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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]

In this paper, we combine the variational iteration method and perturbation theory to solve a time-dependent singularly perturbed reaction-diffusion problem. The problem is considered in the boundary layers and outer region. In the boundary layers, the problem is transformed by the variable substitution, and then the variational iteration method is employed to solve the transformed equation. In the outer region, we use the perturbation theory to obtain the approximation equation and the approximation solution. The final numerical experiments show that this method is accurate. [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 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]

We investigate Banach spaces possessing (or not possessing) the approximation properties APs, 0 < s ≤ 1, in connection with the following known question in the geometric theory of operators: under which conditions on Banach spaces X and Y and on positive numbers r and p does the p-nuclearity of the second adjoint of a continuous operator T from X to Y imply the p-nuclearity of T? Actually, we give necessary and sufficient conditions under which this question is answered affirmatively. In addition, the corresponding counterexamples are obtained in the maximally strong form. For instance, it is shown (and this statement is a significant strengthening of the previous results of that sort) that there exists a pair of separable Banach spaces Z and W such that the spaces Z** and W have Schauder bases, while for every p, 1 ≤ p < 2, there is a non-p-nuclear operator from W to Z with a p-nuclear second adjoint. Earlier, in similar examples, the corresponding spaces did not possess even the Grothendieck approximation property. The technique developed in this paper does not allow us to treat the case p > 2. That case will be studied in a forthcoming paper of the author. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

This paper investigates perturbation operators for variable neighborhood search (VNS) approaches for two related problems, namely the pickup and delivery traveling salesman problem with LIFO loading (TSPPDL) and FIFO loading (TSPPDF). Our study is motivated by the fact that previously published results on VNS approaches on the TSPPDL suggest that the perturbation operation has the most significant effect on solution quality. We propose a new perturbation operator for the TSPPDL that achieves better results on average than the existing best approach. We also devise new perturbation operators for the TSPPDF that combine request removal and request insertion operations, and investigate which combination of request removal and request insertion operations produces the best results. Our resultant VNS that employs our best perturbation operator outperforms the best existing TSPPDF approach on benchmark test data. [ABSTRACT FROM AUTHOR]

In this paper we describe a new measure of remoteness between sets described by nominal values. The introduced measures of perturbation of one set by another are considered instead of commonly used distance between two sets. The operations of the set theory are operated and the considered measures describe changes of the perturbed second set by adding the first one or vice versa. The values of the measure of sets' perturbation are range between 0 and 1, and in general, are not symmetric - it means that the perturbation of one set by another is not the same as the perturbation of the second set by the first one. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the influence of the minimum constraints (MCs) on the reference frame parameters in a free-net solution. The non-estimable part of these parameters (which is not reduced by the available data) is analysed in terms of its stability under a numerical perturbation of the constrained datum functionals. In practice, such a perturbation can be ascribed either to hidden errors in the known coordinates/velocities that participate in the MCs or to a simple change of their a priori values due to a datum switch on a different fiducial dataset. In addition, a perturbation of this type may cause a nonlinear variation to the estimable part of the reference frame parameters, since it theoretically affects the adjusted observations that are implied by the network's nonlinear observational model. The aforementioned effects have an impact on the quality of a terrestrial reference frame (TRF) that is established via a minimum-constrained adjustment, and our study shows that they are both controlled through a characteristic matrix which is inherently linked to the MC system (the so-called TRF stability matrix). The structure of this matrix depends on the network's spatial configuration and the 'geometry' of the datum constraints, while its main role is the filtering of any MC-related errors into the least-squares adjustment results. A number of examples with different types of geodetic networks are also presented to demonstrate the theoretical findings of our study. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of description of the set of parametric perturbation which preserves the spectrum of a discrete linear time varying system. We prove that all perturbations with the Lyapunov exponent lower then a regularity coefficient are characterized with this feature. Moreover, in case of a diagonal system, the perturbations with Lyapunov exponent equal to the regularity coefficient also reveal this feature. [ABSTRACT FROM AUTHOR]

This paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. The work done in this area during the periods 1984-2000 and 2000-2005 has already been surveyed in 2002 and 2007 but our main objective is to produce a collection of important research articles of physical significance. In this paper, the crux of research articles published by numerous researchers during 2006-2010 in referred journals has been presented, and this leads to conclusions and recommendations about what methods to use on singular perturbation problems. [ABSTRACT FROM AUTHOR]

In this paper, we give a self-contained description of three methods of perturbation series summation for the resolvent in the quantum Coulomb problem. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

In this paper, the condition number of singular value is discussed. The expressions of the zero-structured and patterned conditioning are also studied. The numerical tests are reported to provide interesting information about the singular value sensitivity when the perturbations of the matrix have arbitrarily assigned zero-structured and patterned case. [ABSTRACT FROM AUTHOR]

In this paper, several equivalent systems without constraints of the indefinite least squares problem with equality constraints (ILSE) are established. We also derive the perturbation results for the ILSE problem and illustrate our results with numerical tests. [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]

We study in this paper an M/ M/1 queue whose server rate depends upon the state of an independent Ornstein–Uhlenbeck diffusion process ( X( t)) so that its value at time t is μ φ( X( t)), where φ( x) is some bounded function and μ>0. We first establish the differential system for the conditional probability density functions of the couple ( L( t), X( t)) in the stationary regime, where L( t) is the number of customers in the system at time t. By assuming that φ( x) is defined by φ( x)=1− ε(( x ∧ a/ ε) ∨(− b/ ε)) for some positive real numbers a, b and ε, we show that the above differential system has a unique solution under some condition on a and b. We then show that this solution is close, in some appropriate sense, to the solution to the differential system obtained when φ is replaced with Φ( x)=1− ε x for sufficiently small ε. We finally perform a perturbation analysis of this latter solution for small ε. This allows us to check at the first order the validity of the so-called reduced service rate approximation, stating that everything happens as if the server rate were constant and equal to $\mu(1-\varepsilon {\mathbb{E}}(X(t)))$ . [ABSTRACT FROM AUTHOR]

In this paper, we study the bistatic scattering using an advanced integral equation model (AIEM). By keeping all the surface current terms in the Kirchhoff surface fields, the bistatic scattering coefficients are obtained. For simplification, the complete Kirchhoff field did not cast into the derivation of the complementary field. We compare varied updated versions of IEM-based models with the small perturbation model, geometrical optics model, and Kirchhoff approximation standard models at respective regions of validity. The results indicate that the new AIEM provides much more accurate predictions for bistatic scattering. [ABSTRACT FROM AUTHOR]

Abstract.  In this paper we prove that the Grosse–Wulkenhaar type non-commutative orientable complex scalar φ6 3 theory, with two non-commutative coordinates and the third one commuting with the other two, is renormalizable to all orders in perturbation theory. Our proof relies on a multiscale analysis in x space. [ABSTRACT FROM AUTHOR]

In this paper we investigate linear systems with multiple right-handed sides in the form of AX=B and (A ⊗ B)X=C. We derive normwise, mixed and componentwise condition numbers for these linear systems. Examples are given to evaluate the tightness of the first-order perturbation bounds. [ABSTRACT FROM AUTHOR]

We consider general-relativistic rotational perturbations in homogeneous and isotropic Friedmann–Robertson–Walker (FRW) cosmologies. Taking linear perturbations of FRW models, the general solution to the field equations contains tensorial, vectorial and scalar functions. The vectorial terms are in connection with rotations in the given model and due to the Sachs–Wolfe effect they produce contributions to the temperature fluctuations of the cosmic microwave background radiation (CMBR). In this paper we obtain the analytic time dependence of these contributions in a spatially flat FRW model with pressureless ideal fluid, in the presence and the absence of a cosmological constant Λ. We find that the solution can be separated into an integrable and a nonintegrable part, as in the case of scalar perturbations. Analyzing the solutions and using the results of recent observations, we estimate the order of magnitude of the angular velocity corresponding to the rotation tensor at the time of decoupling and today. [ABSTRACT FROM AUTHOR]

