Interpreting divergences and Madelung-type sums via extrapolations of sequence generating polynomials: Method of intersection and area rule

We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the global minimizer of the quasi-optimality function. In some problems this rule fails. We prove that one of the local minimizers of the quasi-optimality function is always a good regularization parameter. For the choice of the proper local minimizer we propose to construct the Q-curve which is the analogue of the L-curve, but on the x-axis we use modified discrepancy instead of discrepancy and on the y-axis the quasi-optimality function instead of the norm of the approximate solution. In the area rule we choose for the regularization parameter such local minimizer of the quasi-optimality function for which the area of the polygon, connecting on Q-curve this minimum point with certain maximum points, is maximal. We also provide a posteriori error estimates of the approximate solution, which allows to check the reliability of the parameter chosen heuristically. Numerical experiments on an extensive set of test problems confirm that the proposed rules give much better results than previous heuristic rules. Results of proposed rules are comparable with results of the discrepancy principle and the monotone error rule, if the last two rules use the exact noise level.

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Rules Over Rights? Legal Aspects of the European Commission Recommendation for Resumption of Dublin Transfers of Asylum Seekers to Greece

German Law Journal ◽

10.1017/glj.2019.54 ◽

2019 ◽

Vol 20 (05) ◽

pp. 637-659

Author(s):

Boryana Gotsova

Keyword(s):

Human Rights ◽

European Commission ◽

Asylum Seekers ◽

Legal Aspects ◽

Eu Law ◽

Human Rights Protection ◽

Rights Protection ◽

Commission Recommendation ◽

Area Rule ◽

Asylum Procedure

AbstractFive years after the Dublin transfers of asylum seekers to Greece were halted—due to recurrent failings in the detention conditions, living conditions, and asylum procedure—the European Commission recommended a resumption of the practice. This Article analyzes the Recommendation in light of the human rights reports preceding and following it. The examination reveals that the renewal of systematic transfers would be premature, posing serious risks to the rights of asylum seekers under European and EU law. The restoration of a flawed system for distribution of asylum claims among the Member States—without fundamental reforms towards greater solidarity—may lead to a repetition of past mistakes. Despite the paramount importance of the Dublin system for the functioning of the Schengen Area, rule enforcement should not supersede human rights protection.

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Analysis of Propagation Between Rows of Conducting Cylinders That Model Solid Surfaces Using the Same Surface Area Rule

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2012.2189695 ◽

2012 ◽

Vol 60 (5) ◽

pp. 2602-2606 ◽

Cited By ~ 1

Author(s):

Alper K. Ozturk ◽

Robert Paknys

Keyword(s):

Surface Area ◽

Solid Surfaces ◽

Area Rule ◽

Conducting Cylinders

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On the use of the equal area rule for the wire-grid representation of metallic surfaces

2006 17th International Zurich Symposium on Electromagnetic Compatibility ◽

10.1109/emczur.2006.214907 ◽

2006 ◽

Cited By ~ 2

Author(s):

A. Rubinstein ◽

C. Rostamzadeh ◽

M. Rubinstein ◽

F. Rachidi

Keyword(s):

Metallic Surfaces ◽

Wire Grid ◽

Equal Area ◽

The Wire ◽

Area Rule

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Transonic equivalence rule: a nonlinear problem involving lift

Journal of Fluid Mechanics ◽

10.1017/s0022112075003011 ◽

1975 ◽

Vol 72 (1) ◽

pp. 161-187 ◽

Cited By ~ 24

Author(s):

H. K. Cheng ◽

M. M. Hafez

Keyword(s):

Transonic Flow ◽

Line Source ◽

Sectional Area ◽

Small Disturbance ◽

Cross Sectional ◽

Outer Flow ◽

Nonlinear Structure ◽

First Order ◽

Lift Control ◽

Area Rule

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.

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