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Riccati
Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice. He is best known for having studied the equation which bears his name. Education Riccati was educated first at the Jesuit school for the nobility in Brescia, and in 1693 he entered the University of Padua to study law. He received a doctorate in law (LL.D.) in 1696. Encouraged by Stefano degli Angeli to pursue mathematics, he studied mathematical analysis. Career Riccati received various academic offers but declined them in order to devote his full attention to the study of mathematical analysis on his own. Peter the Great invited him to Russia as president of the St. Petersburg Academy of Sciences. He was also invited to Vienna as an imperial councillor and was offered a professorship at the University of Padua. He declined all these offers. He was often consulted by the Senate of Venice on the construction of canals and dikes along rivers. Some of his work on multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riccati Equation
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form : y'(x) = q_0(x) + q_1(x) \, y(x) + q_2(x) \, y^2(x) where q_0(x) \neq 0 and q_2(x) \neq 0. If q_0(x) = 0 the equation reduces to a Bernoulli equation, while if q_2(x) = 0 the equation becomes a first order linear ordinary differential equation. The equation is named after Jacopo Riccati (1676–1754). More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation. Conversion to a second order linear equation The non-linear Riccati equation can always be converted to a second order linear ordinary differential equation (ODE): If :y'=q_0(x) + q_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riccati - Opere, 1761 - 1368416
Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice. He is best known for having studied the equation which bears his name. Education Riccati was educated first at the Jesuit school for the nobility in Brescia, and in 1693 he entered the University of Padua to study law. He received a doctorate in law (LL.D.) in 1696. Encouraged by Stefano degli Angeli to pursue mathematics, he studied mathematical analysis. Career Riccati received various academic offers but declined them in order to devote his full attention to the study of mathematical analysis on his own. Peter the Great invited him to Russia as president of the St. Petersburg Academy of Sciences. He was also invited to Vienna as an imperial councillor and was offered a professorship at the University of Padua. He declined all these offers. He was often consulted by the Senate of Venice on the construction of canals and dikes along rivers. Some of his work on mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vincenzo Riccati
Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was a Venetian mathematician and physicist. Life Vincenzo Riccati was the brother of Giordano Riccati, and the second son of Jacopo Riccati. He entered the Society of Jesus on December 20, 1726. He taught ''belles lettres'' in the colleges of the Order in Piacenza (1728), Padua (1729), and Parma (1734). He then went to Rome to study theology. In 1739 he was assigned to the Collegio di San Francesco Saverio of Bologna, where he taught mathematics for thirty years. He was among the first members of the Italian National Academy of Sciences. Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. In 1757 he published the first volume of ''Opusculorum ad res physicas et mathematicas pertinentium'' introducing hyperbolic functions, the second volume appearing in 1762. In collaboration with Hieronymo Sal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giordano Riccati
Giordano Riccati or Jordan Riccati (25 February 1709 – 20 July 1790) was the first experimental mechanician to study material elastic moduli as we understand them today. His 1782 paper on determining the relative Young's moduli of steel and brass using flexural vibrations preceded Thomas Young's 1807 paper on the subject of moduli. The ratio that Riccati found wasBell,J. F., 1971, ''The experimental foundations of solid mechanics'', Handbuch der Physik VIa/I, Springer-Verlag, Berlin. : \frac = 2.06 Even though the experiments were performed more than 200 years ago, this value is remarkably close to accepted values found in engineering handbooks in 2007. Giordano Riccati was the son of the theoretical mechanician Jacopo Riccati Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice. He is best known for having studied the equation which bears his name. Education Riccati was educated first at the Jesuit school for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venice
Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The islands are in the shallow Venetian Lagoon, an enclosed bay lying between the mouths of the Po River, Po and the Piave River, Piave rivers (more exactly between the Brenta (river), Brenta and the Sile (river), Sile). In 2020, around 258,685 people resided in greater Venice or the ''Comune di Venezia'', of whom around 55,000 live in the historical island city of Venice (''centro storico'') and the rest on the mainland (''terraferma''). Together with the cities of Padua, Italy, Padua and Treviso, Italy, Treviso, Venice is included in the Padua-Treviso-Venice Metropolitan Area (PATREVE), which is considered a statistical metropolitan area, with a total population of 2.6 million. The name is derived from the ancient Adri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academy Of Sciences Of The Institute Of Bologna
