A Rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1S2. It describes a rotating black ring. This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

CHARACTERIZATION OF BULK SOIL HUMIN AND ITS ALKALINE-SOLUBLE AND ALKALINE-INSOLUBLE FRACTIONS

Humic substances are the major components of soil organic matter. Among the three humic substance components (humic acid, fulvic acid, and humin), humin is the most insoluble in aqueous solution at any pH value and, in turn, the least understood. Humin has poor solubility mainly because it is tightly bonded to inorganic soil colloids. By breaking the linkage between humin and inorganic soil colloids using inorganic or organic solvents, bulk humin can be partially soluble in alkali, enabling a better understanding of the structure and properties of humin. However, the structural relationship between bulk humin and its alkaline-soluble (AS) and alkaline-insoluble (AIS) fractions is still unknown. In this study, we isolated bulk humin from two soils of Northeast China by exhaustive extraction (25 to 28 times) with 0.1 mol L-1 NaOH + 0.1 mol L-1 Na4P2O7, followed by the traditional treatment with 10 % HF-HCl. The isolated bulk humin was then fractionated into AS-humin and AIS-humin by exhaustive extraction (12 to 15 times) with 0.1 mol L-1 NaOH. Elemental analysis and solid-state 13C cross-polarization magic angle spinning nuclear magnetic resonance (13C CPMAS NMR) spectroscopy were used to characterize and compare the chemical structures of bulk humin and its corresponding fractions. The results showed that, regardless of soil types, bulk humin was the most aliphatic and most hydrophobic, AS-humin was the least aliphatic, and AIS-humin was the least alkylated among the three humic components. The results showed that bulk humin and its corresponding AS-humin and AIS-humin fractions are structurally differed from one another, implying that the functions of these humic components in the soil environment differed.

Employment risk, unemployment insurance and search strategies: a disaggregated equilibrium approach with application to the Swiss labour market in the 1990-ies

The Organization of the Thesis The remainder of the thesis comprises five chapters and a conclusion. The next chapter formalizes the envisioned theory into a tractable model. Section 2.2 presents a formal description of the model economy: the individual heterogeneity, the individual objective, the UI setting, the population dynamics and the equilibrium. The welfare and efficiency criteria for qualifying various equilibrium outcomes are proposed in section 2.3. The fourth section shows how the model-generated information can be computed. Chapter 3 transposes the model from chapter 2 in conditions that enable its use in the analysis of individual labor market strategies and their implications for the labor market equilibrium. In section 3.2 the Swiss labor market data sets, stylized facts, and the UI system are presented. The third section outlines and motivates the parameterization method. In section 3.4 the model's replication ability is evaluated and some aspects of the parameter choice are discussed. Numerical solution issues can be found in the appendix. Chapter 4 examines the determinants of search-strategic behavior in the model economy and its implications for the labor market aggregates. In section 4.2, the unemployment duration distribution is examined and related to search strategies. Section 4.3 shows how the search- strategic behavior is influenced by the UI eligibility and section 4.4 how it is determined by individual heterogeneity. The composition effects generated by search strategies in labor market aggregates are examined in section 4.5. The last section evaluates the model's replication of empirical unemployment escape frequencies reported in Sheldon [67]. Chapter 5 applies the model economy to examine the effects on the labor market equilibrium of shocks to the labor market risk structure, to the deep underlying labor market structure and to the UI setting. Section 5.2 examines the effects of the labor market risk structure on the labor market equilibrium and the labor market strategic behavior. The effects of alterations in the labor market deep economic structural parameters, i.e. individual preferences and production technology, are shown in Section 5.3. Finally, the UI setting impacts on the labor market are studied in Section 5.4. This section also evaluates the role of the UI authority monitoring and the differences in the Way changes in the replacement rate and the UI benefit duration affect the labor market. In chapter 6 the model economy is applied in counterfactual experiments to assess several aspects of the Swiss labor market movements in the nineties. Section 6.2 examines the two equilibria characterizing the Swiss labor market in the nineties, the " growth" equilibrium with a "moderate" UI regime and the "recession" equilibrium with a more "generous" UI. Section 6.3 evaluates the isolated effects of the structural shocks, while the isolated effects of the UI reforms are analyzed in section 6.4. Particular dimensions of the UI reforms, the duration, replacement rate and the tax rate effects, are studied in section 6.5, while labor market equilibria without benefits are evaluated in section 6.6. In section 6.7 the structural and institutional interactions that may act as unemployment amplifiers are discussed in view of the obtained results. A welfare analysis based on individual welfare in different structural and UI settings is presented in the eighth section. Finally, the results are related to more favorable unemployment trends after 1997. The conclusion evaluates the features embodied in the model economy with respect to the resulting model dynamics to derive lessons from the model design." The thesis ends by proposing guidelines for future improvements of the model and directions for further research.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

