFT). Somewhat surpris-ingly, the quality of DSD-DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD-LDA yielding respectable performance. Simple, non-empirical GGAs appear to work best, whereas meta-GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD-PBEhB95, DSD-PBEP86, DSD-PBEPW91, and DSD-PBEPBE. In addition, DSD-PBEP86 and DSD-PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information. [ABSTRACT FROM AUTHOR]

ABSTRACT The relation between vertical and horizontal slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle. [ABSTRACT FROM AUTHOR]

ABSTRACT Traveltime information is crucial for parameter estimation, especially if the medium is described by a set of anisotropy parameters. We can efficiently estimate these parameters if we are able to relate them analytically to traveltimes, which is generally hard to do in inhomogeneous media. I develop traveltime approximations for transversely isotropic media with a horizontal symmetry axis (HTI) as simplified and even linear functions of the anisotropy parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to the anellipticity parameter, η and the azimuth of the symmetry axis (typically associated with the fracture direction) from a generally inhomogeneous, elliptically anisotropic background medium. Such a perturbation is convenient since the elliptically anisotropic information might be obtained from well velocities in HTI media. Thus, we scan for only η and the symmetry-axis azimuth. The resulting approximations can provide a reasonably accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations. They also help extend the inhomogenous background isotropic or elliptically anisotropic models to an HTI one with a smoothly variable η and symmetry-axis azimuth. [ABSTRACT FROM AUTHOR]

Wave-equation migration velocity analysis is a technique designed to extract and update velocity information from migrated images. The velocity model is updated through the process of optimizing the coherence of images migrated with the known background velocity model. The capacity for handling multi-pathing of the technique makes it appropriate in complex subsurface regions characterized by strong velocity variation. Wave-equation migration velocity analysis operates by establishing a linear relation between a slowness perturbation and a corresponding image perturbation. The linear relationship and the corresponding linearized operator are derived from conventional extrapolation operators and the linearized operator inherits the main properties of frequency-domain wavefield extrapolation. A key step in the implementation is to design an appropriate procedure for constructing an image perturbation relative to a reference image that represents the difference between the current image and a true, or more correct image of the subsurface geology. The target of the inversion is to minimize such an image perturbation by optimizing the velocity model. Using time-shift common-image gathers, one can characterize the imperfections of migrated images by defining the focusing error as the shift of the focus of reflections along the time-shift axis. The focusing error is then transformed into an image perturbation by focusing analysis under the linear approximation. As the focusing error is caused by the incorrect velocity model, the resulting image perturbation can be considered as a mapping of the velocity model error in the image space. Such an approach for constructing the image perturbation is computationally efficient and simple to implement. The technique also provides a new alternative for using focusing information in wavefield-based velocity model building. Synthetic examples demonstrate the successful application of our method to a layered model and a subsalt velocity update problem. [ABSTRACT FROM AUTHOR]

Purpose: In light-ion beam dose delivery with the scanning technique the spacing between adjacent spots is an important parameter during treatment planning. In order to study the effect of spot spacing on dose conformity and robustness for single field uniform dose configurations, fundamental geometrical properties of placement of Gaussian beamlets are explored. In particular, the dependence of penumbra width and flatness on spot width and spot spacing is investigated. Methods: Infinitesimal calculus and analytical methods are used to derive simple expressions for the lateral penumbra and the flatness of one-dimensional dose profiles in continuous scanning and uniform discrete spot scanning. In the same way expressions for the fundamental modes of perturbation of the spot sequence are developed. A numerical, matrix-based approach is followed to optimize weights spot-by-spot. Results: Generally the lateral penumbra widths lie between 1.13σb and 1.68σb with σb being the standard deviation of the beam spot profile. For regularly placed spots of equal weight with spot spacing λ the lateral penumbra is given by 1.68σ′ where σ′ results from quadratic subtraction of λ/12 from σb. The quantization error is identified as additional parameter describing the lateral dose conformity. It's variance is given by λ2/12 for a bunch of spots with uniform weights. The matrix-based optimization of weights for a one-dimensional dose box results in a lateral penumbra of typically 1.4σb. This value reduces to about 1.3σb if also the positions of the beam spots are optimized for the considered field size. The analytical formulas for uniform discrete scanning can be used as rough approximations of the best-case scenarios for weight-optimized dose profiles if the spot spacing is defined as effective spot spacing. Conclusions: The trade-off between flatness, quantization error, and robustness on the one side and penumbra width on the other side can be described analytically for equally weighted spots. Treatment planning systems often perform a least-squares optimization of the individual spot weights which results in smaller lateral penumbras and smaller quantization errors than for uniform discrete scanning. However, the benefit of this weight optimization decreases with increasing λ (in the regime λ>σb). The spot spacing, which is obtained from the scenario that the optimization objective is met by uniform discrete scanning, poses a sharp upper limit for the spot spacing λ in weight optimization methods. [ABSTRACT FROM AUTHOR]

We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov-Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well-suited for the study of unstructured point cloud data, which we illustrate through an application in shape classification. [ABSTRACT FROM AUTHOR]

A new method for generating split modes in ring resonators, used as notch filters with three geometries (square, triangular, and circular), is introduced by varying the feed position of electromagnetically coupled feed line. The resonators are fabricated (all at 2.4 GHz nominally) on TMM4 (ℇr = 4.5, h = 0.762 mm) substrates and coupled electromagnetically to a 50 Ω microstrip feed line on separate TMM4 substrate. Only the latter has ground plane under it. The offset distance between the center of feed line and center of resonator is varied and changes in the resonant (notch) frequency, rejection (S21) of single and split modes are recorded at each offset position for all resonators. Experimental results are found to agree with simulated results to a greater degree for square and lesser for other two geometries. Frequency variations have much more disagreements. The angle of crossing between feed line and ring edges appears to be a critical factor. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1747–1752, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23483 [ABSTRACT FROM AUTHOR]