On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Computing programs for the complex exponential integral /

Photocopy. Arlington, Va. : Armed Services Technical Information Agency, [1970] -- 34 leaves ; 26 x 34 cm.

MA160exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam01pdf

Exam questions and solutions in PDF

Identificação experimental e controle ativo de vibrações aplicadas em estruturas inteligentes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Protein-protein interaction investigated by steered molecular dynamics: the TCR-pMHC complex.

We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

Statistics and kinetics of single-molecule electron transfer dynamics in complex environments: A simulation model study

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

Titanium(IV)-EDTA complex - Kinetics of thermal decomposition by non-isothermal procedures

This work aims the evaluation of the kinetic triplets corresponding to the two successive steps of thermal decomposition of Ti(IV)-ethylenediaminetetraacetate complex. Applying the isoconversional Wall-Flynn-Ozawa method on the DSC curves, average activation energy: E=172.4 +/- 9.7 and 205.3 +/- 12.8 kJ mol(-1), and pre-exponential factor: logA = 16.38 +/- 0.84 and 18.96 +/- 1.21 min(-1) at 95% confidence interval could be obtained, regarding the partial formation of anhydride and subsequent thermal decomposition of uncoordinated carboxylate groups, respectively.From E and logA values, Dollimore and Malek methods could be applied suggesting PT (Prout-Tompkins) and R3 (contracting volume) as the kinetic model to the partial formation of anhydride and thermal decomposition of the carboxylate groups, respectively.

Tin(II)-EDTA complex: kinetic of thermal decomposition by non-isothermal procedures

Tin on the oxide form, alone or doped with others metals, has been extensively used as gas sensor, thus, this work reports on the preparation and kinetic parameters regarding the thermal decomposition of Sn(II)-ethylenediaminetetraacetate as precursor to SnO2. Thus, the acquaintance with the kinetic model regarding the thermal decomposition of the tin complex may leave the door open to foresee, whether it is possible to get thin film of SnO2 using Sn(II)-EDTA as precursor besides the influence of dopants added.The Sn(II)-EDTA soluble complex was prepared in aqueous medium by adding of tin(II) chloride acid solution to equimolar amount of ammonium salt from EDTA under N-2 atmosphere and temperature of 50degreesC arising the pH similar to 4. The compound was crystallized in ethanol at low-temperature and filtered to eliminate the chloride ions, obtaining the heptacoordinated chelate with the composition H2SnH2O(CH2N(CH2COO)(2))(2).0.5H(2)O.Results from TG, DTG and DSC curves under inert and oxidizing atmospheres indicate the presence of water coordinated to the metal and that the ethylenediamine fraction is thermally more stable than carboxylate groups. The final residue from thermal decomposition was the SnO2 characterized by X-ray as a tetragonal rutile phase.Applying the isoconversional Wall-Flynn-Ozawa method on the DSC curves, average activation energy: E-a = 183.7 +/- 12.7 and 218.9 +/- 2.1 kJ mol(-1), and pre-exponential factor: log A = 18.85 +/- 0.27 and 19.10 +/- 0.27 min(-1), at 95% confidence level, could be obtained, regarding the loss of coordinated water and thermal decomposition of the carboxylate groups, respectively. The E-a and logA also could be obtained applying isoconventional Wall-Flynn method on the TG curves.From E-a and log A values, Dollimore and Malek procedures could be applied suggesting R3 (contracting volume) and SB (two-parameter model) as the kinetic model to the loss of coordinated water (177-244degreesC) and thermal decomposition of the carboxylate groups (283-315degreesC), respectively. Simulated and experimental normalized DTG and DSC curves besides analysis of residuals check these kinetic models. (C) 2003 Elsevier B.V. All rights reserved.

Synthesis of a functionalized europium complex and deposition of luminescent Langmuir-Blodgett (LB) films

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Wave equation depth migration using complex Padé approximation

Propomos um novo método de migração em profundidade baseado na solução da equação da onda com densidade constante no domínio da freqüência. Uma aproximação de Padé complexa é usada para aproximar o operador de evolução aplicado na extrapolação do campo de ondas. Esse método reduz as imprecisões e instabilidades devido às ondas evanescentes e produz imagens com menos ruídos numéricos que aquelas obtidas usando-se a aproximação de Padé real para o operador exponencial, principalmente em meios com fortes variações de velocidades. Testes em dados de afastamento nulo do modelo de sal SEG/EAGE e nos dados de tiro comum 2-D Marmousi foram realizados. Os resultados obtidos mostram que o método de migração proposto consegue lidar com fortes variações laterais e também tem uma boa resposta para refletores com mergulhos íngremes. Os resultados foram comparados àqueles resultados obtidos com os métodos split-step Fourier (SSF), phase shift plus interpolarion (PSPI) e Fourier diferenças-finitas (FFD).

A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate. (C) 2012 Elsevier B.V. All rights reserved.

Synthesis of a functionalized europium complex and deposition of luminescent Langmuir-Blodgett (LB) films

The synthesis, characterization and formation of Langmuir-Blodgett (LB)films for the luminescent [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] complex, where [(C12H25)(2)(CH3)(2)](N+) is didodecyldimethylammonium and the tta ligand is thenoyltrifluoroacetone, are reported. The coordination of tta ligands to the Eu3+ ion was confirmed by FTIR spectroscopy and the emission spectrum comprised bands corresponding to D-5(0) -> F-7(0-4) transitions. The lifetime (tau) from the emission state (D-5(0))was 0.41 ms, measured by monitoring the hypersensitive D-5(0) -> F-7(2) transition, with the curve being fitted with a first-order exponential function. The surface pressure-area isotherm indicated that the anionic complex may form condensed structures at the air-water interface due to the amphiphilic properties of the counter ion and the beta-diketone ligand. Y-type LB films of [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] were deposited on quartz substrates, with preserved luminescence and a band assigned to the D-5(0) -> F-7(2) transition. The molecular arrangement at the air/water interface and the preserved luminescence in LB films are consistent with theoretical predictions using a semi-empirical Sparkle/AM1 calculation method for the molecule in vacuum. These tools were used for the first time to predict the behavior of organized films.

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.