EFFECT OF RICE STRAW AND NITRATE LEVELS IN SOIL SOLUTION ON NITROUS OXIDE EMISSION

Among the greenhouse gases, nitrous oxide (N2O) is considered important, in view of a global warming potential 296 times greater than that of carbon dioxide (CO2) and its dynamics strongly depend on the availability of C and mineral N in the soil. The understanding of the factors that define emissions is essential to develop mitigation strategies. This study evaluated the dynamics of N2O emissions after the application of different rice straw amounts and nitrate levels in soil solution. Pots containing soil treated with sodium nitrate rates (0, 50 and 100 g kg-1 of NO−3-N) and rice straw levels (0, 5 and 10 Mg ha-1), i.e., nine treatments, were subjected to anaerobic conditions. The results showed that N2O emissions were increased by the addition of greater NO−3 amounts and reduced by large straw quantities applied to the soil. On the 1st day after flooding (DAF), significantly different N2O emissions were observed between the treatments with and without NO−3 addition, when straw had no significant influence on N2O levels. Emissions peaked on the 4th DAF in the treatments with highest NO−3-N addition. At this moment, straw application negatively affected N2O emissions, probably due to NO−3 immobilization. There were also alterations in other soil electrochemical characteristics, e.g., higher straw levels raised the Fe, Mn and dissolved C contents. These results indicate that a lowering of NO−3 concentration in the soil and the increase of straw incorporation can decrease N2O emissions.

Effects of Pig Slurry Application and Crops on Phosphorus Content in Soil and the Chemical Species in Solution

The application of pig slurry rates and plant cultivation can modify the soil phosphorus (P) content and distribution of chemical species in solution. The purpose of this study was to evaluate the total P, available P and P in solution, and the distribution of chemical P species in solution, in a soil under longstanding pig slurry applications and crop cultivation. The study was carried out in soil columns with undisturbed structure, collected in an experiment conducted for eight years in the experimental unit of the Universidade Federal de Santa Maria (UFSM), Santa Maria (RS). The soil was an Argissolo Vermelho distrófico arênico (Typic Hapludalf), subjected to applications of 0, 20, 40, and 80 m3 ha-1 pig slurry. Soil samples were collected from the layers 0-5, 5-10, 10-20, 20-30, 30-40, and 40-60 cm, before and after black oat and maize grown in a greenhouse, for the determination of available P, total P and P in the soil solution. In the solution, the concentration of the major cations, anions, dissolved organic carbon (DOC), and pH were determined. The distribution of chemical P species was determined by software Visual Minteq. The 21 pig slurry applications increased the total P content in the soil to a depth of 40 cm, and the P extracted by Mehlich-1 and from the solution to a depth of 30 cm. Successive applications of pig slurry changed the balance between the solid and liquid phases in the surface soil layers, increasing the proportion of the total amount of P present in the soil solution, aside from changing the chemical species in the solution, reducing the percentage complexed with Al and increasing the one complexed with Ca and Mg in the layers 0-5 and 5-10 cm. Black oat and maize cultivation increased pH in the solution, thereby increasing the proportion of HPO42- and reducing H2PO4- species.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Body composition using bio-impedance analysis in pediatric patients with inflammatory bowel disease. Corcordance with dual energy X-ray absorptiometry and comparison with healthy controls

