THE ONE FIXED POINT IN A CHANGING AGE. AN ANALYSIS OF HALF-SECULAR TRENDS AMONG ORIGINAL PAPERS PUBLISHED INTHE LANCET1945-95

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to colour-render pictures produced by fractal top and stealing colours from a natural picture. Barnsley has used the one-step feed- back process to compute the fractal top. In this paper, the authors introduce a two-step feedback process to compute fractal top for contractive and non-contractive transformations.

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Secular trends of sustained remission in rheumatoid arthritis, a nationwide study in Sweden

Rheumatology ◽

10.1093/rheumatology/kez273 ◽

2019 ◽

Cited By ~ 1

Author(s):

Jon T Einarsson ◽

Minna Willim ◽

Tore Saxne ◽

Pierre Geborek ◽

Meliha C Kapetanovic

Keyword(s):

Symptom Onset ◽

Secular Trend ◽

Secular Trends ◽

Treat To Target ◽

Sustained Remission ◽

Life Table Analysis ◽

Treatment Start ◽

Quality Register ◽

Table Analysis ◽

The One

Abstract Objectives The aim of this study of patients with RA in Sweden was to investigate secular trends in achieving sustained remission (SR), i.e. DAS28 <2.6 on at least two consecutive occasions and lasting for at least 6 months. Methods All adult RA patients registered in the Swedish Rheumatology Quality register through 2012, with at least three registered visits were eligible, a total of 29 084 patients. Year of symptom onset ranged from 1955, but for parts of the analysis only patients with symptom onset between 1994 and 2009 were studied. In total, 95% of patients fulfilled the ACR 1987 classification criteria for RA. Odds of reaching SR for each decade compared with the one before were calculated with logistic regression and individual years of symptom onset were compared with life table analysis. Results Of patients with symptom onset in the 1980s, 1990s and 2000s, 35.0, 43.0 and 45.6% reached SR, respectively (P < 0.001 for each increment), and the odds of SR were higher in every decade compared with the one before. The hazard ratio for reaching SR was 1.15 (95% CI 1.14, 1.15) for each year from 1994 to 2009 compared with the year before. Five years after symptom onset in 2009, 45.3% of patients had reached SR compared with 15.9% in 1999. Conclusion There is a clear secular trend towards increased incidence of SR in patients with RA in Sweden. This trend most likely reflects earlier diagnosis and treatment start, and adherence to national and international guidelines recommending the treat to target approach.

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IX. Remarks concerning the Natural-Historical Determination of Diallage

Transactions of the Royal Society of Edinburgh ◽

10.1017/s0080456800024212 ◽

1826 ◽

Vol 10 (1) ◽

pp. 127-147

Author(s):

W. Haidinger

Keyword(s):

Fixed Point ◽

Natural History ◽

Distinct Species ◽

The Other ◽

Accurate Information ◽

External Appearance ◽

Slight Degree ◽

The One

The following paper contains the results of a series of inquiries, which lead to the conclusion, that the mineral called Smaragdite by Saussure, does not form a species of its own; but that this name has been given to a compound of certain varieties of two distinct species, Augite and Hornblende, the natural-historical species of paratomous and hemiprismatic Augite-spar.Owing in part to the slight degree of resemblance prevailing among its varieties, the authors who have described them differ so essentially in opinion, that I am obliged to go into various details, both respecting the external appearance of the mineral itself, and of the opinions of mineralogists, in order to afford a correct view of the natural-historical species, to which these varieties belong, since this is the basis upon which every system, and, indeed, all accurate information in natural history, is founded, and the fixed point to which the one and the other must be referred.

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On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2019.6.9 ◽

2019 ◽

Vol 24 (6) ◽

Author(s):

Mi Zhou ◽

Xiao-Lan Liu ◽

Adrian Secelean

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Common Property ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Complete Metric Spaces ◽

Contraction Condition ◽

New Type ◽

The One

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

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Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

10.24963/kr.2021/50 ◽

2021 ◽

Author(s):

Jandson S. Ribeiro ◽

Matthias Thimm

Keyword(s):

Fixed Point ◽

Knowledge Base ◽

Special Class ◽

Belief Change ◽

Minimal Change ◽

The Other ◽

Preference Relations ◽

Other Hand ◽

The One ◽

Rationality Postulates

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

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On the Homotopy Property of Nussbaum's Fixed Point Index

Canadian Journal of Mathematics ◽

10.4153/cjm-1982-006-3 ◽

1982 ◽

Vol 34 (1) ◽

pp. 44-62

Author(s):

Gilles Fournier ◽

Reine Fournier

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Fixed Point Index ◽

Point Index ◽

Homotopy Property ◽

Lefschetz Fixed Point Theorem ◽

The One ◽

Compact Map ◽

General Conditions

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

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Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane

Advanced Nonlinear Studies ◽

10.1515/ans-2012-0210 ◽

2012 ◽

Vol 12 (2) ◽

Cited By ~ 13

Author(s):

Alessandro Fonda ◽

Rodica Toader

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Periodic Solutions ◽

Hamiltonian Systems ◽

Point Theorem ◽

Elementary Level ◽

Pendulum Equation ◽

Forced Pendulum ◽

The One

AbstractBy the use of a generalized version of the Poincaré-Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level.

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A general renormalization procedure on the one-dimensional lattice and decay of correlations

Stochastics and Dynamics ◽

10.1142/s0219493719500035 ◽

2019 ◽

Vol 19 (01) ◽

pp. 1950003

Author(s):

Artur O. Lopes

Keyword(s):

Fixed Point ◽

Final Section ◽

Polynomial Decay ◽

Renormalization Procedure ◽

Real Numbers ◽

One Dimensional ◽

Point Potential ◽

Renormalization Operator ◽

The One ◽

Natural Way

We present a general form of renormalization operator [Formula: see text] acting on potentials [Formula: see text]. We exhibit the analytical expression of the fixed point potential [Formula: see text] for such operator [Formula: see text]. This potential can be expressed in a natural way in terms of a certain integral over the Hausdorff probability on a Cantor type set on the interval [0,1]. This result generalizes a previous one by Baraviera, Leplaideur and Lopes where the fixed point potential [Formula: see text] was of Hofbauer type. For the potentials of Hofbauer type (a well-known case of phase transition) the decay is like [Formula: see text], [Formula: see text]. Among other things we present the estimation of the decay of correlation of the equilibrium probability associated to the fixed potential [Formula: see text] of our general renormalization procedure. In some cases we get polynomial decay like [Formula: see text], [Formula: see text], and in others a decay faster than [Formula: see text], when [Formula: see text]. The potentials [Formula: see text] we consider here are elements of the so-called family of Walters’ potentials on [Formula: see text] which generalizes a family of potentials considered initially by Hofbauer. For these potentials some explicit expressions for the eigenfunctions are known. In a final section we also show that given any choice [Formula: see text] of real numbers varying with [Formula: see text] there exists a potential [Formula: see text] on the class defined by Walters which has a invariant probability with such numbers as the coefficients of correlation (for a certain explicit observable function).

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