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When locations of individual-level health data are released in the form of published maps, the identity of these individuals could be identified through reverse geocoding. Spatial data can, therefore, not be released unless the locations have been modified, for example, using aggregation or geographic masking. Geographic masking techniques apply translation or perturbations to decrease the likelihood of re-identification of individuals through reverse geocoding. The current study proposes a new geographic masking technique referred to as “location swapping.” Location swapping replaces an original location with a masked location selected from all possible locations with similar geographic characteristics within a specified neighborhood. Strengths and weaknesses of location swapping will be discussed relative to existing geographic masking techniques. The approach will be illustrated using several example data sets and a custom toolset developed for ArcGIS to automate the location swapping algorithm. [ABSTRACT FROM PUBLISHER]

We review our recent developments in multireference explicitly correlated F12 theories (explicitly correlated internally contracted multireference perturbation and multireference configuration interaction theories) that achieve near-basis-set-limit accuracy of the underlying multireference electron correlation methods with basis sets of medium size. The applicability of the multireference F12 theories is the same as that of their non-F12 counterpart, and therefore it is a computational tool with predictive accuracy for complicated electronic structures with strong correlation. A comparison with the earlier developments by others is also discussed. [ABSTRACT FROM PUBLISHER]

Dinur and Nissim (2003) show that perturbed responses to queries on confidential data that provide a fixed guarantee on the quality of the response, are subject to privacy compromise. In this study, we investigate the impact of the Dinur-Nissim results for masking mechanisms that provide interval responses to queries. Our results indicate that when the width of the interval response is related to the magnitude of the query response, privacy compromise is even more likely than the fixed guarantee situation addressed in Dinur-Nissim. [ABSTRACT FROM AUTHOR]

We study within the framework of density functional theory the behaviour of a two-dimensional fluid with a competing attraction at short distances and repulsion at longer distance in addition to a hard core. The soft part of the interaction is treated by a first-order thermodynamic perturbation theory, which for a homogeneous bulk fluid predicts that thermodynamic quantities reduce to that of the hard-disc reference system. Despite this seemingly simple thermodynamic result, the behaviour of this fluid with competing interactions is rich and intriguing. In this work we follow the insight and inspirations by Reatto and co-workers, who performed computer simulation studies of the same system. [ABSTRACT FROM AUTHOR]

In this article, we give some necessary and sufficient conditions under which the Moore-Penrose inverse of a lower triangular operator has the lower and upper triangular forms, respectively. As a special case, we recover some theorems and corollaries of Chen et al. [Perturbation analysis of the generalized Bott-Duffin inverse of L-zero matrices, Linear Multilinear Algebra 51 (2003), pp. 11-20] and Deng and Chen [A note on the generalized Bott-Duffin inverse, Appl. Math. Lett., 20 (2007), pp. 746-750]. [ABSTRACT FROM AUTHOR]

This work deals with the existence, uniqueness and stability of solutions for semilinear discrete second order evolution equations in Banach spaces by using recent characterization of well-posedness for second order evolution equations in terms of R-boundedness and lp-multipliers. We also give results on boundedness and asymptotic behaviour for semilinear discrete evolution equations. [ABSTRACT FROM AUTHOR]

Many applications in electrical engineering, signal processing and mathematical physics lead to the following approximation problem: let h be a short linear combination of nonincreasing exponentials with complex exponents. Determine all exponents, all coefficients and the number of summands from finitely many equispaced sampled data of h. This is a nonlinear inverse problem. This article is an extension of Potts and Tasche [Parameter estimation for exponential sums by approximate Prony method, Signal Process., 90 (2010), pp. 1631-1642], where only the case of sums of complex exponentials with real frequencies is considered. In the following, we present new results on an approximate Prony method (APM) which is based on Beylkin and Monzon [On approximations of functions by exponential sums, Appl. Comput. Harmon. Anal. 19 (2005), pp. 17-48]. In contrast to their results, we apply perturbation theory for a singular value decomposition of a rectangular Hankel matrix such that we can describe the properties and the numerical behaviour of APM in detail. For this inverse problem, the number of sampled data acts as regularization parameter. The first part of APM recovers the exponents. The second part computes the coefficients by an overdetermined linear Vandermonde-type system. Numerical experiments show the performance of our method. [ABSTRACT FROM AUTHOR]