Introduction: Growth is a central process in paediatrics. Weight and height evaluation are therefore routine exams for every child but in some situation, particularly inflammatory bowel disease (IBD), a wider evaluation of nutritional status needs to be performed. Objectives: To assess the accuracy of bio-impedance analysis (BIA) compared to the gold standard dual energy X-ray absorptiometry (DEXA) in estimating percentage body fat (fat mass; FM) and lean body mass (fat free mass; FFM) in children with inflammatory bowel disease (IBD). To compare FM and FFM levels between patients with IBD and healthy controls. Methods: Twenty-nine healthy controls (12 females; mean age: 12.7 ± 1.9 years) and 21 patients (11 females; 14.3 ± 1.3 years) were recruited from August 2011 to October 2012 at our institution. BIA was performed in all children and DEXA in patients only. Concordance between BIA and DEXA was assessed using Lin's concordance correlation and the Bland-Altman method. Between-group comparisons were made using analysis of variance adjusting for age. Results: BIA-derived FM% showed a good concordance with DEXA-derived values, while BIA-derived FFM% tended to be slightly higher than DEXA-derived values (table). No differences were found between patients and controls regarding body mass index (mean ± SD: 19.3 ± 3.3 vs. 20.1 ± 2.8 kg/m2, respectively; age-adjusted P = 0.08) and FM% (boys: 25.3 ± 10.2 vs. 22.6 ± 7.1%, for patients and controls, respectively; P = 0.20; girls: 28.2 ± 5.7 vs. 26.4 ± 7.7%; P = 0.91). Also, no differences were found regarding FFM% in boys (74.9 ± 10.2 vs. 77.4 ± 7.1%; P = 0.22) and girls (71.8 ± 5.6 vs. 73.5 ± 7.7%; P = 0.85). Conclusion: BIA adequately assesses body composition (FM%) in children with IBD and could advantageously replace DEXA, which is more expensive and less available. No differences in body composition were found between children with IBD and healthy controls.

Evaluation des pratiques d'irrigation, de fertilisation et d'application de pesticides dans l'agriculture périurbaine de Dakar, Sénégal

