Analytic Boundary Research Articles

Construction de quasimodes de Rayleigh à grande durée de vie

Nous savons que pour le système de l'élasticité à l'extérieur d'un obstacle compact convexe à bord analytique en dimension deux avec condition de Neumann sur le bord, il existe exactement deux suites de résonances z k ± (appelées résonances de Rayleigh), vérifiant | ℑ z k ± | ⩽ e − C R z k ± . Nous construisons des quasimodes associés à ces résonances le plus loin possible de l'obstacle dans le cas où le bord de l'obstacle est analytique assez loin dans le complexe et assez proche d'un cercle. Nous étudions ensuite les propriétés de décroissance exponentielle de ces quasimodes par rapport à R z k ± , en fonction de la géométrie de l'obstacle.

Adjoint approach to the physical characterization of a shallow-water environment

In underwater acoustics a variety of different applications of adjoint models has been proposed in recent years. Adjoints have been derived for normal modes and for both the standard parabolic equation and Claerbout’s wide-angle approximation. This paper reviews the analytic nonlocal boundary control approach proposed in an earlier paper by the authors [Meyer & Hermand, ‘‘Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field,’’ J. Acoust. Soc. Am. 117, 2937–2948 (2005)] and presents a numerical extension that allows direct inversion of the geoacoustic parameters that are embedded in a discrete representation of the nonlocal boundary condition at the water-sediment interface. The effectiveness of this numerical adjoint approach for the physical characterization of a shallow-water environment is illustrated with applications for geoacoustic inversion and ocean acoustic tomography. In particular, it is shown how a joint inversion across multiple frequencies can enhance the performance of the optimization process, especially for the case of a sparse receiver array spanning part of the water column. In an additional example we combine the two applications and discuss the feasibility of geoacoustic inversion in the presence of an uncertain sound-speed profile.

ERRATUM

Journal of Analytical PsychologyVolume 51, Issue 2 p. i-i Free Access ERRATUM First published: 24 March 2006 https://doi.org/10.1111/j.0021-8774.2006.00595.xAboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat The author of the article entitled, ‘The unfolding and healing of analytic boundary violations: personal, clinical and cultural considerations’, published in the November 2005 issue of the Journal of Analytical Psychology (Vol. 50, 5), inadvertently left out the name of Thomas Singer as co-author with Sam Kimbles of the development of the cultural complex theory. The author apologizes to Dr. Singer for the regrettable omission of his name in the article as he rightfully deserves recognition. Reference Anonymous (2005). ‘The unfolding and healing of analytic boundary violations: personal, clinical and cultural considerations’. Journal of Analytical Psychology, 50, 5, 661– 691. http://www.blackwell-synergy.com/doi/full/10.1111/j.0021-8774.2005.00563.x Volume51, Issue2April 2006Pages i-i ReferencesRelatedInformation

On boundary critical points for semigroups of analytic functions

We analyze the relationship between boundary fixed points of semigroups of analytic functions and boundary critical points of their infinitesimal generators. As a consequence, we show two new inequalities for analytic self-maps of the unit disk. The first one is about angular derivatives at fixed points of functions belonging to semigroups of analytic functions. The second one deals with angular derivatives at contact points of arbitrary analytic functions from the unit disk into itself.

Analytic Field Propagation TFSF Boundary for FDTD Problems Involving Planar Interfaces: Lossy Material and Evanescent Fields

Recently, total-field scattered-field (TFSF) boundaries have been developed for the finite-difference time-domain (FDTD) method which are essentially perfect. The implementation requires an analytic description of the incident field and hence is termed the analytic field propagation (AFP) TFSF method. Previous papers described the implementation for problems involving homogeneous as well as layered media. In this work we provide the details for problems involving lossy media. Additionally, the case of fields incident beyond the critical angle are considered (i.e., when, for lossless material, there is total reflection of the incoming wave and the fields in the second medium are evanescent)

Numerical analysis of the method of fundamental solution for harmonic problems in annular domains

