scholarly journals Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 928 ◽  
Author(s):  
Raffaele Chiappinelli
Keyword(s):  
Nonlinear Operator ◽  
Measure Of Noncompactness ◽  
Real Hilbert Space ◽  
Main Tool ◽  
Rayleigh Quotient ◽  
Lower And Upper Bounds ◽  
Qualitative And Quantitative ◽  
Quantitative Properties ◽  
Definition Of ◽  
Nonlinear Spectral Theory

We give a new and simplified definition of spectrumfor a nonlinear operator F acting in a real Banach space X, and study some of its features in terms of (qualitative and) quantitative properties of F such as the measure of noncompactness, α ( F ) , of F. Then, using as a main tool the Ekeland Variational Principle, we focus our attention on the spectral properties of F when F is a gradient operator in a real Hilbert space, and in particular on the role played by its Rayleigh quotient R ( F ) and by the best lower and upper bounds, m ( F ) and M ( F ) , of R ( F ) .

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

scholarly journals Exploring International and Inter-Sector Differences of Social Enterprises in the UK and India

2021 ◽  
Vol 13 (11) ◽  
pp. 5870
Author(s):  
Philipp Kruse
Keyword(s):  
Social Entrepreneurship ◽  
Social Enterprise ◽  
Social Enterprises ◽  
Future Research ◽  
Shape Features ◽  
Qualitative And Quantitative ◽  
Clear Cut ◽  
The One ◽  
Definition Of ◽  
The Uk

Social Entrepreneurship (SE) describes a new entrepreneurial form combining the generation of financial and social value. In recent years, research interest in SE increased in various disciplines with a particular focus on the characteristics of social enterprises. Whereas a clear-cut definition of SE is yet to be found, there is evidence that culture and economy affect and shape features of SE activity. In addition, sector-dependent differences are supposed. Building on Institutional Theory and employing a mixed qualitative and quantitative approach, this study sheds light on the existence of international and inter-sector differences by examining 161 UK and Indian social enterprises. A content analysis and analyses of variance were employed and yielded similarities as well as several significant differences on an international and inter-sector level, e.g., regarding innovativeness and the generation of revenue. The current study contributes to a more nuanced picture of the SE landscape by comparing social enterprise characteristics in a developed and a developing country on the one hand and different sectors on the other hand. Furthermore, I highlight the benefits of jointly applying qualitative and quantitative methodologies. Future research should pay more attention to the innate heterogeneity among social enterprises and further consolidate and extend these findings.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

scholarly journals Some New Volterra-Fredholm-Type Discrete Inequalities and Their Applications in the Theory of Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Difference Equations ◽  
Fredholm Type ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Discrete Inequalities ◽  
Quantitative Properties ◽  
Two Independent Variables

Some new Volterra-Fredholm-type discrete inequalities in two independent variables are established, which provide a handy tool in the study of qualitative and quantitative properties of solutions of certain difference equations. The established results extend some known results in the literature.

scholarly journals Comparative evaluation of properties of a clay based ceramic shaped via four techniques

Cerâmica ◽  
2018 ◽  
Vol 64 (370) ◽  
pp. 176-182 ◽  
Author(s):  
C. I. Torres ◽  
N. M. Rendtorff ◽  
M. Cipollone ◽  
E. F. Aglietti ◽  
G. Suárez
Keyword(s):  
Sintering Temperature ◽  
Continuous Process ◽  
Slip Casting ◽  
Textural Properties ◽  
Batch Process ◽  
Ceramic Ware ◽  
Kaolinite Clay ◽  
Qualitative And Quantitative ◽  
Quantitative Properties ◽  
Forming Methods

Abstract The results of qualitative and quantitative properties of clay based ceramic are presented in this work. Four different shaping methods and sintering temperatures were used to understand their influence in the final properties of a ceramic material formulated using kaolinite clay and calcined alumina. This material can be used as a structural ceramic for different applications, and there is no pre-established relation between the forming method and the final sintered properties. Forming methods used to prepare the samples were uniaxial pressing (a batch process that allows application in dry samples), extruding (a continuous process that requires moisture), slip casting (a process that allows to shape complex ceramic ware), and lamination (a batch process that requires moisture). Sintering temperatures were in the range of 1100 and 1400 °C. In order to compare how properties behave as the shaping method and sintering temperature change, textural properties, shrinkage, porosimetry, phase composition and mechanical strength were evaluated and analyzed. Scanning electron microscopy and microtomography were employed for analyzing and comparing the developed microstructures. Differences in the resulting properties are explained in terms of the developed crystalline phases and microstructure.

scholarly journals FOUND: A DEFINITION OF INTELLIGENCE

2021 ◽  
Vol IV(1) ◽  
Author(s):  
Adewunmi Falode ◽  
Keyword(s):  
21St Century ◽  
Pivotal Role ◽  
Process Data ◽  
Effective Utilization ◽  
Qualitative And Quantitative ◽  
Political Group ◽  
Military Planning ◽  
Critical Edge ◽  
State Actors ◽  
Definition Of

Intelligence has come to play a pivotal role in the affairs of states and non-state actors in the 21st century. It not only determines the outcome of conflict when it breaks out but also provides critical edge and foresight in military planning and engagements. However, the effective utilization and deployment of intelligence in any strategic environment may be hampered by the lack of a holistic and generally accepted definition of it. The search for a robust definition has not also been helped by the differing views on what should constitute the basic elements of it. To overcome these challenges, this work argues for and provides a holistic definition of intelligence. It uses both qualitative and quantitative methodologies to provide a more robust and holistic definition of intelligence. The work concludes that any acceptable definition of intelligence must contain five key elements: process, data, actionable information, political group and security.