The little-known Belgian engineer Bernard Chait contributed to business cycle theory by means of a mathematical model, of which the 'law of divergence' was an important building block. The law of divergence has been interpreted as a generalization of the acceleration principle. This paper draws upon published and archival sources to examine the sources of Chait's thinking, explain the basics of his model and assess the impact of his work. His relations with François Divisia and Jan Tinbergen are explored and his claim that Leontief's dynamic input - model was an unacknowledged reformulation of his own work is analysed. [ABSTRACT FROM AUTHOR]

In this paper we study the free boundary problem arising as a limit as ɛ → 0 of the singular perturbation problem $${\textrm{div}(A(x)\nabla u) = \Gamma(x) \beta_\varepsilon(u)}$$ , where A = A( x) is Holder continuous, β ɛ converges to the Dirac delta δ0. By studying some suitable level sets of u ɛ, uniform geometric properties are obtained and show to hold for the free boundary of the limit function. A detailed analysis of the free boundary condition is also done. At last, using very recent results of Salsa and Ferrari, we prove that if A and Γ are Lipschitz continuous, the free boundary is a C 1,γ surface around $${\mathcal{H}^{N-1}}$$ a.e. point on the free boundary. [ABSTRACT FROM AUTHOR]

This paper is concerned with asymptotic behaviour of solutions of perturbed dynamic systems on time scales. A time scale version of the Hartman-Wintner theorem is established for a class of time scales. [ABSTRACT FROM AUTHOR]

The quantum SO(3)-invariants of ℚ-homology 3-spheres can be perturbatively expanded to the Ohtsuki invariant in number theory. On the other hand, it is known that the quantum SU(2)-invariants of 3-manifolds M admits a refinement involving a mod 2 cohomology class of M. A motivation of this paper is to study whether a perturbative expansion can be derived from the refinement. In this paper, we shall prove to be able to derive the perturbative expansion in the case of lens spaces by a concrete calculation, and shall define the perturbative invariant. Furthermore we obtain some properties for the perturbative invariant for covering spaces and connected sums of lens spaces. [ABSTRACT FROM AUTHOR]

In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems where α, β, c > 0 are parameters. Those systems model two-dimensional small amplitude long wavelength water waves. For α ≤ 1, this equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every β, c and almost every α ≤ 1, it admits solutions that are quasiperiodic in time. The proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the Boussinesq system to the center manifold, uses arguments of classical perturbation theory by considering the Hamiltonian formulation of the problem and studying the Birkhoff normal form. [ABSTRACT FROM AUTHOR]

The class of nonlinear reproductive dispersion mixed models (NRDMMs) is an extension of nonlinear reproductive dispersion models and generalized linear mixed models. This paper discusses the influence analysis of the model based on Laplace approximation. The equivalence of case-deletion models and mean-shift outlier models in NRDMMs is investigated, and some diagnostic measures are proposed via the case-deletion method. We also investigate the assessment of local influence of various perturbation schemes. The proposed method is illustrated with an example. [ABSTRACT FROM AUTHOR]

The ESPRIT algorithm is a subspace-based high-resolution method used in source localization and spectral analysis, which provides very accurate estimates of the signal parameters. However, the underlying theory assumes a known model order, which is usually not the case in many applications. In particular, it is well known that underevaluating the model order biases the estimation. In this paper, we analyze the perturbation induced by an erroneous model order, and we present an error bound for the estimated parameters. Based on this theoretical framework, we propose a new method for selecting an appropriate modeling order, which consists in minimizing the error bound. This approach is applied to both synthetic and musical signals, and its performance is compared to that of existing methods, such as the information theoretic criteria. [ABSTRACT FROM AUTHOR]

