Iteration Theory: Dynamical Systems and Functional Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1627-1647 ◽  
Author(s):  
F. Balibrea ◽  
L. Reich ◽  
J. Smítal
Keyword(s):  
Dynamical Systems ◽  
Functional Equations ◽  
Discrete Dynamical Systems ◽  
Iteration Theory ◽  
Open Problems ◽  
Research Directions ◽  
The Past ◽  
New Research

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

scholarly journals RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES

2010 ◽  
Vol 20 (09) ◽  
pp. 2591-2636 ◽  
Author(s):  
F. BALIBREA ◽  
T. CARABALLO ◽  
P. E. KLOEDEN ◽  
J. VALERO
Keyword(s):  
Dynamical Systems ◽  
Open Problems ◽  
Research Directions ◽  
Present Account ◽  
The Past ◽  
Recent Developments ◽  
New Research

This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open problems.

scholarly journals Quantifying Noninvertibility in Discrete Dynamical Systems

10.37236/9475 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Colin Defant ◽  
James Propp
Keyword(s):  
Dynamical Systems ◽  
Real Number ◽  
Arbitrary Function ◽  
Discrete Dynamical Systems ◽  
Open Problems ◽  
Natural Measure ◽  
Stack Sorting ◽  
Finite Set

Given a finite set $X$ and a function $f:X\to X$, we define the \emph{degree of noninvertibility} of $f$ to be $\displaystyle\deg(f)=\frac{1}{|X|}\sum_{x\in X}|f^{-1}(f(x))|$. This is a natural measure of how far the function $f$ is from being bijective. We compute the degrees of noninvertibility of some specific discrete dynamical systems, including the Carolina solitaire map, iterates of the bubble sort map acting on permutations, bubble sort acting on multiset permutations, and a map that we call "nibble sort." We also obtain estimates for the degrees of noninvertibility of West's stack-sorting map and the Bulgarian solitaire map. We then turn our attention to arbitrary functions and their iterates. In order to compare the degree of noninvertibility of an arbitrary function $f:X\to X$ with that of its iterate $f^k$, we prove that \[\max_{\substack{f:X\to X\\ |X|=n}}\frac{\deg(f^k)}{\deg(f)^\gamma}=\Theta(n^{1-1/2^{k-1}})\] for every real number $\gamma\geq 2-1/2^{k-1}$. We end with several conjectures and open problems.  

The Changing Field of Sports History in Australasia

2017 ◽  
Author(s):  
Gary Osmond
Keyword(s):  
Research Directions ◽  
Sports History ◽  
Popular Discourse ◽  
Substantial Growth ◽  
The Past ◽  
Australian Rules Football ◽  
Scholarly Discussion ◽  
Formed Part ◽  
New Research ◽  
Cultural Turn

This chapter focuses on sport historiography in Australia and New Zealand, with three broad aims: to survey historic and historiographic developments, to consider the historiographical predominance of team ball sports, and to chart new and emerging directions. While sport had long formed part of popular discourse in both countries, in the 1980s historians began to analyze sport comprehensively, and the decades since have witnessed a substantial growth in sports historiography produced by academic scholars. Research has had a particular focus on certain sports, especially cricket, rugby, and Australian Rules football, which has been problematic in terms of its exclusivity and yet generative of important scholarly discussion and debate. New research directions, especially those emerging from an increased engagement with the cultural turn in the past decade, have yielded important studies into the fields of affect, bodies, materiality, visuality, and other areas new or rare in sports history.

Mechanical properties of bioactive glasses, glass-ceramics and composites

1998 ◽  
Vol 212 (2) ◽  
pp. 127-136 ◽  
Author(s):  
I D Thompson ◽  
L L Hench
Keyword(s):  
Mechanical Properties ◽  
Quality Index ◽  
Glass Ceramics ◽  
Primary Concern ◽  
High Modulus ◽  
Bioactive Glasses ◽  
Research Directions ◽  
The Past ◽  
New Research ◽  
Carrier Systems

The application of bioactive glass and glass-ceramics has been widely documented over the past twenty years but the high modulus and low fracture toughness has made them less applicable for clinical, load bearing, applications. The development of non-resorbable polyethylene and poly-sulphone matrices for these materials has improved the mechanical properties. However, the primary concern of whether the bioactivity of the composites is reduced is still unresolved. The more recent development of resorbable carrier systems, dextran and collagen, for bioactive glasses does not introduce such problems, hence making this form of composite suitable for novel soft tissue applications. The development of a simple quality index has enabled some of the materials described within this paper to be ranked by their ability to replace bone, thus enabling possible new research directions to be emphasized.

scholarly journals Using the Problem-Based Learning in STEM Teaching About Bamboo Toothpick Houses