This article deals with the uniqueness and stability of coexistence solutions of a basic N-dimensional competition model in the unstirred chemostat by Lyapunov-Schmidt procedure and perturbation technique. It turns out that if the parameter G ≠ 0, which is given in Theorem 1.1, this model has a unique coexistence solution provided that the maximal growth rates a, b of u, v, respectively, lie in a certain range. Moreover, the unique coexistence solution is globally asymptotically stable if G > 0, while it is unstable if G < 0. In the later case, the semitrivial equilibria are both stable. [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]

We consider a periodic pseudodifferential operator H = (- Δ)l + A (l > 0) in Rd which satisfies the following conditions: (i) the symbol of H is smooth in x, and (ii) the perturbation A has order smaller than 2l - 1. Under these assumptions, we prove that the spectrum of H contains a half-line. [ABSTRACT FROM AUTHOR]

This aritcle describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified computational procedure that is employed. As such it should be of interest to teachers of applied mathematics courses, particularly those courses which include perturbation methods. One of the merits of this approach is that it leads on naturally to a scheme based on Taylor's expansions and, consequently, allows the regular perturbation method to be introduced into a course much earlier than is currently common. The method is illustrated by implementing it to four perturbation problems, including two algebraic equations and two initial-value problems. The new approach is compared and contrasted with the traditional perturbation scheme in order to demonstrate its relative merit. [ABSTRACT FROM AUTHOR]

This paper presents a tracking design methodology applicable to multivariable non-affine-in-control systems. The main focus is on solving the tracking problem for non-linear systems whose dynamics depend non-linearly on the control input. The latter is designed to be faster than the main system dynamics. Using singular perturbation theory along with the Lyapunov stability theorems, it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors, provides closed-loop stability, and solves the tracking problem with bounded errors. Simulations illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We consider a linear elastic plate with stress-free boundary conditions and zero Poisson coefficient. We prove that under a local change of Young's modulus infinitely many eigenvalues arise in the essential spectrum which accumulate at a positive threshold. We give estimates on the accumulation rate and on the asymptotical behaviour of the eigenvalues. [ABSTRACT FROM AUTHOR]

Gibbs ensemble Monte Carlo simulations are performed to obtain the vapour-liquid equilibrium of oblate-like fluids interacting through the Kihara intermolecular potential. Results confirm the validity of a perturbation theory for Kihara fluids, whose accuracy for prolate fluids was tested some years ago. As in the case of hard ellipsoids, the symmetry of the phase diagram of oblate and prolate models is analysed. An interesting relation of Boyle temperature and critical parameters with molecular volume is found for the considered models. As a particular application, this relation allows the prediction of some thermodynamic properties of a new promising biofuel 2,5dimethylfuran. [ABSTRACT FROM AUTHOR]

The Landau Hamiltonian governing the behavior of a quantum particle in dimension 2 in a constant magnetic field is perturbed by a compactly supported magnetic field and a similar electric field. We describe how the spectral subspaces change and how the Landau levels split under this perturbation. [ABSTRACT FROM AUTHOR]

The early transition phenomena in a buoyancy-opposed vertical channel flow have been investigated. The spectral method with a weak formulation is employed in the direct numerical simulation to solve the coupled transient 3-D momentum and energy equations. Initial perturbation includes a finite-amplitude 2-D TS wave and a pair of 3-D oblique waves in a K-type disturbance. The results show that after a period of transition time, small-sized vortical structures appear in the central regions of the channel. The subsequent development and breakdown of the vortical structures take place in the central regions of the channel where the shear stress of the laminar base velocity for the buoyancy-opposed flow is significantly larger than that of the isothermal flow. The patterns of the vortical structures in the wall region are almost unchanged during the transition. These transition phenomena are different from those in the buoyancy-assisted and isothermal flows, where the formation and development of the vortical structures initiate from the walls. The simulation results such as the local temperature fluctuations and harmonic energy carried by the different wave modes, are consistent in pointing out a general trend of sudden change from the laminar regime to a different state for the buoyancy-opposed flow, which agrees with the experimental observations obtained for pipe and annulus flows. [ABSTRACT FROM AUTHOR]

