Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.

Harvesting dynamic aspects from a real rational map : the bulb of period 5

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Application of the Extended Kalman filter for speed sensorless control of PM synchronous machines

The increasing interest in the decarbonization process led to a rapidly growing trend of electrification strategies in the automotive industry. In particular, OEMs are pushing towards the development and production of efficient electric vehicles. Moreover, research on electric motors and their control are exploding in popularity. The increase of computational power in embedded control hardware is allowing the development of new control algorithm, such as sensorless control strategy. Such control strategy allows the reduction of the number of sensors, which implies reduced costs and increased system reliability. The thesis objective is to realize a sensorless control for high-performance automotive motors. Several algorithms for rotor angle observers are implemented in the MATLAB and Simulink environment, with emphasis on the Kalman observer. One of the Kalman algorithms already available in the literature has been selected, implemented and benchmarked, with emphasis on its comparison with the Sliding Mode observer. Different models characterized by increasing levels of complexity are simulated. A simplified synchronous motor with ”constant parameters”, controlled by an ideal inverter is first analyzed; followed by a complete model defined by real motor maps, and controlled by a switching inverter. Finally, it was possible to test the developed algorithm on a real electric motor mounted on a test bench. A wide range of different electric motors have been simulated, which led to an exhaustive review of the sensorless control algorithm. The final results underline the capability of the Kalman observer to effectively control the motor on a real test bench.

Geolocalitzáció en temps real sobre Google Maps

L’objectiu d’aquest projecte és crear un sistema de seguiment d’una flota de vehicles amb GPS en temps real. A partir d’un mòdul de captació, el servidor recull la informació geogràfica dels vehicles i l’emmagatzema. I amb un mòdul de processament, es mostra i controla els vehicles, els punts d’interès i els polígons del sistema de Geofencing. En primer lloc, faig una introducció a l’estat de l’art dels sistemes de seguiment de vehicles. A continuació, analitzo els requeriments, especifico el comportament desitjat del sistema, explico el disseny i la implementació. Per últim, faig un seguit de proves per extreure’n les conclusions.

On the injectivity of C1 maps of the real plane

Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Inspeção e diagnóstico de edifícios recentes: estudo de um caso real

Trabalho de Projeto para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Edificações

A fusão de dois mundos: convergência do mundo real e digital nas acções de marketing na rede

No passado, as acções publicitárias eram rotuladas como above the line e below the line, referindo-se à dicotomia de pontos de contacto com os públicos-alvo via Meios de Comunicação Social ou via Ponto de Venda. A esta dicotomia de meios e instrumentos, os anos 90 vieram trazer um terceiro ponto de contacto, crescentemente omnipresente e hegemónico, a world wide web ou rede, a que se acedia via computador. As acções de marketing e comunicação passaram então a rotular-se como online e offline, passando, não já a referir-se aos pontos de contacto, mas aos canais pelos quais circulavam as mensagens e acções das marcas. Desde o início deste século, o poder do digital veio crescendo, em software e hardware, em terminais e tecnologias, assistindo-se a uma transferência de esforços de comunicação, da esfera real para a esfera do digital. O deslumbramento pelo digital conquistou mesmo algumas marcas de dimensão mundial que hoje apostam integralmente o seu orçamento nesta forma de marketing, nas suas múltiplas facetas. Contudo, e porque se tem tornado óbvio que os públicos distribuem os seus favores por múltiplos touch points, para maximizar o impacto, assiste-se agora a um fenómeno único, potenciado por novas tecnologias que surgem todos os dias: em estratégias que se podem denominar de all-line, verifica-se a fusão entre dois mundos, mundo real e mundo digital, em múltiplas actividades de marketing que fazem convergir estas duas realidades em plataformas que vão do computador ao tablet, do smartphone à vending machine interactiva, do facebook ao Google maps, da imprensa tradicional ao pinterest. É esta convergência mundo real - mundo digital que abre agora novas oportunidades à comunicação publicitária, potenciando os ingredientes das marcas de sucesso no futuro: sensações (estímulo dos sentidos), intimidade e mistério, num cocktail suportado por uma nova criatividade.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Assessment of the effects of the expansion of the city of Estarreja on the rational land use

The management of urban environment, together with the preservation of the natural environment and the creation of a sustainable built environment, is a complex challenge for contemporary societies. In the name of progress, cities are contributing for the degradation of all surrounding ecosystems. Therefore there is an arising demand for developing new strategies and a new urban development paradigm settled in the search for the equilibrium between natural and built environments and efficient use of resources. The objective of this paper is to analyse how the urban expansion of the city of Estarreja took place in relation to the land use, based on the land capability classification maps of the area. Based in the results some sustainable development strategies that might be applied to the city are discussed. The obtained results demonstrate that the city has been growing faster then its population, consuming vast portions of land, since its growth as been occurring in a linear form. Despite this fact, results show that most of this expansion took place towards a territory of lower agricultural potential, when comparing to the location of its original settlement.

