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Therefore, for the certain class of solutions of generalized GPE (= for the true one-dimensional condensate and = while using the three dimensional equation in one dimension), two equations are one. Furthermore, taking the λ = 3 {\displaystyle \lambda =3} case with the minus sign and the ϕ {\displaystyle \phi } real, one obtains an attractive ...
The unsteady convection–diffusion problem is considered, at first the known temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection diffusion equation an equation is obtained from the differentiation of this equation.
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
The development of analytical geometry and rigorous integral calculus in the 17th-19th centuries subsumed the method of exhaustion so that it is no longer explicitly used to solve problems. An important alternative approach was Cavalieri's principle , also termed the method of indivisibles which eventually evolved into the infinitesimal ...
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function ( ) = > . where α > 0 is a shape parameter.
The optimization problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. [3] As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph. Every maximum independent set also is maximal, but the converse implication does not necessarily hold.
The extension of the problem to higher dimensions (that is, for -dimensional surfaces in -dimensional space) turns out to be much more difficult to study.Moreover, while the solutions to the original problem are always regular, it turns out that the solutions to the extended problem may have singularities if .
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