RESUMEL'agriculture urbaine et périurbalne - nommée ci-après AU - est un thème fort de recherche transversale, au vu des nombreux enjeux économiques, sociaux et environnementaux. L'objectif de cette recherche était de contribuer à une meilleure connaissance des processus de transfert de polluants et du cycle des nutriments à l'échelle locale, afin de déterminer sous quelles conditions l'AU de Dakar peut être pratiquée sans porter atteinte à la santé et à l'environnement.Une approche basée sur l'étude des processus géochimiques dans ie sol jusqu'à la nappe a été choisie, à l'échelle de la parcelle cultivée et à une échelle un peu plus large de la zone périurbaine de Dakar pour déterminer les influences du type d'occupation du sol.L'évaluation des impacts de l'irrigation avec des eaux usées brutes et des eaux de nappe saumâtres sur la qualité des sols (chapitre 2) a montré que l'alcalinité et les teneurs en calcium élevées des eaux saumâtres induisent la précipitation de CaC03 dans l'horizon superficiel du sol. Na remplace consécutivement Ca sur le complexe argilo-humique du sol et les bicarbonates diminuent dans la solution du sol. Le carbone organique dissout (COD) augmente significativement dans la solution du sol et dans la nappe sous-jacente. Malgré l'alcalinité et les teneurs très élevées en calcium des eaux usées, il y a peu de précipitation de CaC03 dans l'horizon superficiel du sol et une faible augmentation du sodium échangeable ESP. La nitrification de l'ammonium des eaux usées (moy 190mg/L à Pikine) produit des protons, qui ne sont plus tamponnés par les bicarbonates exportés hors du profil. Il y a alors une nette baisse de pH des sols irrigués par des eaux usées non traitées. Les sols irrigués par des eaux usées et saumâtres stockent moins de C et Ν que les sols de référence.L'évaluation de l'influence de l'occupation des sols en zone périurbaine sur à la nappe phréatique peu profonde (chapitre 3) a permis de déterminer les traceurs représentatifs de l'occupation du sol, à savoir Br/CI, NO3/CI et δ180-Ν03 pour l'irrigation par des eaux usées, pH et δ15Ν-Ν03 pour l'irrigation par des eaux de nappe, et Rb+Cr et Κ pour les lixiviats de fosses septiques. Ce chapitre a mis en évidence des points importants de la dynamique de l'azote en zone périurbaine sous deux occupations du sol : (1) la dénitrification est un processus important dans l'agrosystème périurbain de Dakar en bas de dune, dans les gleysols où l'on trouve des conditions temporairement réduites et un substrat organique favorables aux microorganismes de la dénitrification. Les teneurs en nitrates sont presque nulles avec irrigation d'eau de nappe. (2) en bas de pente, mais avec irrigation quotidienne par les eaux usées, l'apport continu d'ammonium inhibe probablement la dénitrification, mais favorise la volatilisation. (3) la nitrification de l'ammonium dans la nappe lors de la lixiviation des fosses septiques se distingue de la nitrification de l'ammonium dans la zone non saturée dans la zone d'agriculture périurbaine par la composition isotopique de l'oxygène de l'eau. Une comparaison des flux d'azote entre l'agrosystème et les quartiers périurbains de Dakar (chapitre 4) ont révélé que ces derniers étaient du même ordre de grandeur par unité de surface, à savoir 2-4 tonnes Ν /ha/an.L'évaluation des flux de pesticides dans l'agrosystème et des risques induits pour les eaux souterraines (chapitre 5) a révélé un fiux total de pesticides de 60kg/ha/an, totalisant 15 matières actives. Seules deux de ces matières actives sont autorisées par le comité des pesticides sahélien. Les pesticides les plus utilisés par les producteurs sont l'organochloré dicofol, les organophosphorés methamidophos, dimethoate et fenithrotion ainsi que le cabamate methomyl. Les flux les plus importants sont de 9 à 7 kg/ha/an (methomyl, methamidophos, ethoprophos et dicofol). Les pesticides qui présentent un risque élevé de contamination des eaux souterraines et qui devraient être prioritaires pour un suivi analytique sont : le carbofuran, le dimethoate, l'ethoprophos et le methomyl.En conclusion, une meilleure gestion de la fertilisation est nécessaire dans la zone d'AU de Dakar, afin de (1) réduire les pertes gazeuses qui contribuent à l'effet de serre, (2) de ralentir la minéralisation du carbone et de l'azote organiques pour créer un stock de C et Ν dans ces sols, (3) de limiter le lessivage dans la nappe et enfin, 4) d'augmenter l'efficacité d'utilisation de Ν par les plantes. Une optimisation de l'irrigation devrait limiter l'alcalinisation secondaire. Enfin, la mise en place d'une lutte intégrée ou biologique