This paper provides a multiscale analytical study of steady incompressible turbulent flow through a channel of either Couette or pressure-driven Poiseuille type. Mathematically, the paper's two most novel features are that (1) the analysis begins with an underdetermined singular perturbation problem, namely the Reynolds averaged mean momentum balance equation, and (2) it leads to the existence of an infinite number of length scales. (These two features are probably linked, but the linkage will not be pursued.) The paper develops a credible assumption of a mathematical nature which, when added to the initial underdetermined problem, results in a knowledge of almost the complete layer (scaling) structure of the mean velocity and Reynolds stress profiles. This structure in turn provides a lot of other important information about those profiles. The possibility of almost-logarithmic sections of the mean velocity profile is given special attention. The sense in which the length scales are asymptotically proportional to the distance from the wall is determined. Most traditional theoretical analyses of these wall-bounded flows are based ultimately on either the classical overlap hypothesis, mixing length concepts, or similarity arguments. The present paper avoids those approaches and their attendant assumptions. Empirical data are also not used, except that the Reynolds stress takes on positive values. Instead, reasonable criteria are proposed for recognizing scaling layers in the flow, and they are then used to determine the scaling structure and much more information. [ABSTRACT FROM AUTHOR]

An efficient method for fast wide-band eigenmode analysis is presented in this paper. The finite-element solution space is projected to a subspace containing frequency-dependent information obtained at a single frequency by a Lanczos algorithm and modified perturbation theory, resulting in a single-point reduced-order model accurate over an extremely wide frequency range. A numerical procedure is developed to extract a desired mode from the reduced-order model for fast frequency sweep and is then applied to several practical problems, which demonstrate the solution accuracy and computational efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally according to the signal behaviour, and then the translates should get different scalings that match the local data density. Furthermore, if there is a local anisotropy in the data, the radial basis functions should possibly be distorted into functions with ellipsoids as level sets. In such cases, the symmetry and the definiteness of the matrices are no longer guaranteed. However, this brief note is the first paper to provide sufficient conditions for the unique solvability of such interpolation processes. The basic technique is a simple matrix perturbation argument combined with the Ball–Narcowich–Ward stability results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a singularly perturbed control system involving differential inclusions in Banach spaces with slow and fast solutions. Using the averaging approach, we obtain sufficient conditions for the Hausdorff convergence of the set of slow solutions in the supremum norm. We present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi-Lipschitz solutions. [ABSTRACT FROM AUTHOR]

In this paper we study the stability of integrable Hamiltonian systems under small perturbations, proving a weak form of the KAM/Nekhoroshev theory for viscosity solutions of Hamilton Jacobi equations. The main advantage of our approach is that, only a finite number of terms in an asymptotic expansion are needed in order to obtain uniform control. Therefore there are no convergence issues involved. An application of these results is to show thai Diophantine invariant tori and Aubry-Mather sets are stable under small perturbations. [ABSTRACT FROM AUTHOR]

This paper considers the robust stability of descriptor systems with structured perturbations. It presents a maximum perturbation bound for keeping a system regular, impulse-free and stable, by using the technique of Kronecker product and the structured singular value μ. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the existence of periodic solutions emerging of the equilibrium points of the spatial Hill lunar problem having the following equations of motion:ϵ is a small parameter andFi,i∈ {1, 2, 3}, are smooth periodic functions intwhich define a perturbation in resonancep:qwith some of the periodic solutions of the spatial Hill lunar problem beingpandqpositive relatively prime integers. [ABSTRACT FROM AUTHOR]

In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of the underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of admissible controls under this problem setup. Specifically, we establish a rigorous first order approximation of the value function associated to a fixed zeroth order suboptimal trading strategy, which is derived heuristically in [J.-P. Fouque, R. Sircar, and T. Zariphopoulou, Math. Finance, 2016]. Then, we show that this zeroth order suboptimal strategy is asymptotically optimal in a specific family of admissible trading strategies. Finally, we show that our assumptions are satisfied by a particular fully solvable model. [ABSTRACT FROM AUTHOR]

The iFlow modelling framework is a widthaveraged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the understanding of the underlying physics and the testing of parameter sensitivity. A comparison of the model results to measurements shows a good qualitative agreement. iFlow is written in Python and is available as open source code under the LGPL license. [ABSTRACT FROM AUTHOR]

