A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

Bond graph models of DC-DC converters operating in both CCM and DCM

In this paper, Bond Graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a Modulated Transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a Boost and Buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operation area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the Normalised Root Means Square Error and the Maximum Absolute Error remaining adequately low. The model is also experimentally tested on a Buck topology.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

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.

An alternative approach for general covariant Horava-Lifshitz gravity and matter coupling

Recently, in [3] Horava and Melby-Thompson proposed a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduces the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of. to be lambda = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general lambda.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Modelo matemático de um agitador eletromagnético

O objetivo deste trabalho é estudar os efeitos eletromagnéticos e fluido-dinâmicos induzidos no aço, decorrentes do uso de um agitador eletromagnético. Para tal, foi proposta a construção de um modelo numérico que resolva, de forma acoplada, os problemas de eletromagnetismo e fluido-dinâmica. O modelo numérico do problema eletromagnético, em elementos finitos, foi construído utilizando-se o software Opera-3d/Elektra da Vector Fields. O mesmo foi validado com medidas experimentais de densidade de fluxo magnético feitas na usina. O escoamento decorrente da agitação eletromagnética foi resolvido fazendo-se o acoplamento das forças de Lorentz com as equações de Navier-Stokes. Essas últimas foram resolvidas pelo método de volumes finitos, usando-se o software CFX-4 da AEA Technology. O modelo eletromagnético mostrou que existe um torque máximo dependente da freqüência do campo magnético. Também foi observado que a força magnética aumenta em quatro vezes seu valor, quando a corrente é duplicada. O perfil de escoamento produzido no molde, sob agitação eletromagnética, indica, que as situações de lingotamento testadas, não propiciam o arraste da escória. A velocidade crítica de arraste, determinada via modelo físico, não foi atingida para nenhum caso testado. O modelo fluido-dinâmico e térmico apresentou um aumento do fluxo de calor cedido pelo fluido para a casca solidificada com o uso do agitador eletromagnético. Como conseqüência, observou-se uma queda na temperatura do banho. Também foi observado, que o uso do agitador propicia a remoção de inclusões das camadas mais externas do tarugo. Ao mesmo tempo, notou-se que o uso do agitador aumenta o índice de remoção de inclusões para as duas seções de molde analisadas.

Campos de Killing, curvatura média e translações

D. Hoffman, R. Osserman e R. Schoen mostraram que se a aplicação de Gauss de uma superfície orientada completa de curvatura média constante M imersa em R³ está contida em um hemisfério fechado de S² (equivalentemente, a função não muda de sinal em M, onde n é um vetor unitário normal de M e v algum vetor não nulo de R³), então M é invariante por um subgrupo a um parâmetro de translações de R³ (aquele determinado por v). Neste trabalho obtemos uma extensão deste resultado para o caso em que o espaço ambiente é uma variedade riemanniana e M uma hipersuperfície em N requerendo que a função não mude de sinal em M, onde V é um campo de Killing em N. Na parte final deste trabalho consideramos uma variedade riemanniana Killing paralelizável N para definir uma translação Y: M -> Rn de uma hipersuperfície M de N que é uma extensão natural da aplicação de Gauss de uma hipersuperfície de Rn. Considerando as mesmas hipóteses para a imagem de y obtemos uma extensão do resultado original de Hoffman-Osserman-Schoen.

Essays on economic growth

A fundamental question in development economics is why some economies are rich and others poor. To illustrate the income per capita gap across economies consider that the average gross domestic product (GDP) per capita of the richest 10 percent of economies in the year 2010 was a factor of 40-fold that of the poorest 10 percent of economies. In other words, the average person in a rich economy produces in just over 9 days what the average person in a poor economy produces in an entire year. What are the factors that can explain this difference in standard of living across the world today? With this in view, this dissertation is a conjunction of three essays on the economic growth field which we seek a possible responses to this question. The first essay investigates the existence of resource misallocation in the Brazilian manufacturing sector and measures possible distortions in it. Using a similar method of measurement to the one developed by Hsieh and Klenow (2009) and firm-level data for 1996-2011 we find evidence of misallocation in the manufacturing sector during the observed period. Moreover, our results show that misallocation has been growing since 2005, and it presents a non-smooth dynamic. Significantly, we find that the Brazilian manufacturing sector operates at about 50% of its efficient product. With this, if capital and labor were optimally reallocated between firms and sectors we would obtain an aggregate output growth of approximately 110-180% depending on the mode in which the capital share is measured. We also find that the economic crisis did not have a substantial effect on the total productivity factor or on the sector's misallocation. However, small firms in particular seem to be strongly affected in a global crisis. Furthermore, the effects described would be attenuated if we consider linkages and complementarity effects among sectors. Despite Brazil's well-known high tax burden, there is not evidence that this is the main source of resource misallocation. Moreover, there is a distinct pattern of structural change between the manufacturing sectors in industrialized countries and those in developing countries. Therefore, the second essay demonstrate that this pattern differs because there are some factors that distort the relative prices and also affect the output productivity. For this, we present a multi-sector model of economic growth, where distortions affect the relative prices and the allocation of inputs. This phenomenon imply that change of the production structure or perpetuation of the harmful structures to the growth rate of aggregate output. We also demonstrate that in an environment with majority decision, this distortion can be enhanced and depends on the initial distribution of firms. Furthermore, distortions in relative prices would lead to increases in the degree of misallocation of resources, and that imply that there are distinct patterns of structural changes between economies. Finally, the calibrated results of the framework developed here converge with the structural change observed in the firm-level data of the Brazilian manufacturing sector. Thereafter, using a cross-industry cross-country approach, the third essay investigates the existence of an optimal level of competition to enhance economic growth. With that in mind, we try to show that this optimal level is different from industrialized and under development economies due to the technology frontier distance, the terms of trade, and each economy's idiosyncratic characteristics. Therefore, the difference in competition industry-country level is a channel to explain the output for worker gap between countries. The theoretical and empirical results imply the existence of an inverted-U relationship between competition and growth: starting for an initially low level of competition, higher competition stimulates innovation and output growth; starting from a high initial level of competition, higher competition has a negative effect on innovation and output growth. Given on average industries in industrialized economies present higher competition level. With that if we control for the terms of trade and the industry-country fixed effect, if the industries of the developing economy operated under the same competition levels as of the industrialized ones, there is a potential increase of output of 0.2-1.0% per year. This effect on the output growth rate depends on the competition measurement used.