Financial Markets and Real Ecinomy: Four Essays in International Trade

Financial markets play an important role in an economy performing various functions like mobilizing and pooling savings, producing information about investment opportunities, screening and monitoring investments, implementation of corporate governance, diversification and management of risk. These functions influence saving rates, investment decisions, technological innovation and, therefore, have important implications for welfare. In my PhD dissertation I examine the interplay of financial and product markets by looking at different channels through which financial markets may influence an economy.My dissertation consists of four chapters. The first chapter is a co-authored work with Martin Strieborny, a PhD student from the University of Lausanne. The second chapter is a co-authored work with Melise Jaud, a PhD student from the Paris School of Economics. The third chapter is co-authored with both Melise Jaud and Martin Strieborny. The last chapter of my PhD dissertation is a single author paper.Chapter 1 of my PhD thesis analyzes the effect of financial development on growth of contract intensive industries. These industries intensively use intermediate inputs that neither can be sold on organized exchange, nor are reference-priced (Levchenko, 2007; Nunn, 2007). A typical example of a contract intensive industry would be an industry where an upstream supplier has to make investments in order to customize a product for needs of a downstream buyer. After the investment is made and the product is adjusted, the buyer may refuse to meet a commitment and trigger ex post renegotiation. Since the product is customized to the buyer's needs, the supplier cannot sell the product to a different buyer at the original price. This is referred in the literature as the holdup problem. As a consequence, the individually rational suppliers will underinvest into relationship-specific assets, hurting the downstream firms with negative consequences for aggregate growth. The standard way to mitigate the hold up problem is to write a binding contract and to rely on the legal enforcement by the state. However, even the most effective contract enforcement might fail to protect the supplier in tough times when the buyer lacks a reliable source of external financing. This suggests the potential role of financial intermediaries, banks in particular, in mitigating the incomplete contract problem. First, financial products like letters of credit and letters of guarantee can substantially decrease a risk and transaction costs of parties. Second, a bank loan can serve as a signal about a buyer's true financial situation, an upstream firm will be more willing undertake relationship-specific investment knowing that the business partner is creditworthy and will abstain from myopic behavior (Fama, 1985; von Thadden, 1995). Therefore, a well-developed financial (especially banking) system should disproportionately benefit contract intensive industries.The empirical test confirms this hypothesis. Indeed, contract intensive industries seem to grow faster in countries with a well developed financial system. Furthermore, this effect comes from a more developed banking sector rather than from a deeper stock market. These results are reaffirmed examining the effect of US bank deregulation on the growth of contract intensive industries in different states. Beyond an overall pro-growth effect, the bank deregulation seems to disproportionately benefit the industries requiring relationship-specific investments from their suppliers.Chapter 2 of my PhD focuses on the role of the financial sector in promoting exports of developing countries. In particular, it investigates how credit constraints affect the ability of firms operating in agri-food sectors of developing countries to keep exporting to foreign markets.Trade in high-value agri-food products from developing countries has expanded enormously over the last two decades offering opportunities for development. However, trade in agri-food is governed by a growing array of standards. Sanitary and Phytosanitary standards (SPS) and technical regulations impose additional sunk, fixed and operating costs along the firms' export life. Such costs may be detrimental to firms' survival, "pricing out" producers that cannot comply. The existence of these costs suggests a potential role of credit constraints in shaping the duration of trade relationships on foreign markets. A well-developed financial system provides the funds to exporters necessary to adjust production processes in order to meet quality and quantity requirements in foreign markets and to maintain long-standing trade relationships. The products with higher needs for financing should benefit the most from a well functioning financial system. This differential effect calls for a difference-in-difference approach initially proposed by Rajan and Zingales (1998). As a proxy for demand for financing of agri-food products, the sanitary risk index developed by Jaud et al. (2009) is used. The empirical literature on standards and norms show high costs of compliance, both variable and fixed, for high-value food products (Garcia-Martinez and Poole, 2004; Maskus et al., 2005). The sanitary risk index reflects the propensity of products to fail health and safety controls on the European Union (EU) market. Given the high costs of compliance, the sanitary risk index captures the demand for external financing to comply with such regulations.The prediction is empirically tested examining the export survival of different agri-food products from firms operating in Ghana, Mali, Malawi, Senegal and Tanzania. The results suggest that agri-food products that require more financing to keep up with food safety regulation of the destination market, indeed sustain longer in foreign market, when they are exported from countries with better developed financial markets.Chapter 3 analyzes the link between financial markets and efficiency of resource allocation in an economy. Producing and exporting products inconsistent with a country's factor endowments constitutes a serious misallocation of funds, which undermines competitiveness of the economy and inhibits its long term growth. In this chapter, inefficient exporting patterns are analyzed through the lens of the agency theories from the corporate finance literature. Managers may pursue projects with negative net present values because their perquisites or even their job might depend on them. Exporting activities are particularly prone to this problem. Business related to foreign markets involves both high levels of additional spending and strong incentives for managers to overinvest. Rational managers might have incentives to push for exports that use country's scarce factors which is suboptimal from a social point of view. Export subsidies might further skew the incentives towards inefficient exporting. Management can divert the export subsidies into investments promoting inefficient exporting.Corporate finance literature stresses the disciplining role of outside debt in counteracting the internal pressures to divert such "free cash flow" into unprofitable investments. Managers can lose both their reputation and the control of "their" firm if the unpaid external debt triggers a bankruptcy procedure. The threat of possible failure to satisfy debt service payments pushes the managers toward an efficient use of available resources (Jensen, 1986; Stulz, 1990; Hart and Moore, 1995). The main sources of debt financing in the most countries are banks. The disciplining role of banks might be especially important in the countries suffering from insufficient judicial quality. Banks, in pursuing their rights, rely on comparatively simple legal interventions that can be implemented even by mediocre courts. In addition to their disciplining role, banks can promote efficient exporting patterns in a more direct way by relaxing credit constraints of producers, through screening, identifying and investing in the most profitable investment projects. Therefore, a well-developed domestic financial system, and particular banking system, would help to push a country's exports towards products congruent with its comparative advantage.This prediction is tested looking at the survival of different product categories exported to US market. Products are identified according to the Euclidian distance between their revealed factor intensity and the country's factor endowments. The results suggest that products suffering from a comparative disadvantage (labour-intensive products from capital-abundant countries) survive less on the competitive US market. This pattern is stronger if the exporting country has a well-developed banking system. Thus, a strong banking sector promotes exports consistent with a country comparative advantage.Chapter 4 of my PhD thesis further examines the role of financial markets in fostering efficient resource allocation in an economy. In particular, the allocative efficiency hypothesis is investigated in the context of equity market liberalization.Many empirical studies document a positive and significant effect of financial liberalization on growth (Levchenko et al. 2009; Quinn and Toyoda 2009; Bekaert et al., 2005). However, the decrease in the cost of capital and the associated growth in investment appears rather modest in comparison to the large GDP growth effect (Bekaert and Harvey, 2005; Henry, 2000, 2003). Therefore, financial liberalization may have a positive impact on growth through its effect on the allocation of funds across firms and sectors.Free access to international capital markets allows the largest and most profitable domestic firms to borrow funds in foreign markets (Rajan and Zingales, 2003). As domestic banks loose some of their best clients, they reoptimize their lending practices seeking new clients among small and younger industrial firms. These firms are likely to be more risky than large and established companies. Screening of customers becomes prevalent as the return to screening rises. Banks, ceteris paribus, tend to focus on firms operating in comparative-advantage sectors because they are better risks. Firms in comparative-disadvantage sectors finding it harder to finance their entry into or survival in export markets either exit or refrain from entering export markets. On aggregate, one should therefore expect to see less entry, more exit, and shorter survival on export markets in those sectors after financial liberalization.The paper investigates the effect of financial liberalization on a country's export pattern by comparing the dynamics of entry and exit of different products in a country export portfolio before and after financial liberalization.The results suggest that products that lie far from the country's comparative advantage set tend to disappear relatively faster from the country's export portfolio following the liberalization of financial markets. In other words, financial liberalization tends to rebalance the composition of a country's export portfolio towards the products that intensively use the economy's abundant factors.