In this paper we consider a singularly perturbed Markov decision process with the limiting average cost criterion. We assume that the underlying process is composed of n separate irreducible processes, and that the small perturbation is such that it ‘unites’ these processes into a single irreducible process. We formulate the underlying control problem for the singularly perturbed MDP, and call it the ‘limit Markov control problem’ (limit MCP). We prove the validity of the ‘the limit control principle’ which states that an optimal solution to the perturbed MDP can be approximated by an optimal solution of the limit MCP for any sufficiently small perturbation. We also demonstrate that the limit Markov control problem is equivalent to a suitably constructed nonlinear program in the space of long-run state-action frequencies. This approach combines the solutions of the original separated irreducible MDPs with the stationary distribution of a certain ‘aggregated MDP’ and creates a framework for future algorithmic approaches. [ABSTRACT FROM AUTHOR]

Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating functional methods have been proposed, in addition to the well-known Padé approximant, namely, the "Fractional Power of Polynomial" and the "Fractional Power of Rational functions" methods. Since combinations of these methods also give interpolating functions, we may end up with multitudes of the possible approaches. So a criterion for choosing an appropriate interpolating function is very much needed. In this paper, we propose reference quantities which can be used for choosing a good interpolating function. In order to validate the prescription based on these quantities, we study the degree of correlation between "the reference quantities" and the "actual degree of deviation between the interpolating function and the true function" in examples where the true functions are known. [ABSTRACT FROM AUTHOR]

In this paper, an implicit net with perturbations for solving the mixed equilibrium problems and fixed point problems has been constructed and it is shown that the proposed net converges strongly to a common solution of the mixed equilibrium problems and fixed point problems. Also, as applications, some corollaries for solving the minimum-norm problems are also included. [ABSTRACT FROM AUTHOR]

The property (gR), introduced in [Aiena, P., Guillen, J. and Peña, P., Property (gR) and perturbations, to appear in Acta Sci. Math. (Szeged), 2012], is an extension to the context of B-Fredholm theory, of property (R), introduced in [Aiena, P., Guillen, J. and Peña, P., Property (R) for bounded linear operators, Mediterr. J. Math. 8 (4), 491-508, 2011]. In this paper we continue the study of property (gR) and we consider its preservation under perturbations by finite rank and nilpotent operators. We also prove that if T is left polaroid (resp. right polaroid) and N is a nilpotent operator which commutes with T then T +N is also left polaroid (resp. right polaroid). [ABSTRACT FROM AUTHOR]

This paper considers the impacts on attractors of function perturbations in Boolean networks via semi-tensor product of matrices. Two types of function perturbations: one-bit perturbation and modifications of update schedule, are investigated. First, the algebraic form of perturbed Boolean networks under one-bit perturbation is given, based on which several necessary and sufficient conditions of different kinds of effects on state transition and attractors are obtained. Besides, a Boolean network with update schedule is studied and the definition of its adjacent diagraph is first presented in this paper. Furthermore, transition matrix of the updated network is calculated to analyze the changes of fixed points and limit cycles. At last, identifying function perturbations with its application in a Drosophila melanogaster segmentation polarity gene network is shown to demonstrate the practicability and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

We discuss the Camassa-Holm equation perturbed in Schwartz class around a suitable constant. This paper is concerned with the wave breaking mechanism for periodic case where two special classes of initial data were involved. The asymptotic behavior of solutions is also analyzed in the following sense: the corresponding solution to initial data with algebraic decay at infinity will retain this property at infinity in its lifespan. [ABSTRACT FROM AUTHOR]

In this paper, a semilinear elliptic equation with a nonlinear boundary condition and a perturbation in the reaction term is studied. The existence of a positive solution and another non-zero solution to the problem is proved when |λ| is small enough without any specific assumptions on the perturbation term. Moreover, it is shown that the non-zero solution becomes a positive one for small λ>0 under suitable assumptions on the perturbation term. [ABSTRACT FROM AUTHOR]

