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Luís Barreira
Luís Barreira (born 25 September 1968) is a Portuguese mathematician and a professor in the department of mathematics of Instituto Superior Técnico. He is the author or coauthor of 13 books, many with Clàudia Valls, including among them Análise Complexa e Equações Diferenciais, Exercícios de Análise Complexa e Equações Diferenciais, Lyapunov Exponents and Smooth Ergodic Theory, Nonuniform Hyperbolicity, Stability of Nonautonomous Differential Equations, and Dimension and Recurrence in Hyperbolic Dynamics. He's also the author of several scientific articles, predominantly in Differential Equations, Dynamic Systems, Ergodic Theory and Multifractal Analysis. Education Barreira got his degree in 1991 in Applied Mathematics and Computation, from Instituto Superior Técnico. He got his PhD in 1996 at the University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instituto Superior Técnico
Instituto Superior Técnico MHSE • MHIP (IST, also known colloquially as Técnico, and stylized TÉCNICO LISBOA) is a public school of engineering and technology, part of University of Lisbon. It was founded as an autonomous school in 1911, and integrated in the Universidade Técnica de Lisboa in 1930. IST is the largest school of engineering in Portugal by number of enrolled students, faculty size, scientific production and patents. IST has three ''campi'', all located in the Lisbon metropolitan area: Alameda in Lisbon, Taguspark in Oeiras and Tecnológico e Nuclear Campus in Loures, and consists of ten departments that are responsible for teaching the undergraduate and postgraduate programs. Each department is organized in sections, which group together specific subjects within its scientific area. In addition, the laboratories of the several departments support the teaching and research activities carried out at IST. It offers 18 undergraduate programmes attended by mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clàudia Valls
Clàudia Valls Anglés is a mathematician and an expert in dynamical systems. She is an associate professor in the Instituto Superior Técnico of the University of Lisbon in Portugal. Education Valls completed a doctorate at the University of Barcelona The University of Barcelona ( ca, Universitat de Barcelona, UB; ; es, link=no, Universidad de Barcelona) is a public university located in the city of Barcelona, Catalonia, in Spain. With 63,000 students, it is one of the biggest universities i ... in 1999. Her dissertation, ''The Classical Arnold Example of Diffusion with Two Equal Parameters'', was supervised by . Books Valls is the co-author of books with Luís Barreira and others, including: *''Instability in Hamiltonian systems'' (with Antonio Pumariño, Electronic Journal of Qualitative Theory of Differential Equations Monograph Series, Vol. 1, 2005) *''Stability of nonautonomous differential equations'' (with Luís Barreira, Lecture Notes in Mathematics, Vol. 1926, Spri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Articles
: ''For a broader class of literature, see Academic publishing.'' Scientific literature comprises scholarly publications that report original empirical and theoretical work in the natural and social sciences. Within an academic field, scientific literature is often referred to as the literature. Academic publishing is the process of contributing the results of one's research into the literature, which often requires a peer-review process. Original scientific research published for the first time in scientific journals is called the primary literature. Patents and technical reports, for minor research results and engineering and design work (including computer software), can also be considered primary literature. Secondary sources include review articles (which summarize the findings of published studies to highlight advances and new lines of research) and books (for large projects or broad arguments, including compilations of articles). Tertiary sources might include encycl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manifo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multifractal Analysis
A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed. Multifractal systems are common in nature. They include the length of coastlines, mountain topography, fully developed turbulence, real-world scenes, heartbeat dynamics, human gait and activity, human brain activity, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed to mathematical convergence effects related to the central limit theorem that have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models, as well as the geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universities by numerous organizations and scholars. While the university dates its founding to 1740, it was created by Benjamin Franklin and other Philadelphia citizens in 1749. It is a member of the Ivy League. The university has four undergraduate schools as well as twelve graduate and professional schools. Schools enrolling undergraduates include the College of Arts and Sciences, the School of Engineering and Applied Science, the Wharton School, and the School of Nursing. Among its highly ranked graduate schools are its law school, whose first professor wrote the first draft of the United States Constitution, its medical school, the first in North America, and Wharton, the first collegiate business school. Penn's endowment is US$20.7 billio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pennsylvania Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1968 Births
The year was highlighted by protests and other unrests that occurred worldwide. Events January–February * January 5 – " Prague Spring": Alexander Dubček is chosen as leader of the Communist Party of Czechoslovakia. * January 10 – John Gorton is sworn in as 19th Prime Minister of Australia, taking over from John McEwen after being elected leader of the Liberal Party the previous day, following the disappearance of Harold Holt. Gorton becomes the only Senator to become Prime Minister, though he immediately transfers to the House of Representatives through the 1968 Higgins by-election in Holt's vacant seat. * January 15 – The 1968 Belice earthquake in Sicily kills 380 and injures around 1,000. * January 21 ** Vietnam War: Battle of Khe Sanh – One of the most publicized and controversial battles of the war begins, ending on April 8. ** 1968 Thule Air Base B-52 crash: A U.S. B-52 Stratofortress crashes in Greenland, discharging 4 nuclear bombs. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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