scholarly journals Cutting-edge microangio-CT: new dimensions in vascular imaging and kidney morphometry

2018 ◽  
Vol 314 (3) ◽  
pp. F493-F499 ◽  
Author(s):  
Ruslan Hlushchuk ◽  
Cédric Zubler ◽  
Sébastien Barré ◽  
Carlos Correa Shokiche ◽  
Laura Schaad ◽  
...  
Keyword(s):  
Data Sets ◽  
Micro Ct ◽  
Quantitative Methodology ◽  
Micro Computed Tomography ◽  
Qualitative And Quantitative ◽  
Correlative Imaging ◽  
Contrast Enhanced ◽  
Consistent Assessment ◽  
Definition Of ◽  
X Ray Absorption

In the last decades, the contrast-enhanced micro-computed tomography (micro-CT) imaging of a whole animal kidney became increasingly important. The visualization was mainly limited to middle-sized vessels. Since modern desktop micro-CT scanners provide the necessary detail resolution, we developed an approach for rapid visualization and consistent assessment of kidney vasculature and glomeruli number. This method is based on μAngiofil, a new polymerizing contrast agent with homogenous X-ray absorption, which provides continuous filling of the complete vasculature and enables correlative imaging approaches. For rapid and reliable kidney morphometry, the microangio-CT (µaCT) data sets from glial cell line-derived neurotrophic factor (GDNF)+/− mice and their wild-type littermates were used. The results were obtained much faster compared with the current gold standard, histology-based stereology, and without processing artifacts. The histology-based morphometry was done afterward on the same kidneys. Both approaches revealed that the GDNF+/− male mice had about 40% fewer glomeruli. Furthermore, our approach allows for the definition of sites of interest for further histological investigation, i.e., correlative morphology. The polymerized μAngiofil stays in perfused vessels and is autofluorescent, which is what greatly facilitates the matching of histological sections with µaCT data. The presented approach is a time-efficient, reliable, qualitative, and quantitative methodology. Besides glomerular morphometry, the µaCT data can be used for qualitative and quantitative analysis of the kidney vasculature and correlative morphology.

Uncertainty and Velocity

2016 ◽  
Author(s):  
Martin Shubik ◽  
Eric Smith
Keyword(s):  
Financial Markets ◽  
Stochastic Analysis ◽  
Control Mechanisms ◽  
Qualitative And Quantitative ◽  
Monetary Systems ◽  
Monetary Economy ◽  
Velocity Of Money ◽  
Quantitative Properties ◽  
Complex Features ◽  
And Control

In this chapter the two features of uncertainty and the variability of the velocity of money are considered. Both of these are fundamental to considering the more subtle features of a monetary economy. They are interlinked and both add further complex features to the information, perception and control mechanisms of modern monetary systems. There has been an explosive development in the study of both the qualitative and quantitative properties of risk. The power of careful modeling and sophisticated stochastic analysis has already shown itself in the context of the stockmarket and other financial markets, but as the various qualitative aspects of risk are being uncovered and made well-defined, the scope of a useful econo-physics stretches far beyond the confines of the dynamics of paper traded on paper in the financial markets to the broad control mechanisms of the economy as a whole.

Designing a PhD Proposal in Mixed Method Research

2019 ◽  
pp. 36-48
Author(s):  
Ndungi wa Mungai
Keyword(s):  
Mixed Method ◽  
Quantitative Methods ◽  
Research Proposal ◽  
Mixed Method Research ◽  
Hypothetical Case ◽  
Mixed Method Approach ◽  
Qualitative And Quantitative ◽  
Qualitative And Quantitative Methods ◽  
Definition Of ◽  
Method Approach

This chapter reviews the challenges and advantages of writing a mixed method research (MMR) proposal. The argument put forward is that a mixed method approach overcomes the shortcomings of the commonly used qualitative and quantitative methods. A brief definition of a research proposal is followed by a discussion on the different interpretations of a mixed method and what makes mixed methods ideal in the proposal example that follows. A mixed method can be either one that utilizes qualitative and quantitative methods to different degrees or it can be regarded as a distinct method by itself. A mixed method is suitable where both different types of data can be collected, when the data adds value to what would be achieved using one approach and where cost also justifies it. A hypothetical case example where an application is being made to conduct an evaluation of an anti-truancy program is presented.

scholarly journals Understanding Immobility: Moving Beyond the Mobility Bias in Migration Studies

2019 ◽  
Vol 54 (2) ◽  
pp. 328-355 ◽  
Author(s):  
Kerilyn Schewel
Keyword(s):  
Interdisciplinary Research ◽  
Research Agenda ◽  
Quantitative Research ◽  
Analytical Tool ◽  
Future Directions ◽  
Qualitative And Quantitative ◽  
Migration Research ◽  
Migration Flows ◽  
Definition Of ◽  
Migration Theories

This article suggests that there is a mobility bias in migration research: by focusing on the “drivers” of migration — the forces that lead to the initiation and perpetuation of migration flows — migration theories neglect the countervailing structural and personal forces that restrict or resist these drivers and lead to different immobility outcomes. To advance a research agenda on immobility, it offers a definition of immobility, further develops the aspiration-capability framework as an analytical tool for exploring the determinants of different forms of (im)mobility, synthesizes decades of interdisciplinary research to help explain why people do not migrate or desire to migrate, and considers future directions for further qualitative and quantitative research on immobility.

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