In this study, we investigate the application of the method of fundamental solutions (MFS) to the Dirichlet problem for Laplace's equation in an annular domain. We examine the properties of the resulting coefficient matrix and its eigenvalues. The convergence of the method is proved for analytic boundary data. An efficient matrix decomposition algorithm using fast Fourier transforms (FFTs) is developed for the computation of the MFS approximation. We also tested the algorithm numerically on several problems confirming the theoretical predictions. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005

The unfolding and healing of analytic boundary violations: personal, clinical and cultural considerations

Jungian analysts are not exempt from an unconscious engagement in a group complex. The author hypothesizes that there is a silent, dark legacy of belief in the superiority of men's judgment and the inferiority of women's, left by Jung, that has had a wounding impact on some Jungian analysands. Conscious and public mourning may be needed to heal our cultural complex. The author, a woman, traces the origins of her own patriarchal complexes and reveals how in her first analysis these mingled with the patriarchal complex shared by Jungian institute, her two male analysts and their former analyst, a pillar of the institute's community. Her first analyst aborted her analysis to begin a personal partnership with her. Her second analyst unconsciously colluded with the first analyst in not exploring this outcome as a violation. This resulted in a second compromised treatment. The senior analyst who had been these two analysts' own analyst was consulted, and he too failed to address the transgression. After experiencing severe symptomatology, the patient entered a third analysis with a woman where transference and regression were the focus. Eventually, meaning was found in the confrontations with the particular Jungian organization and its ethics committee, who acknowledged the first analyst's behaviour to be unethical. The author sees this process as a paradigm for the enactment and healing of a group complex.

Towards an Effectivisation of the Riemann Theorem

Let Q be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane ℂ. Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper, we find an explicit form of this map for a broad class of domains with analytic boundaries.

Uniqueness of the solution to inverse obstacle scattering problem

It is proved that the scattering amplitude known at a fixed frequency, a fixed direction of the incident plane wave and all directions of the scattered wave in a solid angle, however small, determine uniquely the shape of a strictly convex obstacle with a smooth but not analytic boundary on which the Dirichlet boundary condition is assumed.

Existence of the Boundary Value of a Polyharmonic Function

We establish a criterion for existence of an L2-limit and a weak L2-limit of a polyharmonic function on a regular analytic boundary of a bounded plane domain.

Finite analytic boundary condition for a higher-order finite analytic scheme

A higher-order finite analytic scheme based on one-dimensional finite analytic solutions is used to discretize three-dimensional equations governing turbulent incompressible free surface flow. In order to preserve the accuracy of the numerical scheme, a new, finite analytic boundary condition is proposed for an accurate numerical solution of the partial differential equation. This condition has higher-order accuracy. Thus, the same order of accuracy is used for the boundary. Boundary conditions were formulated and derived for fluid inflow, outflow, impermeable surfaces and symmetry planes. The derived boundary conditions are treated implicitly and updated with the solution of the problem. The basic idea for the derivation of boundary conditions was to use the discretized form of the governing equations for the fluid flow simplified on the boundaries and flow information. To illustrate the influence of the higher-order effects at the boundaries, another, lower-order finite analytic boundary condition, is suggested. The simulations are performed to demonstrate the validity of the present scheme and boundary conditions for a Wigley hull advancing in calm water. Copyright © 2005 John Wiley & Sons, Ltd.

Existence of boundary values for biharmonic functions

Criteria for the existence of an -limit and a weak -limit of a biharmonic function at the regular analytic boundary of a bounded two-dimensional domain are established.

Further calculations for Israeli options

Recently Kifer introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment not less than the holder's claim had they exercised at that moment. Kifer shows that pricing and hedging of these options reduces to evaluating a stochastic saddle point problem associated with Dynkin games. Kyprianou, A.E. (2004) "Some calculations for Israeli options", Fin. Stoch. 8, 73-86 gives two examples of perpetual Israeli options where the value function and optimal strategies may be calculated explicity. In this article, we give a third example of a perpetual Israeli option where the contingent claim is based on the integral of the price process. This time the value function is shown to be the unique solution to a (two sided) free boundary value problem on (0, ∞) which is solved by taking an appropriately rescaled linear combination of Kummer functions. The probabilistic methods we appeal to in this paper centre around the interaction between the analytic boundary conditions in the free boundary problem, Itô's formula with local time and the martingale, supermartingle and submartingale properties associated with the solution to the stochastic saddle point problem.