Collective oscillations in thermal equilibrium are shown to represent only a small fraction of the degrees of freedom of a liquid metal, the important fraction being associated to uncorrelated motions of the atoms. The present paper, however, justifies the basic interest for these oscillations in the theory of diffusion. In fact, they can be explained in the framework of a collective coordinate formulation, where the relevant Fourier components of the pair potential are only those corresponding to the wavevectors of the collective modes. Since the matrix elements for atomic scattering processes are proportional to the Fourier coefficients, it follows that, in this formulation, the only important processes are collisions where the wavevector change of an atom is a wavevector of the collective modes. A reduction in the number of these modes, as produced by a temperature rise, implies a reduction in the scattering processes and, subsequently, of the resistance presented by the liquid to the motion of a diffusing atom. This explains the strong rise with temperature of the self-diffusion coefficient, as recently observed in liquid lithium. Perturbation theory can be used to account for those Fourier components, which have been neglected in the above formulation. In this case, the results are fully consistent with the theory of diffusion developed earlier [M. Omini, Phil. Mag. 86 1643 (2006)]. [ABSTRACT FROM AUTHOR]

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is employed to calculate critical parameters of several model fluids. It is found that no matter how dis-continuous or continuous attractive perturbation part of whole interaction potential is, the 3rd-order TPT is accurate reliably for prediction of the critical parameters only on condition that the interaction potential is long-ranged or intermediate-ranged. Even when the 2nd-order macroscopic compressibility approximation TPT (2nd-order MCA-TPT) completely fails, the 3rd-order TPT still performs well. The 3rd-order TPT is then used to investiagte in detail validity and range of a recently emerging empirical [image omitted] rule. It is found that the empirical rule only applies for potentials consisting of a hard sphere core and a continuous and attractive perturbation tail, whether the attractive perturbation tail is differentiable with respect to particle separation or not does not matter. But for potentials with dis-continuous perturbation tail and those diaplaying two fluid-fluid critical points, the empirical rule fails completely. [ABSTRACT FROM AUTHOR]

We consider viscosity solutions of fully nonlinear elliptic equations [image omitted] for which u ≡ 0 is a solution. We assume F is smooth and uniformly elliptic only in a neighborhood of the points (0, 0, 0, x), and show that u is smooth in the interior if ‖u‖L∞ is sufficiently small. [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]

A new approach and corresponding method are presented which can be of use in resolving the problem of determination of the eigen frequencies for confined systems, such as resonators, wave guides, and the like, filled with a temporally and spatially dispersive medium. The problem of excitation of such systems by external current is considered. The theory of local and small perturbations as applied to those systems, is presented. [ABSTRACT FROM AUTHOR]

In article [Abdel-Aziz, M.R., 2004, Relative perturbation theory for matrix eigenproblems in free vibration analysis (International J. of Computer Mathematics, Vol. 81, No. 4, pp. 505–514) 1], we have introduced bounds for eigenvalues of eigenproblems in free vibration analysis, when the perturbation happens in either the mass matrix or in the stiffness matrix. This article aims to bound the additive and multiplicative relative distances and ,respectively, where ? and µ are eigenvalues and one is the perturbation of the other. These bounds are investigated when the perturbation happens in both the mass and the stiffness matrices. Numerical experiments show that the investigated bounds are satisfied and their values are depend on the element-wise perturbation of the matrix. [ABSTRACT FROM AUTHOR]

We give conditions under which a system of the formwill have constant or periodic solutions ( x ( t ), y (? t )) for and sufficiently small, such that for Here [ t ] denotes the greatest integer function. [ABSTRACT FROM AUTHOR]

In this article we study the solitary waves for nonlinear Klein–Gordon equation in an n-dimensional space, n?=?3. We prove the existence of a sequence (u?) of radial solutions of perturbed equation, with (u?) ? 0, ?? > 0, such that , where u is the solution of the limit problem. [ABSTRACT FROM AUTHOR]

A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt— Poincaré. [ABSTRACT FROM AUTHOR]

A two-electron effective operator V 2 is constructed to reproduce, to lowest order of perturbation theory, the effect of p-electron admixtures in configurations of f electrons occurring in rare-earth ions located at octahedral sites in elpasolite crystals. These admixtures can arise from excitations of the type f → p as well as p → f, the latter including electron transfer from neighbouring ligands to the central rare-earth ion. The effective operator is decomposed into nine orthogonal components . For octahedral symmetry their strengths are specified by coefficients that depend on just two parameters. The insensitivity of the crystal splitting of of to some , as found by McCaw and Denning, is related to exceptionally small values of the corresponding reduced matrix elements of . The discrepancies that these authors have found in fitting their experimental data for other levels to the standard one-electron crystal-field Hamiltonian V 1 are examined. The effective operator V 2 is found to reproduce the general trends of these discrepancies provided allowance is made for transitions of the type f ← f ′ which are implicit in the spin-correlated crystal-field model. [ABSTRACT FROM AUTHOR]