PEGylated polyethyleneimine-entrapped gold nanoparticles for enhanced and targeted gene delivery applications

Gene therapy, which involves the transfer of nucleic acid into target cells in patients, has become one of the most important and widely explored strategies to treat a variety of diseases, such as cancer, infectious diseases and genetic disorders. Relative to viral vectors that have high immunogenicity, toxicity and oncogenicity, non-viral vectors have gained a lot of interest in recent years. This is largely due to their ability to mimic viral vector features including the capacity to overcome extra- and intra-cellular barriers and to enhance transfection efficiency. Polyethyleneimine (PEI) has been extensively investigated as a non-viral vector. This cationic polymer, which is able to compact nucleic acid through electrostatic interactions and to transport it across the negatively charged cell membranes, has been shown to effectively transfect nucleic acid into different cell lines. Moreover, entrapment of gold nanoparticles (Au NPs) into such an amine-terminated polymer template has been shown to significantly enhance gene transfection efficiency. In this work, a novel non-viral nucleic acid vector system for enhanced and targeted nucleic acid delivery applications was developed. The system was based on the functionalization of PEI with folic acid (FA; for targeted delivery to cancer cells overexpressing FA receptors on their surface) using polyethylene glycol (PEG) as a linker molecule. This was followed by the preparation of PEI-entrapped Au NPs (Au PENPs; for enhancement of transfection efficiency). In the synthesis process, the primary amines of PEI were first partially modified with fluorescein isothiocyanate (FI) using a molar ratio of 1:7. The formed PEI-FI conjugate was then further modified with either PEG or PEGylated FA using a molar ratio of 1:1. This process was finally followed by entrapment of Au NPs into the modified polymers. The resulting conjugates and Au PENPs were characterized by several techniques, namely Nuclear Magnetic Resonance, Dynamic Light Scattering and Ultraviolet-Visible Spectroscopy, to assess their physicochemical properties. In the cell biology studies, the synthesized conjugates and their respective Au PENPs were shown to be non-toxic towards A2780 human ovarian carcinoma cells. The role of these materials as gene delivery agents was lastly evaluated. In the gene delivery studies, the A2780 cells were successfully transfected with plasmid DNA using the different vector systems. However, FA-modification and Au NPs entrapment were not determinant factors for improved transfection efficiency. In the gene silencing studies, on the other hand, the Au PENPs were shown to effectively deliver small interfering RNA, thereby reducing the expression of the B-cell lymphoma 2 protein. Based on these results, we can say that the systems synthesized in this work show potential for enhanced and targeted gene therapy applications.

Desenvolvimento de nanosistemas farmacêuticos para terapia gênica

Gene therapy is one of the major challenges of the post-genomic research and it is based on the transfer of genetic material into a cell, tissue or organ in order to cure or improve the patient s clinical status. In general, gene therapy consists in the insertion of functional genes aiming substitute, complement or inhibit defective genes. The achievement of a foreigner DNA expression into a population of cells requires its transfer to the target. Therefore, a key issue is to create systems, vectors, able to transfer and protect the DNA until it reaches the target. The disadvantages related to the use of viral vectors have encouraged efforts to develop emulsions as non-viral vectors. In fact, they are easy to produce, present suitable stability and enable transfection. The aim of this work was to evaluate two different non-viral vectors, cationic liposomes and nanoemulsions, and the possibility of their use in gene therapy. For the two systems, cationic lipids and helper lipids were used. Nanoemulsions were prepared using sonication method and were composed of Captex® 355; Tween® 80; Spam® 80; cationic lipid, Stearylamine (SA) or 1,2-dioleoyl-3-trimethylammoniumpropane (DOTAP) and water (Milli-Q®). These systems were characterized by average droplet size, Polidispersion Index (PI) and Zeta Potential. The stability of the systems; as well as the DNA compaction capacity; their cytotoxicity and the cytotoxicity of the isolated components; and their transfection capacity; were also evaluated. Liposomes were made by hydration film method and were composed of DOTAP; 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), containing or not Rhodaminephosphatidylethanolamine (PE- Rhodamine) and the conjugate Hyaluronic Acid DOPE (HA-DOPE). These systems were also characterized as nanoemulsions. Stability of the systems and the influence of time, size of plasmid and presence or absence of endotoxin in the formation of lipoplexes were also analyzed. Besides, the ophthalmic biodistribution of PE-Rhodamine containing liposomes was studied after intravitreal injection. The obtained results show that these systems are promising non-viral vector for further utilization in gene therapy and that this field seems to be very important in the clinical practice in this century. However, from the possibility to the practice, there is still a long way

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bi-Lipschitz A-triviality of map germs and Newton filtrations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)