The radial differential equations associated with separable perturbations of Kerr-Newman black holes are known to admit Liouvillian (closed-form) solutions for constrained frequencies and black hole parameters. In this paper, we show that the parameter constraints are satisfied exactly in the case of no rotation and thereby obtain a countable infinity of exact purely damped quasi-normal modes of fields on a Reissner-Nordstrom background at special values of the black hole charge-mass ratio. We show that with rotation the parameter constraints for Liouvillian quasi-normal modes are satisfied approximately in two distinct physical scenarios, where analytical approximations for angular eigenvalues are known. We arrive at functional expressions for quasi-normal frequencies and wave-functions in the case of near-extremal slow rotation and in a particular case of highly damped scalar modes of Kerr and Kerr-Newman. In the near-extremal case, our formulas extend a recent result of Hod to electromagnetic and gravitational perturbations. [ABSTRACT FROM AUTHOR]

In this paper, we study the bifurcation of limit cycles of a class of planar quadratic reversible system ẋ = y +4x², ẏ = -x+2xy under quadratic perturbations. It is proved that the cyclicity of the period annulus is equal to two. [ABSTRACT FROM AUTHOR]

Subdivision schemes are special multi-resolution analysis (MRA) methods that have become prevalent in computer-aided geometric design. This paper draws useful analogies between the mathematics of subdivision schemes and the hierarchical structures of music compositions. Based on these analogies, we propose new methods for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. We demonstrate that the structure and recursive nature of the recently proposed subdivision models [S. Hed and D. Levin, Subdivision models for varying-resolution and generalized perturbations, Int. J. Comput. Math. 88(17) (2011), pp. 3709–3749; S. Hed and D. Levin, A ‘subdivision regression’ model for data analysis, 2012, in preparation] are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The analysis methods demonstrated enable the compression and decompression (reconstruction) of selected musical pieces and derive useful features of the pieces, laying groundwork for music classification. [ABSTRACT FROM PUBLISHER]

We perform a smoothed analysis of the GCC-condition number $${\fancyscript{C}(A)}$$ of the linear programming feasibility problem $${\exists x\in\mathbb{R}^{m+1}\,Ax < 0}$$. Suppose that $${\bar{A}}$$ is any matrix with rows $${\overline{a}_i}$$ of euclidean norm 1 and, independently for all i, let a be a random perturbation of $${\overline{a}_i}$$ following the uniform distribution in the spherical disk in S of angular radius arcsin σ and centered at $${\overline{a}_i}$$. We prove that $${\mathbb{E}({\rm ln}\,\fancyscript{C}(A)) =\mathcal{O} (mn/\sigma)}$$. A similar result was shown for Renegar's condition number and Gaussian perturbations by Dunagan et al. (Math Program Ser A, 2009). Our result is robust in the sense that it easily extends to radially symmetric probability distributions supported on a spherical disk of radius arcsin σ, whose density may even have a singularity at the center of the perturbation. Our proofs combine ideas from a recent paper of Bürgisser et al. (Math Comp 77(263), 2008) with techniques of Dunagan et al. [ABSTRACT FROM AUTHOR]

Abstract In this research paper, Artificial Bee Colony algorithm is modified with multiple update rules and K-opt operation to solve the Traveling Salesman Problem. Here the features of swap sequences and swap operations on the sequence of cities (solution/path) of the problem are used to create different solution (path) update rules of the algorithm. Eight different rules are proposed to update solutions in the algorithm. Updation of a solution by an employed bee or by an onlooker bee is done by a randomly selected rule from the rule set using Roulette Wheel selection process. In the scout bee phase of the algorithm, the perturbation technique, K-opt operation is applied on any stagnant solution for a fixed number of times for the possible improvement of it. The K-opt operation is again used at the end of the search process to improve the quality of the final solution (if possible). Proposed method is tested with a set of benchmark test problems from TSPLIB and it is observed that the efficiency of the algorithm is adequate with respect to the accuracy and the consistency for solving standard TSPs (Symmetric as well as Asymmetric) compared to the existing algorithms in the literature. [ABSTRACT FROM AUTHOR]