Convergence of Julia polynomials

We study the approximation of conformal mappings with the polynomials defined by Keldysh and Lavrentiev from an extremal problem considered by Julia. These polynomials converge uniformly on the closure of any Smirnov domain to the conformal mapping of this domain onto a disk. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angles at the boundary.

Analytic sets extending the graphs of holomorphic mappings

Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies that if the graph of ƒ extends as an analytic set to a neighborhood of a point (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a.

Numerical analysis of the MFS for certain harmonic problems

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace's equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem which is applicable even in the cases when the MFS matrix might be singular. We prove the convergence of the method for analytic boundary data and perform a stability analysis of the method with respect to the distance of the singularities from the origin and the number of degrees of freedom. Finally, we test the algorithm numerically.

Approximation of Conformal Mapping via the Szegő Kernel Method

We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angle at the boundary. Furthermore, we show that the rate of approximation on compact subsets inside the domain is essentially the square of that on the closure. Two standard applications to the rate of decay for the contour orthogonal polynomials inside the domain, and to the rate of locally uniform convergence of Fourier series are also given.

International Relations Theory and Internal Conflict: Insights from the Interstices

The presumption that international relations theory can help explain internal conflict is widely shared and accounts for the hubris of many who came late to the topic of domestic violence and civil war from the study of international politics.' There has been some useful arbitrage with theories of interstate war providing insights into the causes of intrastate war. But the belief that international relations theory has something uniquely important to contribute to the study of internal violence is wrong-or at least misstated. Rather, we are approaching a single, unified theory of political violence of which interstate and intrastate war may be particular forms. I emphasize approaching because this general theory has not yet been fully worked out and may because the particular forms of violence and the relationships between them have not yet been defined. Nonetheless, considerable progress has been made. The real question is what does this general theory tell us about violence? What are the commonalities between interstate and intrastate war? What are the differences? How can the study of one help inform our understanding of the other? If so far scholars have arbitraged from international relations to civil war, it is important to recognize that trade is a two-way process; we should seek to exploit opportunities for gain in both directions. Doing so highlights the irrelevance of some analytic boundaries long taken for granted in the field of political science and focuses our attention for future research on the role of extremists within both domestic groups and states.

A new quantum Monte Carlo algorithm in the momentum representation: The sign problem and the Hess-Fairbank effect

An exact numerical algorithm based on the diagrammatic quantum Monte Carlo method in the momentum representation is proposed; in many cases, this algorithm is free of the sign problem and extends the class of models that can be analyzed by cluster methods. The weakening of the sign problem is demonstrated via the determination of the ground state of electrons on a chain in the Hubbard model. The algorithm is applied to the investigation of the behavior of a one-dimensional boson system with attraction in a rotating ring in the region of the Hess-Fairbank effect predicted by Ueda and Leggett. The existence of this effect for a comparatively small number of particles N ∼ 10 is confirmed. An analytic boundary of this effect is determined in the limit as N → ∞.

The Analyst's Secret Delinquencies

Despite a burgeoning literature on major analytic boundary violations, there has been little investigation of what might be called analytic delinquencies or misdemeanors—the small and virtually ubiquitous ways in which analysts deliberately withdraw from the therapeutic endeavor. I consider the impact of professional misdemeanors on patient and analyst and compare both with more serious analytic “crimes” and enactments. Professional delinquencies may reflect a therapeutic reenactment, an expression of the analyst's split-off or disavowed need, or an unconscious attempt to self-regulate or to negotiate space within the constraints of the treatment setting. Because the professional ideal leaves so little room for the analyst's humanity, it is often difficult for us to address and work with evidence of our own need when it clashes with what we regard as the analytic contract.