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Jacob Palis
__NOTOC__ Jacob Palis Jr. (born 15 March 1940) is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, attractors and chaotic systems. Biography Jacob Palis was born in Uberaba, Minas Gerais. His father was a Lebanese immigrant, and his mother was a Syrian immigrant. The couple had eight children (five men and three women), and Jacob was the youngest. His father was a merchant, owner of a large store, and supported and funded the studies of his children. Palis said that he already enjoyed mathematics in his childhood.http://www.faperj.br/downloads/revista/Rio_Pesquisa_4_2008.pdf At 16, Palis moved to Rio de Janeiro to study engineering at the University of Brazil – now UFRJ. He was approved in first place in the entrance exam, but was not old enough to be accepted; he then had to take the university's entry exam again a year later, at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uberaba
Uberaba () is a city in the state of Minas Gerais, southeast Brazil. It is located in the Brazilian Highlands at above sea level on the Uberaba River, and away from the state capital, Belo Horizonte. The city status was granted in 1856, and its name comes from the Tupi language meaning "bright water". As of 2021 the population was 340,277 inhabitants. History The history of Uberaba begins in 1810 when capt. Major Eustaquio founded a settlement in the vicinity of the ancient route of Anhanguera (also known as the 'Goyazes road') to serve as a stopping point for locals and travelers during the 19th century. Given the strategic location of the village and as a crossroads, local farmers started to cultivate crops and domesticate cattle for commerce which led the establishment of a strong livestock network for that region. The territory of Uberaba was part of the Captaincy of Goias until 1816, being annexed to the Captaincy of Minas Gerais in the same year. It was raised to pari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UFRJ
The Federal University of Rio de Janeiro or University of Brazil (UFRJ; pt, Universidade Federal do Rio de Janeiro or ') is a public university, public research university located in the state of Rio de Janeiro (state), Rio de Janeiro, Brazil. It is the largest federal university in the country and is one of the Brazilian centers of excellence in teaching and research. In terms of scientific, artistic and cultural productions it is recognized nationally and internationally due to the great professors, researchers, reviews and assessments made by international agencies. In 2017 ''Times Higher Education World University Rankings, QS World University Rankings'' ranked UFRJ as the best Brazilian federal university, as well as the third best university in the country occupying the seventh position among institutions of Latin America. In 2016 and 2017 the Ranking Universitário Folha (RUF) ranked UFRJ as the best university in Brazil and the best Federal University in the country. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Brazil
The Federal University of Rio de Janeiro or University of Brazil (UFRJ; pt, Universidade Federal do Rio de Janeiro or ') is a public research university located in the state of Rio de Janeiro, Brazil. It is the largest federal university in the country and is one of the Brazilian centers of excellence in teaching and research. In terms of scientific, artistic and cultural productions it is recognized nationally and internationally due to the great professors, researchers, reviews and assessments made by international agencies. In 2017 ''QS World University Rankings'' ranked UFRJ as the best Brazilian federal university, as well as the third best university in the country occupying the seventh position among institutions of Latin America. In 2016 and 2017 the Ranking Universitário Folha (RUF) ranked UFRJ as the best university in Brazil and the best Federal University in the country. The Center for World University Rankings (CWUR) published in 2017, rated UFRJ as the second best ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syria
Syria ( ar, سُورِيَا or سُورِيَة, translit=Sūriyā), officially the Syrian Arab Republic ( ar, الجمهورية العربية السورية, al-Jumhūrīyah al-ʻArabīyah as-Sūrīyah), is a Western Asian country located in the Eastern Mediterranean and the Levant. It is a unitary republic that consists of 14 governorates (subdivisions), and is bordered by the Mediterranean Sea to the west, Turkey to the north, Iraq to the east and southeast, Jordan to the south, and Israel and Lebanon to the southwest. Cyprus lies to the west across the Mediterranean Sea. A country of fertile plains, high mountains, and deserts, Syria is home to diverse ethnic and religious groups, including the majority Syrian Arabs, Kurds, Turkmens, Assyrians, Armenians, Circassians, Albanians, and Greeks. Religious groups include Muslims, Christians, Alawites, Druze, and Yazidis. The capital and largest city of Syria is Damascus. Arabs are the largest ethnic group, and Mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebanon
Lebanon ( , ar, لُبْنَان, translit=lubnān, ), officially the Republic of Lebanon () or the Lebanese Republic, is a country in Western Asia. It is located between Syria to the north and east and Israel to the south, while Cyprus lies to its west across the Mediterranean Sea; its location at the crossroads of the Mediterranean Basin and the Arabian hinterland has contributed to its rich history and shaped a cultural identity of religious diversity. It is part of the Levant region of the Middle East. Lebanon is home to roughly six million people and covers an area of , making it the second smallest country in continental Asia. The official language of the state is Arabic, while French is also formally recognized; the Lebanese dialect of Arabic is used alongside Modern Standard Arabic throughout the country. The earliest evidence of civilization in Lebanon dates back over 7000 years, predating recorded history. Modern-day Lebanon was home to the Phoenicians, a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uberaba, Minas Gerais
Uberaba () is a city in the state of Minas Gerais, southeast Brazil. It is located in the Brazilian Highlands at above sea level on the Uberaba River, and away from the state capital, Belo Horizonte. The city status was granted in 1856, and its name comes from the Tupi language meaning "bright water". As of 2021 the population was 340,277 inhabitants. History The history of Uberaba begins in 1810 when capt. Major Eustaquio founded a settlement in the vicinity of the ancient route of Anhanguera (also known as the 'Goyazes road') to serve as a stopping point for locals and travelers during the 19th century. Given the strategic location of the village and as a crossroads, local farmers started to cultivate crops and domesticate cattle for commerce which led the establishment of a strong livestock network for that region. The territory of Uberaba was part of the Captaincy of Goias until 1816, being annexed to the Captaincy of Minas Gerais in the same year. It was raised to pari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic System
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attractor
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an ''n''-dimensional vector. The attractor is a region in ''n''-dimensional space. In physical systems, the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate. If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them . Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bifurcations, which can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolicity
In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic groups. Definitions In this paragraph we give various definitions of a \delta-hyperbolic space. A metric space is said to be (Gromov-) hyperbolic if it is \delta-hyperbolic for some \delta > 0. Definition using the Gromov product Let (X,d) be a metric space. The Gromov product of two points y, z \in X with respect to a third one x \in X is defined by the formula: :(y,z)_x = \frac 1 2 \left( d(x, y) + d(x, z) - d(y, z) \right). Gromov's definition of a hyperbolic metric space is then as follows: X is \delta-hyperbolic if and only if all x,y,z,w \in X satisfy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Stability
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to the system (unique "ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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