A Note on the Convergence Analysis of a Diffuse-domain Approach

2012 ◽  
Vol 12 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Sebastian Franz ◽  
Hans-Görg Roos ◽  
Roland Gärtner ◽  
Axel Voigt
Keyword(s):  
Differential Equation ◽  
Convergence Analysis ◽  
Plane Problem ◽  
Half Plane ◽  
Numerical Experiments ◽  
Two Dimensions ◽  
Elliptic Differential Equation ◽  
One Dimension ◽  
Approximation Quality

Abstract We analyse the error behaviour of a diffuse-domain approximation of an elliptic differential equation. In one dimension and for a half-plane problem in two dimensions an approximation quality of order one in the interface parameter is shown. Some supporting numerical experiments are also presented.

On meshfree numerical differentiation

2018 ◽  
Vol 16 (05) ◽  
pp. 717-739
Author(s):  
Leevan Ling ◽  
Qi Ye
Keyword(s):  
A Priori ◽  
Noisy Data ◽  
Numerical Differentiation ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Positive Definite Kernels ◽  
Approximation Quality ◽  
Symmetric Positive Definite ◽  
Optimal Kernel

We combine techniques in meshfree methods and Gaussian process regressions to construct kernel-based estimators for numerical derivatives from noisy data. Specially, we construct meshfree estimators from normal random variables, which are defined by kernel-based probability measures induced from symmetric positive definite kernels, to reconstruct the unknown partial derivatives from scattered noisy data. Our developed theories give rise to Tikhonov regularization methods with a priori parameter, but the shape parameters of the kernels remain tunable. For that, we propose an error measure that is computable without the exact values of the derivative. This allows users to obtain a quasi-optimal kernel-based estimator by comparing the approximation quality of kernel-based estimators. Numerical examples in two dimensions and three dimensions are included to demonstrate the convergence behavior and effectiveness of the proposed numerical differentiation scheme.

scholarly journals The Democratic Quality of Institutional Regimes: A Conceptual Framework

2002 ◽  
Vol 50 (2) ◽  
pp. 313-331 ◽  
Author(s):  
André Kaiser ◽  
Matthias Lehnert ◽  
Bernhard Miller ◽  
Ulrich Sieberer
Keyword(s):  
Two Dimensions ◽  
One Dimension ◽  
Trade Off ◽  
Individual Preferences ◽  
Majoritarian Democracy ◽  
Democratic Quality ◽  
Input Characteristic ◽  
Actual Policy ◽  
Institutional Regimes

Lijphart's spectrum of democracies – recently expanded by Jack Nagel to a sub-majoritarian sphere of pluralitarian systems which use disproportional electoral systems in order to manufacture majority governments from minorities in the electorate – is based on only one dimension: inclusion of preferences. Political scientists in the Lijphartian tradition wrongly assume that inclusion of preferences, which is an input characteristic, automatically leads to responsiveness, which refers to actual policy decisions and hence is an output characteristic. We therefore add ‘responsibility’ as a second input characteristic and employ it alongside the inclusiveness of institutional regimes. We argue that in representative democracies there exists a trade-off between inclusiveness and responsibility. This trade-off helps us to measure the democratic quality of institutional regimes. The now expanded spectrum of democracies based on these two dimensions shows that majoritarian democracy proper – in which governments represent a majority of individual preferences but not more than necessary – is the best possible combination of the two democratic values.

Mind-mindedness in adult and adolescent mothers: Relations to maternal sensitivity and infant attachment

2010 ◽  
Vol 34 (6) ◽  
pp. 529-537 ◽  
Author(s):  
Isabelle Demers ◽  
Annie Bernier ◽  
George M. Tarabulsy ◽  
Marc A. Provost
Keyword(s):  
Adolescent Mothers ◽  
Maternal Sensitivity ◽  
Emotional Valence ◽  
Mental States ◽  
Two Dimensions ◽  
One Dimension ◽  
Strange Situation ◽  
Infant Attachment

This article examines the quality of maternal mind-mindedness among adult and adolescent mothers, using an assessment of the appropriateness and emotional valence of maternal mind-related comments while interacting with their infants. Twenty-nine adult mothers and 69 adolescent mothers participated in two assessments with their 18-month-old infants. Results showed that adult mothers used more mind-related comments when interacting with their child, especially comments referring to infant mental states. Adult mothers also used more appropriate and positive mind-related comments. Home observations and strange situation assessments revealed that two dimensions of mind-mindedness were associated with maternal sensitivity and three with infant attachment in adult mothers, whereas only one dimension was associated with maternal sensitivity in adolescent mothers.

scholarly journals Out of the lockdown: democratic trust in the management of epidemic crises

2020 ◽  
Author(s):  
Roberto Frega
Keyword(s):  
Political Theory ◽  
Political Trust ◽  
Two Dimensions ◽  
One Dimension ◽  
Democratic Quality

