When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.

We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.

We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.

This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.

We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.

We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.

We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula.

Made available in DSpace on 2014-06-11T19:22:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-18Bitstream added on 2014-06-13T19:07:35Z : No. of bitstreams: 1 maia_scm_me_botfca.pdf: 3637798 bytes, checksum: 42c60ca08ea3f3717b8ba3a464ed6462 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Técnicas de manejo que possibilitem a maximização de absorção de N pelo feijoeiro são de extrema importância, em razão do alto custo dos fertilizantes nitrogenados e das perdas de N, que podem representar prejuízos aos produtores e riscos ao ambiente. Nesse sentido, a estimativa da necessidade de N pelo feijoeiro mediante a leitura indireta de clorofila, pelo clorofilômetro portátil, pode ser uma alternativa viável. Contudo, ainda existe a necessidade de estabelecimento de critérios para a utilização desse aparelho na cultura do feijão. Os objetivos do presente trabalho foram: a) verificar a correlação entre o índice relativo de clorofila (IRC), obtido mediante leituras do clorofilômetro portátil (SPAD- 502), e o teor de N da folha de dois cultivares de feijão (IAC Alvorada e Pérola) em diversos estádios de desenvolvimento; b) verificar o comportamento do IRC e do índice de suficiência de N (ISN) em função dos manejos de N aplicado em cobertura; c) avaliar o ISN calculado com base nas medidas IRC nas folhas como indicador do momento de aplicação de N em cobertura na cultura do feijão e, d) verificar qual valor do ISN (90% e 95%) em relação ao tratamento referência é o mais adequado para indicar o momento da adubação nitrogenada em cada cultivar utilizado. O trabalho foi constituído de um experimento conduzido durantes as safras “das águas” e “da seca” do ano agrícola 2009/2010, na Fazenda Experimental Lageado da FCA/UNESP - Botucatu-SP. O delineamento experimental foi em blocos ao acaso, em esquema de parcela subdividias, com quatro repetições. As parcelas foram constituídas por dois cultivares de feijão (Pérola e IAC Alvorada) e as subparcelas por seis manejos do N M1: 40 kg ha-1 de N na semeadura + 80 kg ha-1 de N aos 15 dias após a emergência (DAE) + 80 kg ha-1 de N aos 30 DAE; M2: 20 kg ha-1 de N na semeadura... (Complete abstract click electronic access below) / Management techniques that allow the maximization of N uptake by bean crop are extremely important, because of high cost of nitrogen fertilizers and N losing, which may represent losses to producers and risks to the environment. In this sense, the estimation of N needs of common bean crop by indirect reading of chlorophyll can be a viable alternative. However, there is remains the need to establish criteria for using this device in the bean. The aims of this study were: a) determine the correlation between relative chlorophyll index (RCI), obtained by reading of chlorophyll (SPAD 502) and leaf N content of two bean cultivars (IAC Alvorada and Pérola) in various stages of development; b) verify the behavior of the RCI and N sufficiency index (NSI) for different sidedressing N management practices; c) evaluated the NSI calculated based on the measures RCI leaves as an indicator of time of N application in sidedressing on bean crop and d) verify that value of NSI (90% and 95%) compared to the reference treatment is most appropriate to indicate the moment of fertilization in each cultivar. The work was composed of an experiment conducted in rainy and dry season of agricultural year 2009/2010 at the Experimental Lageado Farm FCA/UNESP - Botucatu-SP. A randomized block in split plot scheme, with four replications was used. Plots consisted of two bean cultivars (IAC Alvorada and Pérola) and subplots of six N managements M1: 40 kg ha-1 N at sowing + 80 kg ha-1 at 15 days after emergence (DAE) + 80 kg ha-1 N at 30 DAE; M2: 20 kg ha-1 N at sowing + 40 kg ha-1 N at 15 DAE + 40 kg ha-1 N at 30 DAE; M3: 10 kg ha-1 N at sowing + 20 kg ha-1 N at 15 DAE + 20 kg ha-1 N at 30 DAE; M4: 20 kg ha-1 N at sowing + 30 kg ha-1 N when chlorophyll meter readings indicated NSI <95%; M5: 20 kg ha-1 N at sowing + 30 kg N ha-1 N when chlorophyll meter readings indicated NSI <90% and, M6: control (without nitrogen)... (Complete abstract click electronic access below)

The problem of this study is (1) to expand the 980 division (designated by the term History: South America, Latin America, Spanish America) of the Dewey Decimal Classification for the history of Latin America as a whole and for national histories of several typical countries, and (2) to translate the expanded tables into Spanish.