Boundedly rational credit cycles

We propose an evolutionary model of a credit market. We show that theeconomy exhibits credit cycles. The model predicts dynamics which are consistent with some evidence about the Great Depression. Real shocks triggerepisodes of credit--crunch which are observed in the process of adjustmenttowards the post shock equilibrium.

2008 Iowa Real Property Appraisal Manual, May 2008

********NOTE: There are nine sections to this manual, all in separate files.************* **********NOTE: Large files may take longer to open******** The basis of real property assessment in Iowa is market value as defined in Iowa Code §441.21. Iowa Code §§ 421.17(17) and 441.21(h) provide that assessment jurisdictions follow the guidelines and rules in this manual to help achieve uniformity in assessments. Assessors are encouraged to use the International Association of Assessing Officers’ Standard on Mass Appraisal of Real Property in their mass appraisal practices. Estimating market value in mass appraisal involves accurately listing properties, developing a sales file that includes the primary influences on market value, and developing models for subsets of properties that share common market influences using recognized mass appraisal techniques. The assessment of an individual property should not be based solely on the sale price. The Uniform Standards of Professional Appraisal Practice (USPAP) standard 6 says “In developing a mass appraisal, an appraiser must be aware of, understand, and correctly employ those recognized methods and techniques necessary to produce and communicate credible mass appraisals.” Accurate listing of property is the basis of a good mass appraisal program. On-site inspection and listing of property is essential in developing a good data base for revaluation. A physical review, including an on-site verification of property characteristics, should be conducted at least every four to six years. Land values should be reviewed every two years. Factors influencing the market of each property type should be identified and collected so that these factors can be considered in the mass appraisal model. It is equally important to maintain the data once it is collected. Accessing local government permit systems should be a part of a good data maintenance program along with an inspection program. Current cadastral maps and geographical information systems (GIS) are tools that are integral in checking accuracy of listings and maintaining a comprehensive data base.