2020 ◽  
Vol 13 (12) ◽  
pp. 70
Author(s):  
Ngoc-Giang Nguyen
Keyword(s):  
Teaching Methods ◽  
Problem Based Learning ◽  
Research Process ◽  
Ho Chi Minh City ◽  
Research Directions ◽  
Cooperative Teaching ◽  
The Past ◽  
International College ◽  
New Research ◽  
Stem Teaching

In Vietnam, there are currently stable and comprehensive innovations in the field of education. Educational scientists have shifted from knowledge-focused teaching to competency teaching. Since then, there have been more new research directions in teaching than in the past, such as integrated teaching, practical application of mathematics and STEM teaching, etc. In these directions, STEM teaching is a new and broad topic. In particular, there are many teaching methods used in STEM teaching. Some people use project teaching, some use discovery teaching, and some others use cooperative teaching methods. Through the research process, we found that STEM is an integrated area, so we should choose one of the most appropriate ways to approach it. That is a problem-based learning method. How does STEM teaching work with problem-based learning? To illustrate this STEM teaching work, we will use the design and implementation of the model of a bamboo toothpick house at Ho Chi Minh City International College.

scholarly journals MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW

2005 ◽  
Vol 15 (11) ◽  
pp. 1779-1794 ◽  
Author(s):  
HARALAMPOS HATZIKIROU ◽  
ANDREAS DEUTSCH ◽  
CARLO SCHALLER ◽  
MATTHIAS SIMON ◽  
KRISTIN SWANSON
Keyword(s):  
Mathematical Modelling ◽  
Tumour Growth ◽  
State Of The Art ◽  
Vascular Tumour ◽  
Open Problems ◽  
Malignant Brain Tumour ◽  
The Past ◽  
Research Perspectives ◽  
Current State ◽  
New Research

During the past several years mathematical models have been applied to various aspects of cancer dynamics, in particular avascular and vascular tumour growth, invasion, angiogenesis, and metastasis. This paper focuses on the most common and malignant brain tumour, glioblastoma, and surveys the growing number of studies dealing with mathematical modelling of this tumour. We attempt to classify these studies by their biomedical relevance and critically analyse their results. The aim of this review is to provide a meaningful reference, to both biomedical and mathematical researchers, of the current state of the art of glioma tumour modelling. The discussion attempts to identify current open problems as well as new research perspectives in the mathematical modelling of glioblastoma growth.

scholarly journals All’s well? Comparing on- and off-site pollen samples and exploring the potential of pollen from man-made contexts

2019 ◽  
Vol 29 (2) ◽  
pp. 125-131 ◽  
Author(s):  
Yvonne F. van Amerongen
Keyword(s):  
The Netherlands ◽  
Bronze Age ◽  
Pollen Analysis ◽  
Forest Cover ◽  
Research Directions ◽  
The Past ◽  
Time Period ◽  
Pollen Traps ◽  
Preservation Conditions ◽  
New Research

Abstract Pollen analysis has long been used as a tool to make an assessment of regional vegetation. On-site pollen samples are taken for the same purpose at some excavations, because they are often the only available contexts with good preservation conditions. This paper shows that the analysis of on- and off-site pollen samples from the same region (West Frisia, the Netherlands) and time period (Dutch Bronze Age; ca. 2000–800 bc) can give very conflicting results on the type and amount of regional vegetation, in this case forest cover. Reasons for this discrepancy are discussed in relation to the use of on-site contexts by people in the past, as well as their location within a settlement. Furthermore, the potential of these contexts for the assessment of locally performed subsistence-related activities is outlined. New research directions are required to test this potential, so that wells and other man-made pollen traps can become a valuable future tool for reconstructing the past.

INNOVATION CAPABILITY, ABSORPTIVE CAPACITY AND SMES PERFORMANCE IN PAKISTAN: THE MODERATING EFFECT OF BUSINESS STRATEGY

2018 ◽  
Vol 13 (Number 2) ◽  
pp. 1-11
Author(s):  
Muhammad Zulqarnain Arshad ◽  
Darwina Arshad
Keyword(s):  
Economic Growth ◽  
Absorptive Capacity ◽  
Business Strategy ◽  
Innovation Capability ◽  
Research Directions ◽  
Conceptual Paper ◽  
And Performance ◽  
New Research ◽  
The Relationship ◽  
Crucial Part

The small and medium-sized enterprises (SMEs) play a crucial part in county’s economic growth and a key contributor in country’s GDP. In Pakistan SMEs hold about 90 percent of the total businesses. The performance of SMEs depends upon many factors. The main aim for the research is to examine the relationship between Innovation Capability, Absorptive Capacity and Performance of SMEs in Pakistan. This conceptual paper also extends to the vague revelation on Business Strategy in which act as a moderator between Innovation Capability, Absorptive Capacity and SMEs Performance. Conclusively, this study proposes a new research directions and hypotheses development to examine the relationship among the variables in Pakistan’s SMEs context.

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