The Academy of Sciences of the Institute of Bologna (''Accademia delle Scienze dell'Istituto di Bologna'') is an academic society in Bologna, Italy, that was founded in 1690 and prospered in the Age of Enlightenment. Today it is closely associated with the University of Bologna. Origins By the end of the seventeenth century the University of Bologna, one of the world's oldest and once a thriving center of artistic and scientific discovery, had entered a long period of decline. The ''Academy degli Inquieti'' was founded in Bologna around 1690 by Eustachio Manfredi as a place where mathematical topics could be discussed. At first, the academy held its meetings in Manfredi's house, where it began to attract scholars working in other disciplines such as anatomy and physiology, from Bologna and from nearby provinces. In 1694 the academy moved to the house of Jacopo Sandri, a professor of anatomy and medicine at the University of Bologna. In 1704 the academy acquired a more formal struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: * hyperbolic sine "" (), * hyperbolic cosine "" (),''Collins Concise Dictionary'', p. 328 from which are derived: * hyperbolic tangent "" (), * hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maria Gaetana Agnesi
Maria Gaetana Agnesi ( , , ; 16 May 1718 – 9 January 1799) was an Italian mathematician, philosopher, theologian, and humanitarian. She was the first woman to write a mathematics handbook and the first woman appointed as a mathematics professor at a university. She is credited with writing the first book discussing both differential and integral calculus and was a member of the faculty at the University of Bologna, although she never served. She devoted the last four decades of her life to studying theology (especially patristics) and to charitable work and serving the poor. She was a devout Catholic and wrote extensively on the marriage between intellectual pursuit and mystical contemplation, most notably in her essay ''Il cielo mistico'' (The Mystic Heaven). She saw the rational contemplation of God as a complement to prayer and contemplation of the life, death and resurrection of Jesus Christ. Maria Teresa Agnesi Pinottini, clavicembalist and composer, was her sister ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1676 Births
Events January–March * January 29 – Feodor III becomes Tsar of Russia. * January 31 – Universidad de San Carlos de Guatemala, the oldest institution of higher education in Central America, is founded. * January – Six months into King Philip's War, Metacomet (King Philip), leader of the Algonquian tribe known as the Wampanoag, travels westward to the Mohawk nation, seeking an alliance with the Mohawks against the English colonists of New England; his efforts in creating such an alliance are a failure. * February 10 – After the Nipmuc tribe attacks Lancaster, Massachusetts, colonist Mary Rowlandson is taken captive, and lives with the Indians until May. * February 14 – Metacomet and his Wampanoags attack Northampton, Massachusetts; meanwhile, the Massachusetts Council debates whether a wall should be erected around Boston. * February 23 – While the Massachusetts Council debates how to handle the Christian Indians they had exile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Young (scientist)
Thomas Young FRS (13 June 177310 May 1829) was a British polymath who made notable contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony, and Egyptology. He was instrumental in the decipherment of Egyptian hieroglyphs, specifically the Rosetta Stone. Young has been described as "The Last Man Who Knew Everything". His work influenced that of William Herschel, Hermann von Helmholtz, James Clerk Maxwell, and Albert Einstein. Young is credited with establishing the wave theory of light, in contrast to the particle theory of Isaac Newton. Young's work was subsequently supported by the work of Augustin-Jean Fresnel. Personal life Young belonged to a Quaker family of Milverton, Somerset, where he was born in 1773, the eldest of ten children. At the age of fourteen Young had learned Greek and Latin. Young began to study medicine in London at St Bartholomew's Hospital in 1792, moved to the University of Edinburgh Medical School i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress \sigma (force per unit area) and axial strain \varepsilon (proportional deformation) in the linear elastic region of a material and is determined using the formula: E = \frac Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa). Example: * Silly Putty (increasing pressure: length increases quickly, meaning tiny E) * Aluminum (increasing pressure: length increases slowly, meaning high E) Higher Young's modulus corresponds to greater (lengthwise) stiffness. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1754 Deaths
Events January–March * January 28 – Horace Walpole, in a letter to Horace Mann, coins the word ''serendipity''. * February 22 – Expecting an attack by Portuguese-speaking militias in the Viceroyalty of the Río de la Plata, the indigenous Guarani people residing in the Misiones Orientales stage an attack on a small Brazilian Portuguese settlement on the Rio Pardo in what is now the Brazilian state of Rio Grande do Sul. The attack by 300 Guarani soldiers from the missions at San Luis, San Lorenzo and San Juan Bautista is repelled with a loss of 30 Guarani and is the opening of the Guarani War * February 25 – Guatemalan Sergeant Major Melchor de Mencos y Varón departs the city of Santiago de los Caballeros de Guatemala with an infantry battalion to fight British pirates that are reportedly disembarking on the coasts of Petén (modern-day Belize), and sacking the nearby towns. * March 16 – Ten days after the death of British Prime Minister Henry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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