This paper presents a preliminary inquiry into the democratic role of trust in the management of epidemic crises, by shedding some light on one dimension political theory has systematically neglected, which is trust of elites in citizens. The paper proceeds as follows. After an introduction, the first section distinguishes two dimensions of political trust. I then proceed to explain why elites’ trust in citizens is as important as citizens’ trust in elites for the democratic quality of a regime. The following section discusses in further details the democratic implications of elites’ trust in citizens. The fourth and last section introduces the idea of democratic experiments as opportunities to reinforce elites’ trust in citizens.

scholarly journals TIME ACCURATE FAST THREE-STEP WAVELET-GALERKIN METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 04 (01) ◽  
pp. 65-79 ◽  
Author(s):  
MANI MEHRA ◽  
B. V. RATHISH KUMAR
Keyword(s):  
Galerkin Method ◽  
Numerical Experiments ◽  
Nonlinear Problems ◽  
Taylor Series Expansion ◽  
Two Dimensions ◽  
One Dimension ◽  
Advection Equation ◽  
Galerkin Methods ◽  
Present Scheme ◽  
Wavelet Galerkin Method

We introduce the concept of three-step wavelet-Galerkin method based on the Taylor series expansion in time. Unlike the Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving nonlinear problems. Numerical schemes taking advantage of the wavelet bases capabilities to compress the operators and sparse representation of functions which are smooth, except for localized regions, up to any given accuracy are presented. Here numerical experiments deal with advection equation with the spiky solution in one dimension, two dimensions and nonlinear equation with a shock in solution in two dimensions. Numerical results indicate the versatility and effectiveness of the proposed scheme.

Quality of life in Hungarian polio survivors

2021 ◽  
Author(s):  
Erika Viktória Miszory ◽  
Melinda Járomi ◽  
Annamária Pakai
Keyword(s):  
Quality Of Life ◽  
Mental Health ◽  
Sample Selection ◽  
Cross Sectional Study ◽  
Two Dimensions ◽  
Cross Sectional ◽  
Emotional Role ◽  
The Difference ◽  
Polio Survivors

Abstract Aim The number of Hungarian polio patients can be estimated at approximately 3000. Polio infection is currently affecting people 56–65 years of age. The aim of the study was to reveal the quality of life of patients living with polio virus in Hungary. Subject and methods The quantitative cross-sectional study was conducted in January–April 2017 among polyomyelitis patients living in Hungary. In the non-random, targeted, expert sample selection, the target group was composed of patients infected with poliovirus (N = 268). We have excluded those who refused to sign the consent statement. Our data collection method was an SF-36 questionnaire. Using the IBM SPSS Statistics Version 22 program, descriptive and mathematical statistics (χ2-test) were calculated (p < 0.05). Results The mean age of the members of the examined population is 63.5 years; 68.1% were women and 31.90% were men. The majority of the respondents were infected by the polyovirus in 1956 (11.9%), 1957 (24.3%), and 1959 (19.5%). Polio patients, with the exception of two dimensions (mental health, social operation), on the scale of 100 do not reach the “average” quality of life (physical functioning 23 points, functional role 36 points, emotional role 47 points, body pain 48 points, general health 42 points, vitality 50 points, health change 31 points). Conclusion The quality of life of polio patients is far below the dimensions of physical function, while the difference in mental health compared to healthy people is minimal. It would be important to educate health professionals about the existing disease, to develop an effective rehabilitation method.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Giacomo Innocenti ◽  
Paolo Paoletti
Keyword(s):  
Control Strategy ◽  
Feedback Loop ◽  
Controller Design ◽  
Natural Control ◽  
Standard Methods ◽  
Approximation Quality ◽  
Linear Controller ◽  
Benchmark System ◽  
Global Linearization

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

Separation Standards—II

1966 ◽  
Vol 19 (2) ◽  
pp. 169-186 ◽  
Author(s):  
P. G. Reich
Keyword(s):  
One Dimension ◽  
Collision Risk ◽  
Practical Applications ◽  
Upper Limit ◽  
Intensive Observation ◽  
Relative Errors ◽  
Separation Standards

In the first part of this series of papers an outline was given of the approach made at the Royal Aircraft Establishment to the problems of estimating collision risk and of specifying the quality of navigation needed to make separation standards safe. It was stressed that estimates should be based on intensive observation of flying errors, rather than on speculative theories, and that it is more feasible to develop ‘upper limit’ estimating techniques than those which purport to give the exact risk. In summary, a list of seven ‘requirements’ was given, as a reminder of the essential principles which can so easily be overlooked in the piecemeal task of relating separation standards to collision risk.The purpose of this paper is to show some of the theoretical techniques which have been developed at R.A.E. to satisfy five of these requirements. (The remaining two do not call for special techniques and will be dealt with when practical applications are described in Part III.) The paper contains three Appendixes, dealing with the frequency of losing separation in one dimension, the computation of P's from the assumed tail shapes, and the treatment of relative errors. These are not included here but will appear in the off-printed version which may be obtained from the Royal Aircraft Establishment.Both this paper and the paper that follows by Mr. Attwooll are crown copyright and are reproduced with the permission of H.M. Stationery Office.

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