Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

M-deformations of A-simple germs from R(n) to R(n+1)

All A-simple corank-1 germs from R(n) to R(n+1), where n not equal 4, have an M-deformation, that is a deformation in which the maximal numbers of isolated stable singular points are simultaneously present in the image.

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Real map germs and higher open book structures

The paper focusses on the existence of higher open book structures defined by real map germs psi : (R(m), 0) -> (R(p), 0) such that Sing psi boolean AND psi(-1)(0) subset of {0}. A general existence criterion is proved, with view to weighted-homogeneous maps.

Influence of super-ohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.

O global e o contextual no aprendizado gerencial de multinacionais: uma perspectiva brasileira

The major purpose of this thesis is to verify, from a Brazilian perspective, how global and contextual issues influence the management learning in Multinationals. The management learning derived from the interaction of holding and sidiaries/colligates of Multinational corporation is supposed to be subject to convergent and divergent forces, the former related to global and standardized organizational practices, and the latter, is seen as a social practice subject to cultural and organizational singularities. A model was constructed to relate the dichotomy between the universality of the management practices and technologies and the particularity of the contexts where they operate, to the dichotomy between the singularities in organization and national level. This model is composed of the international, global, managerial and inter-organizational dimensions related, respectively, to the cultural and political diversity; to the universal forces of practices and values; to the managerial capabilities and resources in the organization, consolidated as best practices and to the interaction between holding and subsidiaries and the resulted learning. The combined result of these dimensions influences the knowledge flow and the learning derived from it. The field research was constituted of five cases of internationalized Brazilian firms, with a solid experience in their management systems. The main subjects of this study were executives and ofessionals/managers who respond to the management development. The data were first collected in the headquarters and complemented with visits to subsidiaries/joint ventures in other countries, in loco or with expatriated people who return to Brazil. The central supposition was validated. So, the management learning ¿ is driven by the global capitalism practices and by the global culture where they are immersed, reproducing a hegemonic vision and a common language (global dimension); ¿ incorporates the more propagated and dominant managerial values, although there are some variations when they are applied in the subsidiaries/joint ventures; is the product of the assimilation of international recognized and planned managerial practices, with the acculturation power, although not completely; is the result mainly of the managerial practice in work; is impacted not only by cross-cultural and managerial factors, but also by the business environment of the firm; is given according to the capabilities and resources in the organization, guiding the form of assimilation of practices and technologies, with global application or not (managerial dimension); ¿ is affected by the cross-cultural diversity involving the countries of the holding and the subsidiaries/joint ventures where the firm is and is given as a reproduction of the political context of the holding and subsidiaries countries (international dimension); ¿ faces aligned concurrent institutional pressures between corporate or global systems, practices of other subsidiaries/joint ventures and local practices; is more difficult to reach when there is not permeability between organizational cultures and identities of a Multinational firm; is affected by how much the relationship process across these unities is self-referenced; is facilitated by the construction and improvement of the knowledge network (interorganizational dimension). Finally some contributions of this study are exposed, including extensions of the proposed model and suggestions, recommendations for future research.

O desafio de reconhecimento do sujeito cego em espaços públicos de representação

This work is funded based on the uneasiness with the concept of State as a public machine for development. Of State as a public machine to deliberate valid practices for valid methods and to limit valid subjects in valid spaces. In midst of this specific context, this work dedicates itself to investigate the following research problem: the mistaken recognition of the blind subject in public spaces of representation. For this reason, it was addressed the following question: how the blind subject is recognized in public spaces of representation? To answer the question, it was necessary to contextualize how the blind subject is being recognized in various public spaces of representation. In the international scope, the human rights debate held between the National States was analyzed (BRAND, 2005; KOERNER, 2002; UN, 2006). In the national arena, constitutional rights, federal laws, public policies and institutions representing the blind subject were examined (CABRAL, 2008; SARAVIA, 2006). Finally, in a local context, the fundaments of the concept of citizen for the subject recognition were investigated (AGAMBEN, 2002; RORTY, 1999, DELEUZE AND GUATTARI, 1996). The methodology included reports of national and international representatives in the Lusophone Countries Meeting for Dissemination and Implementation of the Convention on the Rights of Persons with Disabilities and, mainly, interviews with blind subjects. The data was processed by content analysis and was discussed based on the following categories: representation spaces; representation modes; representation amplitude; representation premises. The results show, regarding such spaces of representation, the growing importance of thinking the rights of persons with disabilities ¿ group in which belongs the blind subject ¿ as of the international and national scenario. However, the blind subjects announced alternative local spaces for representation: church, internet, radio, etc. Regarding the representation modes, the role of law and standards has been advocated specially in the human rights field. The importance of the cooperation between the States and the civil society to ensure, in practice, the rights achieved was also emphasized. But other forms of representation, directly linked to each interviewee¿ history, was important. Regarding the representation amplitude, there were arguments in defense of a conception of human dignity and freedom to all inhabitants of the globe. The lusophone event highlighted the concern of the cultural peculiarities of those involved in the meeting. The blind interviewees argued for citizenship as construction of instruments for freedom and autonomy, but recognized that this is not a clear desire between the blind people in general, and even less in society as a whole. With respect to the representation premises, the fundaments for the recognition of the blind subject were based on the primacy of reason at the expense of personal experimentation. Experimentation that serves as the foundation of a new form of recognition of the blind subject in public spaces of representation, one more interested in singularities, impenetrable by reason, unmovable to another, and which are irreducible to each subject. The final considerations suggest that if the State has a reason to be, this is not another than to offer instruments to manifest as many as the existential possibilities of the subject. This is the concept of State for development.