We report static electric (hyper)polarizability values of the three linear isomers of (CN) 2 . Large, flexible basis sets have been especially designed for all three molecules and the electric properties have been obtained from finite-field Møller-Plesset perturbation theory and coupled cluster calculations. All three molecules are characterized by large polarizability anisotropies. Self-consistent field calculations of near-Hartree-Fock quality yield the following mean polarizabilities: for CN-NC, 32.42 for NC-CN and 33.46 for CN-CN. For the second hyperpolarizability we obtain for CN-NC, 3090 for NC-CN and 3748 for CN-CN. Thus, electric (hyper)polarizability increases in the order NC-CN

Thermodynamic perturbation theory is used to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in a good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. Monte Carlo simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer-to-colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces. [ABSTRACT FROM AUTHOR]

A robust output feedback control is developed for the stabilization of a class of multivariable nonlinear systems including nonlinear actuators. The class of systems under consideration can be transformed into global normal form with no zero dynamics. The plant model is allowed to depend on constant unknown parameters which do not change the vector relative degree of the system. It is proven that if the actuator dynamics are sufficiently fast, the proposed controller will stabilize the origin of the actual system and will be robust with respect to the unknown parameters. It is also proven that the actuator dynamic need not be faster than the observer dynamics. [ABSTRACT FROM AUTHOR]

Some transport theoretical calculations determine the exiting currents on the boundary of a volume from the entering currents. To do so, they need the so called response matrix. If the volume is symmetric, the response matrix is a cyclic matrix. If the volume is symmetric but the material distribution is a sum of a symmetric function and a small perturbation, we are no longer able to say anything about the response matrix, we have to calculate the perturbation for each element. A more effective approach is proposed by considering perturbations of specific asymmetry, such as a tilt along an axis. We point out the relationship between symmetries of material distribution in a volume and symmetries of the response matrix. The method can be generalized to a number of boundary value problems. [ABSTRACT FROM AUTHOR]

This paper deals with the analytic determination of the nonlinear state feedback of nonlinear singularly perturbed systems in the optimal control problem with respect to a quadratic performance criterion. The designer controller is simplified by the use of the tensors representations and the singular perturbation approach, which generate a nonlinear reduced order model described by a vectorial polynomial state equation truncated at the third order. Thus the nonlinear suboptimal control based upon the reduced model is applied to the control of the full dimensional model. In a simulation study, the obtained suboptimal trajectories indicate the efficiency of this approach when compared with the optimal solution of the problem. [ABSTRACT FROM AUTHOR]

The article examines the sensitivity of posterior expectations to perturbations of prior marginals using a local method. Inferences drawn from a Bayesian data analysis depend on the prior distribution over the parameter space. For this reason, there is a substantial Bayesian robustness literature concerned with quantifying the degree to which posterior quantities depend on the prior. This article, however, addresses the changes induced in posterior quantities by changes in various parts of the prior. The majority of Bayesian robustness work uses a global method. All possible inferences arising from a class of priors are considered, the hope being that the resulting class of inferences is small and hence robust to the prior. But the global approach is often limited by the difficulty of computing the range of a posterior quantity as the prior varies in a class. Although there is an inherent Bayesian robustness in many simple iid sampling settings where the data quickly swamp the prior, the article authors explore sensitivity in more complex situations.

Potential relief along the direction perpendicular to the face of the cube for oxygen atom located in Mg--O--Nb chain in Pb(Mg 1/3 Nb 2/3 )O 3 (PMN) is considered. Accurate total energy cluster calculations are performed in the framework of ab initio restricted Hartree-Fock (RHF) method plus 2nd order Moller-Plesset perturbation theory (MP2) electron correlation corrections. It is found that the equilibrium oxygen position is shifted by 0.0664 Å from the middle point towards Nb atom. It is shown that electron correlation effects strongly influence on the equilibrium atomic positions in PMN. [ABSTRACT FROM AUTHOR]