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Alembert Winthrop Brayton , also known as d'Alembert's test, a test for the convergence of a series
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Alembert and its variants may refer to: People: *Jean le Rond d'Alembert (1717–1783), French mathematician, mechanician, physicist, philosopher, and music theorist * Sandy D'Alemberte (1933–2019), American lawyer and politician Places: * D'Alembert (crater), a lunar impact crater Mathematics and Physics: *d'Alembert's formula, a mathematical formula *d'Alembert's paradox, a statement concerning inviscid flow *d'Alembert's principle, a statement of the fundamental classical laws of motion *d'Alembert–Euler condition, a mathematical and physical condition *D'Alembert operator, an operator of the Einstein equation *Ratio test In mathematics, the ratio test is a test (or "criterion") for the convergence of a series :\sum_^\infty a_n, where each term is a real or complex number and is nonzero when is large. The test was first published by Jean le Rond d'Alembert a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Le Rond D'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie''. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French. Early years Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau, with who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sandy D'Alemberte
Talbot "Sandy" D'Alemberte (June 1, 1933 – May 20, 2019) was an American lawyer, professor, politician, educational administrator, president of the American Bar Association, and president of Florida State University (FSU), from 1994 to 2003. Early life Born in Tallahassee, Florida, D'Alemberte was educated in public schools in Tallahassee and Chattahoochee, Florida. In 1955, he earned his Bachelor of Arts degree in political science with honors from the University of the South in Sewanee, Tennessee and also attended summer school at Florida State University and the University of Virginia. After military service as a lieutenant in the United States Navy Reserve, D'Alemberte studied on a Rotary Foundation fellowship at the London School of Economics. In 1962, he received his juris doctor with honors from the University of Florida where he was named to the Order of the Coif, served as president of the Student Bar Association, was captain of the moot court team, served as articles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert (crater)
d'Alembert is a large lunar impact crater located in the northern hemisphere on the far side of the Moon, to the northeast of the somewhat smaller walled plain Campbell. Astride the southwest rim of d'Alembert is Slipher. To the north is the crater Yamamoto, and to the south-southwest lies Langevin. This walled plain has the same diameter as Clavius on the near side, making it one of the largest such formations on the Moon. As with many lunar walled plains of comparable dimensions, the outer rim of this formation has been worn and battered by subsequent impacts. Besides Slipher, the most notable of these craters is d'Alembert Z intruding into the northern rim. There is also a small crater on the northwest inner wall that has a wide cleft in its eastern side, and a smaller crater along the southeastern inner wall. As eroded as the rim may be, its form can still be readily discerned as a roughly circular ridge line in the lunar terrain. The interior floor of d'Alembert is a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert's Formula
In mathematics, and specifically partial differential equations (PDEs), d'Alembert's formula is the general solution to the one-dimensional wave equation u_(x,t) = c^2 u_(x,t) (where subscript indices indicate partial differentiation, using the d'Alembert operator, the PDE becomes: \Box u = 0). The solution depends on the initial conditions at t = 0: u(x, 0) and u_t(x, 0). It consists of separate terms for the initial conditions u(x,0) and u_t(x,0): u(x,t) = \frac\left[u(x-ct, 0) + u(x+ct, 0)\right] + \frac \int_^ u_t(\xi, 0) \, d\xi. It is named after the mathematician Jean le Rond d'Alembert, who derived it in 1747 as a solution to the problem of a String vibration, vibrating string. Details The method of characteristics, characteristics of the PDE are x \pm ct = \mathrm (where \pm sign states the two solutions to quadratic equation), so we can use the change of variables \mu = x + ct (for the positive solution) and \eta = x-ct (for the negative solution) to transform the PD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert's Paradox
In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid.Grimberg, Pauls & Frisch (2008). Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox. D’Alembert, working on a 1749 Prize Problem of the Berlin Academy on flow drag, concluded: ''"It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers .e. mathematicians - the two terms were used interchangeably at that timeto e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert's Principle
D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert. D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing ''forces of inertia'' which, when added to the applied forces in a system, result in ''dynamic equilibrium''. The principle does not apply for irreversible displacements, such as sliding friction, and more general specification of the irreversibility is required. D'Alembert's principle is more general than Hamilton's principle as it is not restricted to holonomic constraints that depend only on coordinates and time but not on velocities. Statement of the principle The principle states that the sum of the differences between the forces acting on a system of massive particles and the time derivatives of the momenta of the system itself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert–Euler Condition
In mathematics and physics, especially the study of mechanics and fluid dynamics, the d'Alembert-Euler condition is a requirement that the streaklines of a flow are irrotational. Let x = x(X,''t'') be the coordinates of the point x into which X is carried at time ''t'' by a (fluid) flow. Let \ddot=\frac be the second material derivative of x. Then the d'Alembert-Euler condition is: :\mathrm\ \mathbf=\mathbf. \, The d'Alembert-Euler condition is named for Jean le Rond d'Alembert and Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ... who independently first described its use in the mid-18th century. It is not to be confused with the Cauchy–Riemann conditions. References * See sections 45–48.d'Alembert–Euler conditionson the Springer Encyclopedi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert Operator
In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: \Box), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (''cf''. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates , it has the form : \begin \Box & = \partial^\mu \partial_\mu = \eta^ \partial_\nu \partial_\mu = \frac \frac - \frac - \frac - \frac \\ & = \frac - \nabla^2 = \frac - \Delta ~~. \end Here \nabla^2 := \Delta is the 3-dimensional Laplacian and is the inverse Minkowski metric with :\eta_ = 1, \eta_ = \eta_ = \eta_ = -1, \eta_ = 0 for \mu \neq \nu. Note that the and summation indices range from 0 to 3: see Einstein notation. We have assumed units such that the speed of light = 1. (Some authors alternatively use the negative metric signature of , with \eta_ = -1,\; \eta_ = \eta_ = \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