Responsabilidade social empresarial no mercado de seguros brasileiro: influências culturais e implicações relacionais

The Brazilian insurance market is the ambience in which this research study takes place in search for a better understanding of how cultural characteristics are related with organizational signs, practices and expectations on social responsibility. The concepts of social responsibility as well as the concept of culture are presented and discussed from different points of view, in accordance with different authors and trough several methodological approaches, in order to establish a coherent theoretical basis for qualitative data analysis. The phenomenological attitude assumed by the researcher in especial dialogues situations during the field research phase added new possibilities of apprehension or emergence of each studied organization self orientation in terms of pre-occupation with social issues intimately related with their insurance activities in the market place. Final reflections show the complexity of the insurance cultural context in the studied Brazilian segment, in which cultural and subcultural national and organizational singularities appear. However leaving space for common values and coherent orientation toward the peculiar understanding of social responsibility as inherent to any insurance company activities, themselves. Last comments point out that future research studies may give additional contribution for the continuity of the discussions initiated in this dissertation, expecting that some changes in the organizational posture and practices may happen, especially those related with risk taking and broad processes of communication with clients and society as a whole.

Formação de agenda e processo decisório nos governos FHC e Lula: uma análise sobre a dinâmica e as oportunidades de negociação no processo de tomada de decisão do setor elétrico

O objetivo principal desta tese é analisar as particularidades de dois processos decisórios relacionados a políticas públicas do governo federal brasileiro, a saber, a formação de agenda e as escolhas de alternativas. Tais particularidades do processo decisório caracterizam-se por limitar, em um primeiro momento, o leque de temas que potencialmente poderiam ocupar um lugar de destaque frente aos governantes e, em seguida, por selecionar as alternativas viáveis de serem implementadas pelo poder público. Dessa maneira, serão objetos desta tese a compreensão do por que apenas determinados temas fazem parte da agenda de um governo e qual o grau de influência dos atores sociopolíticos sobre o processo de escolha de alternativas, de tal forma que algumas são seriamente consideradas enquanto outras são negligenciadas. Para analisar as particularidades dos processos decisórios foram feitas análises sobre dois casos do setor elétrico: a expansão da geração de energia elétrica durante o período que antecedeu a crise de 2001 e a criação de um novo modelo para o setor, nos anos de 2003 e 2004. Esta tese traz como hipótese que aspectos centrais de uma política não são alterados enquanto a coalizão dominante que a instituiu estiver no poder ¿ ainda que aspectos secundários possam vir a ser alterados durante esse período.

Paisagem, um patrimônio esquecido: subsídios para a construção de uma metodologia de valoração e proteção do cenário natural litorâneo

The so-called "residential tourism" came to intensify the previous occupation of the coastal zones, characterized by traditional beach houses, and brought significant consequences for their spatial configuration, and especially for its scenic value of the landscape. Although there is the intention to regulate the activities of enterprising groups by some legal instruments to control the use and occupation of land, and to contain some negative effects, the actions of government are still inefficient in trying to follow the implications on the landscape from the accelerated growth of the real estate and touristic sectors. Supported in the speech of economic development and income generation, public managers prioritize areas to attract tourists to the detriment of preserving important physical attributes of the natural environment that contribute significantly to the quality of life. The result can be noticed in the use of natural elements as one of the major components in the land valorization, and in the immediate attraction of investors and enterprising. Therefore, the objective of this work is to contribute to the debate on the landscape preservation a little detailed thematic in view of their relevance in the current context - by indicating subsidies to the creation of a methodology for the evaluation and protection of coastal zones that may assist the government in creating new instruments, and better prepare it in control of the occupation of these areas. For such, was followed two ways to analysis: the indirect method and the direct method. The first is grounded in the evaluation of landscape attributes, which is based on the work of Raquel Tardin (2008) and Eduardo Cuesta, Encarnación Algarra and Isabel Pastor (2001). The second, based on the research of Leticia and Carlos Hardt (2010) and on the concepts of phenomenology - expressed by Antonio Christofoletti (1985) and Yi-Fu Tuan (1983) - considers the population perspective on the quality of the natural scenery. Developed through cartographic materials, photographic collections and quantitative tables, this dissertation utilized as a case study the beaches of Barra de Tabatinga and Camurupim, located in the city of Nísia Floresta/RN. Despite already being sighted spaces of advanced stage of landscape degradation in these locations, areas of remarkable scenic value can still be found, what reinforce the urgency in adopting preservationists actions. The absence of laws focused on the management and protection of the landscape singularities associated with the inefficiency of the government to invigilate the land occupation in coastal zones, encourage the excessive action of the real estate-tourism, and consequently make the government the main responsible for the environmental and landscape impacts in these areas - by its omission or by their connivance. Therefore, the legislation permeates this entire process and constitutes itself as the most effective way to guarantee the right to the landscape to present and future generations. Are also pointed some important considerations to build a methodology, especially concerning possibilities of improvements and adaptations of its applicability in each case