Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Fixed point results for multivalued contractions on graphs and their applications

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS.

Twierdzenia o punktach stałych pewnych klas operatorów nieliniowych wraz z ich zastosowaniami

Wydział Matematyki i Informatyki

La inclusión de la gestión del riesgo de desastres en la administración pública a nivel departamental. Una mirada desde el sistema de respuesta a emergencias en Antioquia y Tolima (2010-2014)

La gestión del riesgo de desastres ha cobrado importancia en los últimos años a causa de las devastadoras consecuencias de los distintos desastres naturales. Por eso, esta política pública se ha establecido en las administraciones públicas de los diferentes países; en Colombia se ha implementado a través de la Ley 1523 del 2012. Sin embargo, no se ha podido hacer una inclusión integral en todas las entidades territoriales. Entonces, la presente investigación pretende demostrar los factores presentes en el sistema de respuesta a emergencias, en dos importante departamentos del país, que influyen en la inclusión integral de la gestión del riesgo de desastres en la administración pública departamental.

Inclusion Properties for Certain Classes of Analytic Functions Involving a Family of Fractional Integral Operators

2000 Math. Subject Classification: 30C45

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Exact controllability of generalized Hammerstein type equation

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Programa Mais Educação : um instrumento para uma política educativa integral no Brasil

Tese de mestrado, Ciências da Educação (Área de especialidade em Administração Educacional), Universidade de Lisboa, Instituto de Educação, 2015

Climate change and social inclusion: opportunities for justice and empowerment

...the greatest untapped resource at our disposal lies in the disadvantaged Australians living in our most excluded communities. (Nicholson 2007 p. 4)

The commons are where justice and sustainability converge, where ecology and equity meet. (Shiva 2005 p. 50)

Since 1990, the Intergovernmental Panel on Climate Change (IPCC) has recognised human induced climate change to be primarily a result of burning fossil fuels and land clearing (Lee 2007). Changes to the world's climate patterns have been occurring for decades, but only in recent times has climate change arrived in our collective conscious. An onslaught of extreme weather events, destruction and failure of crops, increasing levels of water restrictions, government announcement of desalination plants. proposed increase in prices for utilities such as power and water - have ushered climate change into the Australian lexicon.

The challenges for all of us are many and varied and perhaps even unimaginable. as many propose a global reduction in annual C02 emissions of between 60-80% (compared to 1990 levels) by 2050.

We are not talking just about the re-construction of our world, but about its re-invention. Ryan (2007)

How will climate change affect us? Who is most vulnerable? What will be the features of policies and strategies to combat climate change that ensure an equitable and just response across our entire society? Are our present social-cultural justice paradigms of social exclusion and inclusion adequate in addressing the impending health consequences that are likely to result from climate change, and in supporting an equitable. harmonious and fruitful life for all population groups in the future?

This paper, written in the spirit of solution-oriented research. focusing on the causes of positive health rather than the causes of disease and other problems (Robinson & Sirard 2005). explores the possibility of a paradigm shift which imagines the social inclusion of specific population groups, not as an appended extra, but integral to the design of an equitable, sustainable low carbon society of the future.

The Role of TAFE as an Equity Pathway to Social Inclusion, Employment, and to University : a submission from The Deakin University Social Work/Gordon TAFE Community Services Work, Geelong Based Project Team

Executive Summary

The Deakin University Social Work/Gordon TAFE Community Services Work Geelong Based Project Team (the Project Team) was assisted by Higher Education Partnership and Participation funding made available through Deakin University Participation and Partnerships Program (DUPPP) to carry out research and project work in 2012/13.

In the following submission to the House of Representatives Inquiry into the role of Technical and Further Education (TAFE) system and its operation, this Project Team seeks to establish a case for:

1. Funding to enable TAFE to continue as:

a) an equity pathway to social inclusion, employment, and to university, particularly in regional areas.
b) an integral complement to the University education sector to deliver on the ambitious objectives of the Federal Government’s widening participation agenda, as a mechanism to deliver the skills, knowledge and workforce needed now, and in the future, in the Australian economy.
2. Increased resources for separate and joint sector development
a) Publicly funded TAFEs need funding to be restored and increased to enable them to maintain the high quality education they provide and to maintain their successful work in supporting communities, regions and disadvantaged individuals to gain skills, training and employment.
b) Universities need increased funding to increase staffing levels and therefore free up teaching staff to spend the necessary time to develop relationships with and provide support to students. This is important for the achieving the goals of the widening participation agenda of increasing access without increasing attrition at the same time.
c) TAFEs and Universities need funding to do the work required to further develop and formalise diploma-degree pathways so that disadvantaged individuals can exit into employment at the diploma level or be supported in an efficient and seamless way to undertake further study.
3. Active use of localised and nuanced partnership approaches by education institutions. This includes:
• Cross teaching by TAFEs and Universities in courses that can be articulated, such as professional practice diplomas and degrees
• Programs negotiated and designed according to the needs of students in each location. TAFEs and Universities need resources in order to do this work
• Focus on regional centres where there is a particular opportunity for government to make an impact on TAFE pathways to employment and/or further education
• Workforce development in regional areas due to new industries is a particular area of need
4. Recognise and capitalise on the complementary and symbiotic nature of each sector’s skills, strengths and capacities.
The submission responds to the second, third and fifth points of the Terms of Reference of the Inquiry and is based on the research work carried out by the Project Team in 2012/13.

We provide evidence of Gordon TAFE in Geelong working as an equity mechanism in the particular case of the welfare/ community services diploma to social work degree pathway. The project team considers that there is a strong case for additional resourcing of TAFE to enable it to continue what it does well. TAFE is the key training and education sectorthe ‘education and social hub’that can successfully attract, retain, and graduate people who may not otherwise access education due to one or more combinations of:

1. having a low SES current or past background;
2. living in regional areas;
3. receiving interrupted primary and secondary education;
4. having disabilities;
5. being sole parents;
6. being from refugee backgrounds;
7. having English as an additional language/culture;
8. retrenchment from employment in dying industries;
9. short, medium and long term unemployment;
10. past and/or current caring roles;
11. marriage/relationship breakdowns;
12. domestic violence;
13. gender, class, age, race/ethnicity and dis/ability discriminations; and
14. socialised expectations and fears.

The recommendations in this submission are based on research findings about important similarities and differences between Gordon TAFE welfare and Deakin University social work students in Geelong, and their respective institutional organisations and contexts. The two institutions employ a repertoire of diverse administrative, teaching, learning and support approaches to meet different mission goals, requirements and needs.

Report on the Expert Group Meeting on the Comprehensive and Integral International Convention to Promote and Protect the Rights and Dignity of Persons with Disabilities

The main objective of the meeting was to present recommendations to the Ad Hoc Committee established by the United Nations to consider proposals and elements for inclusion in an international convention aimed at protecting and promoting the rights and dignity of persons with disabilities. Attending the meeting were key stakeholders from the human rights and disabled community, public and private sector, the academic community, and members of the United Nations system.