scholarly journals Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hendrik Baumann
Keyword(s):  
Continued Fractions ◽  
Convergence Theory ◽  
Convergence Criterion ◽  
Convergence Results ◽  
Starting Point ◽  
Special Cases ◽  
Definition Of ◽  
Generalized Continued Fractions

Abstract In the literature, many generalizations of continued fractions have been introduced, and for each of them, convergence results have been proved. In this paper, we suggest a definition of generalized continued fractions which covers a great variety of former generalizations as special cases. As a starting point for a convergence theory, we prove a Pringsheim-type convergence criterion which includes criteria for the aforementioned special cases. Furthermore, we address several fields in which our definition may be applied.

scholarly journals The Mathematical Structure of Integrated Information Theory

2021 ◽  
Vol 6 ◽  
Author(s):  
Johannes Kleiner ◽  
Sean Tull
Keyword(s):  
Information Theory ◽  
Conscious Experience ◽  
Mathematical Structure ◽  
Starting Point ◽  
Special Cases ◽  
Axiomatic Definition ◽  
Definition Of ◽  
The Brain ◽  
Integrated Information Theory ◽  
Integrated Information

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et al., as well as the Quantum IIT introduced by Zanardi et al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background.

Holism, Chinese Medicine and Systems Ideologies: Rewriting the Past to Imagine the Future

2018 ◽  
Author(s):  
Volker Scheid
Keyword(s):  
Eighteenth Century ◽  
Chinese Medicine ◽  
Medical Humanities ◽  
Science And Technology Studies ◽  
Human Beings ◽  
The Past ◽  
Starting Point ◽  
The Us ◽  
Shared Objective ◽  
Definition Of

This chapter explores the articulations that have emerged over the last half century between various types of holism, Chinese medicine and systems biology. Given the discipline’s historical attachments to a definition of ‘medicine’ that rather narrowly refers to biomedicine as developed in Europe and the US from the eighteenth century onwards, the medical humanities are not the most obvious starting point for such an inquiry. At the same time, they do offer one advantage over neighbouring disciplines like medical history, anthropology or science and technology studies for someone like myself, a clinician as well as a historian and anthropologist: their strong commitment to the objective of facilitating better medical practice. This promise furthermore links to the wider project of critique, which, in Max Horkheimer’s definition of the term, aims at change and emancipation in order ‘to liberate human beings from the circumstances that enslave them’. If we take the critical medical humanities as explicitly affirming this shared objective and responsibility, extending the discipline’s traditional gaze is not a burden but becomes, in fact, an obligation.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Digital competences of the workforce – a research topic?

2017 ◽  
Vol 23 (3) ◽  
pp. 721-734 ◽  
Author(s):  
Matthias Murawski ◽  
Markus Bick
Keyword(s):  
Research Topic ◽  
Future Research ◽  
Digital Competence ◽  
Content Type ◽  
Research Activities ◽  
Starting Point ◽  
Pros And Cons ◽  
Definition Of ◽  
The Individual ◽  
Practical Implications

Purpose Considering working in the digital age, questions on the consequences for the individual workers are, so far, often neglected. The purpose of this paper is to deal with the question of whether the digital competences of the workforce is a research topic. The authors argue for the thesis that it is indeed a research topic. Design/methodology/approach In addition to a literature analysis of the top IS, HR, and learning publications, non-scientific sources, as well as the opinions of the authors, are included. The authors’ thesis is challenged through a debate of corresponding pros and cons. Findings The definition of digital competences lacks scientific depth. Focussing on the workforce is valid, as a “lifelong” perspective is not mandatory for research. Digital competence research is a multidisciplinary task to which the IS field can make a valuable contribution. Research limitations/implications Although relevant references are included, some aspects are mainly driven by the opinions of the authors. The theoretical implications encompass a call for a scientific definition of digital competences. Furthermore, scholars should focus on the competences of the workforce, including occupations, roles, or industries. The authors conclude by providing a first proposal of a research agenda. Practical implications The practical implications include the alignment of multiple stakeholders for the design of “digital” curricula and the integration by HR departments of the construct of digital competences, e.g. for compensation matters and job requirements. Originality/value This paper is one of very few contributions in the area of the digital competences of the workforce, and it presents a starting point for future research activities.

On the Description and Definition of Human Factors/Ergonomics

1998 ◽  
Vol 42 (10) ◽  
pp. 671-674 ◽  
Author(s):  
Michael S. Wogalter ◽  
Peter A. Hancock ◽  
Patrick G. Dempsey
Keyword(s):  
Human Factors ◽  
Engineering Science ◽  
Human Factors Engineering ◽  
Lay Persons ◽  
Starting Point ◽  
Technical Report ◽  
Definition Of ◽  
Engineering Psychology

This work examines the terms most frequently used to describe our field, which has variously been named Ergonomics, Human Factors, Human Factors Engineering, and Engineering Psychology. A large number of definitions were collected, including those assembled in an earlier technical report by Licht, Polzella, and Boff (1990). First, the definitions were stripped of connector words. Second, the prefix root terms that had the same meaning were combined and third, the words were tabulated and sorted to reveal the content terms most frequently employed. These data may be used to develop core, concise definitions or longer more expository descriptions of the field. The list of terms could also be used as a starting point for the development of definitions oriented for different target audiences (e.g., lay persons vs. other engineering/science experts) as a method of disseminating information concerning what we do.

Beyond the heuristic approach to Kolmogorov-Smirnov theorems

1982 ◽  
Vol 19 (A) ◽  
pp. 359-365 ◽  
Author(s):  
David Pollard
Keyword(s):  
Weak Convergence ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Heuristic Approach ◽  
Convergence Theory ◽  
Simple Method ◽  
Starting Point ◽  
Kolmogorov Smirnov ◽  
The Subject

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

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