contre les ravageurs est indispensable afin de minimiser les risques pour les eaux souterraines et les mares permanentes.ABSTRACTUrban and periurban agriculture (UA) is an important issue in southern countries, because of its key role in their social and economical development and its environmental concern. The goal of this study was to contribute to a better understanding of pollutant transfer and nutrient cycling at the local scale, in order to implement the necessary improvements to guarantee the sustainability of this practice.An approach based on geochemical processes occurring in the vadose zone from the surface down to the groundwater level was chosen, at the scale of cultivated plots and at the regional scale of Dakar periurban areas, to determine the influence of land use.The assessment of irrigation with untreated domestic wastewater and brackish water on soil quality (chapter 2) showed: (1) that the high alkalinity and calcium contents of brackish water induce CaC03 precipitation in the top layer of the soil and therefore a replacement of Ca by Na on the clay- humic complexes, strongly marked during the dry season. Dissolved organic carbon (DOC) increased significantly in the soil solution and in the underlying groundwater. (2) in spite of the similarly high alkalinity and Ca contents of waste water, there is only little CaC03 precipitation and a low increase of the percentage of exchangeable sodium (ESP) in the soil top layer. The nitrification of the ammonium of wastewater (mean 190 mg/L in Pikine) produces protons, which are not any more buffered by bicarbonates exported out of the soil profile, which leads to a net decline of soil pH. Both soils irrigated with untreated wastewater and brackish water store less of C and Ν than soils irrigated with non saline groundwater.The assessment of the impact of land use on the shallow groundwater (chapter 3) allowed determining representative tracers of the land use. Low Br/CI ratio, high NO3/CI ratio and low δ1βΟ- nitrate indicated the influence of wastewater; high pH and high 515N-nitrates indicated the influence of brackish water together with high amendments of organic fertilizers; high Rb+Cr and Κ indicated the influence of poor sanitation facilities in periurban districts (septic tank leakage). This chapter also pointed out the following facts about the nitrogen dynamics : (1) denitrification is a key-process in the Dakar UA agrosystem in the gleysols irrigated with groundwater. The underlying groundwater is almost nitrate free. (2) in the Gleysols irrigated with waste water, ammonium inhibits denitrification but facilitate ammoniac volatilization. A comparison of nitrogen balance between the UA agrosystem and the periurban districts of Dakar (chapter 4) revealed similar flows per surface unit, namely 2-4 tons Ν / ha / year.The evaluation of pesticides use in the UA agrosystem and the risk assessment for the groundwater (chapter 5) revealed a total flow of pesticides of 60kg / ha / year, totalizing 15 active substances. Only two of these are authorized by the Sahelian Pesticides Committee. The most used pesticides are dicofol (organochlorinated), methamidophos, dimethoate and fenithrotion (organophosphate) as well as methomyl. (carbamate). The most important flows vary between 9 to 7 kg / ha / year. Pesticides with a high risk of groundwater contamination - according to SIRIS and EPRIP 2 indicators - are: carbofuran, dimethoate, ethoprophos and methomyl. These substances should be established as a priority for an analytical follow-up in the different environmental compartments.In conclusion, a better management of the fertilization is necessary in the Dakar UA, (1) to reduce the gaseous losses which contribute to greenhouse emissions (2) to slow down the mineralization of the organic carbon and the nitrogen, in order to enhance the C and Ν stock in these soils, (3) to limit the nitrate leaching in the groundwater and finally, 4) to increase the N-use efficiency of plants. An optimization of the irrigation scheme should limit the secondary sodisation if coupled with an increase the stable organic matter of the soil. An integrated or biologic crop pest strategy is urgently needed to minimize risks with respect to ground and surface water (ponds used for fishing).RESUME LARGE PUBLICL'agriculture mondiale connaît actuellement une crise majeure, affectée par les changements climatiques, la sécurité alimentaire et les dégradations de l'environnement. Elle n'a plus le rôle unique de produire, mais devient un élément essentiel de la protection des ressources naturelles et du paysage. Les politiques