Orientador: Rogério Peres Soratto / Banca: Roberto Lyra Villas Boas / Banca: Marcelo Andreotti / Resumo: Técnicas de manejo que possibilitem a maximização de absorção de N pelo feijoeiro são de extrema importância, em razão do alto custo dos fertilizantes nitrogenados e das perdas de N, que podem representar prejuízos aos produtores e riscos ao ambiente. Nesse sentido, a estimativa da necessidade de N pelo feijoeiro mediante a leitura indireta de clorofila, pelo clorofilômetro portátil, pode ser uma alternativa viável. Contudo, ainda existe a necessidade de estabelecimento de critérios para a utilização desse aparelho na cultura do feijão. Os objetivos do presente trabalho foram: a) verificar a correlação entre o índice relativo de clorofila (IRC), obtido mediante leituras do clorofilômetro portátil (SPAD- 502), e o teor de N da folha de dois cultivares de feijão (IAC Alvorada e Pérola) em diversos estádios de desenvolvimento; b) verificar o comportamento do IRC e do índice de suficiência de N (ISN) em função dos manejos de N aplicado em cobertura; c) avaliar o ISN calculado com base nas medidas IRC nas folhas como indicador do momento de aplicação de N em cobertura na cultura do feijão e, d) verificar qual valor do ISN (90% e 95%) em relação ao tratamento referência é o mais adequado para indicar o momento da adubação nitrogenada em cada cultivar utilizado. O trabalho foi constituído de um experimento conduzido durantes as safras "das águas" e "da seca" do ano agrícola 2009/2010, na Fazenda Experimental Lageado da FCA/UNESP - Botucatu-SP. O delineamento experimental foi em blocos ao acaso, em esquema de parcela subdividias, com quatro repetições. As parcelas foram constituídas por dois cultivares de feijão (Pérola e IAC Alvorada) e as subparcelas por seis manejos do N M1: 40 kg ha-1 de N na semeadura + 80 kg ha-1 de N aos 15 dias após a emergência (DAE) + 80 kg ha-1 de N aos 30 DAE; M2: 20 kg ha-1 de N na semeadura... (Complete abstract click electronic access below) / Abstract: Management techniques that allow the maximization of N uptake by bean crop are extremely important, because of high cost of nitrogen fertilizers and N losing, which may represent losses to producers and risks to the environment. In this sense, the estimation of N needs of common bean crop by indirect reading of chlorophyll can be a viable alternative. However, there is remains the need to establish criteria for using this device in the bean. The aims of this study were: a) determine the correlation between relative chlorophyll index (RCI), obtained by reading of chlorophyll (SPAD 502) and leaf N content of two bean cultivars (IAC Alvorada and Pérola) in various stages of development; b) verify the behavior of the RCI and N sufficiency index (NSI) for different sidedressing N management practices; c) evaluated the NSI calculated based on the measures RCI leaves as an indicator of time of N application in sidedressing on bean crop and d) verify that value of NSI (90% and 95%) compared to the reference treatment is most appropriate to indicate the moment of fertilization in each cultivar. The work was composed of an experiment conducted in "rainy" and "dry" season of agricultural year 2009/2010 at the Experimental Lageado Farm FCA/UNESP - Botucatu-SP. A randomized block in split plot scheme, with four replications was used. Plots consisted of two bean cultivars (IAC Alvorada and Pérola) and subplots of six N managements M1: 40 kg ha-1 N at sowing + 80 kg ha-1 at 15 days after emergence (DAE) + 80 kg ha-1 N at 30 DAE; M2: 20 kg ha-1 N at sowing + 40 kg ha-1 N at 15 DAE + 40 kg ha-1 N at 30 DAE; M3: 10 kg ha-1 N at sowing + 20 kg ha-1 N at 15 DAE + 20 kg ha-1 N at 30 DAE; M4: 20 kg ha-1 N at sowing + 30 kg ha-1 N when chlorophyll meter readings indicated NSI <95%; M5: 20 kg ha-1 N at sowing + 30 kg N ha-1 N when chlorophyll meter readings indicated NSI <90% and, M6: control (without nitrogen)... (Complete abstract click electronic access below) / Mestre