agricoles basées sur les marchés mondiaux devront se réorienter vers une agriculture locale basée sur le développement durable.La production alimentaire située dans l'enceinte des villes, nommée agriculture urbaine ou périurbaine (AU ci-après) joue un rôle important dans le contexte actuel d'accroissement de la population et de la pauvreté urbaines. L'AU concerne en effet la majorité des mégapoies du monde, fait vivre plus de 200 millions de personnes dans les pays du Sud, fournit jusqu'à 80% de la demande urbaine en certains produits frais, fait barrière à l'extension urbaine et permet un recyclage de certains déchets urbains. L'AU a pour particularité d'être à cheval entre des politiques rurales et urbaines, d'où un délaissement ce cette activité au secteur informel. Ce qui a développé de nombreuses stratégies à risques, comme à Dakar, où les petits producteurs périurbains irriguent quotidiennement avec des eaux usées domestiques par manque d'accès à une eau de bonne qualité et pour raccourcir les cycles de production. L'extrême précarité foncière des acteurs de l'AU de Dakar les empêchent d'investir à long terme et induit des pratiques inadéquates d'irrigation, d'usage de pesticides et de fertilisation de ces sols sableux.L'objectif de cette recherche était de contribuer à une meilleure connaissance des processus de transfert de polluants et du cycle des nutriments à l'échelle des parcelles cultivées par des eaux usées et des eaux saumâtres, afin de déterminer sous quelles conditions l'AU de Dakar peut être pratiquée et surtout maintenue sans porter atteinte à la santé et à l'environnement. Pour cela, une approche basée sur l'étude des processus géochimiques dans le sol jusqu'à la nappe a été choisie, à l'échelle de la parcelle cultivée et à une échelle un peu plus large de la zone périurbaine de Dakar pour déterminer les influences du type d'occupation du sol.Les résultats principaux de cette étude ont montré que (1) il y a un processus de salinisation anthropique des sols (sodisation) lors d'irrigation avec des eaux de nappe saumâtres, un processus accentué en saison sèche et lors d'années à pluviométrie déficitaire. Bien que les eaux usées soient aussi salines que les eaux de nappe, la salinisation des sols irrigués' par des eaux usées est limitée par l'ammonium présent dans les eaux usées (moy 190mg NH4/L à Pikine) qui produit de l'acidité lors de la transformation en nitrates dans le sol (nitrification). (2) les sols irrigués par des eaux usées (EU) stockent moins de C et Ν que les sois de référence, ce qui montrent bien que l'azote des eaux usées n'est pas disponible pour les plantes, mais est lessivé dans la nappe (100 à 450 mg/L N03 sous irrigation par EU, alors que la limite de OMS est de 50mg/L). (3) l'utilisation des isotopes stables des nitrates et des éléments traces, notamment le bore et le brome, ont permis de distinguer l'influence de l'irrigation par des eaux usées, de l'irrigation par des eaux de nappe et des lixiviats de fosses septiques sur les propriétés de la nappe. (4) Le processus de la dénitrification (atténuation naturelle des concentrations en nitrates de la nappe par biotransformation en azote gazeux) est important dans les zones basses de l'agrosystème périurbain de Dakar, sous irrigation par eaux naturelles (ΝΟ3 < 50mg/L). Tandis que sous habitat sans assainissement adéquat, les nitrates atteignent 300 à 700 mg/L. (5) Le flux total de pesticides dans l'AU est énorme (60kg/ha/an) totalisant 15 pesticides, dont deux seulement sont autorisés. Les pesticides les plus utilisés sont des insecticides organophosphorés et organochlorés classés extrêmement dangereux à dangereux par l'OMS, appliqués à des doses de 2 à 9 kg/ha/an. Les pesticides qui ont montré un risque élevé de contamination des eaux souterraines avec les indicateurs SIRIS et EPRIP2 sont : le carbofuran, le dimethoate, l'ethoprophos et le methomyl.En conclusion, nous recommandons la reconstitution d'un horizon superficiel des sols riche en matière organique stable et structuré par production locale de compost. Cette mesure réduira les pertes gazeuses contribuant à l'effet de serre, augmentera le stock de Ν dans ces sols, alors utilisable par les plantes et permettra de diminuer l'irrigation car la capacité de rétention de l'eau dans le sol sera accru, ce qui limitera le lessivage des nitrates dans la nappe et l'alcalinisation secondaire. Enfin, la mise en place d'une lutte intégrée ou biologique contre les ravageurs est indispensable afin de minimiser les risques pour les eaux souterraines et lesmares permanentes.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.