منابع مشابه
On Hermitian Operators over the Cayley Algebra.
With the aid of equations (72) and (76) we can determine the horizontal displacement q(t), using its operational representation given in equation (65). 4. Summary.-An exact solution is given for the motion of the surface of a uniform elastic half-space produced by a point pressure pulse situated at a depth H below the surface. The time variation of the pressure pulse is assumed to be given by t...
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Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...
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The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.
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Let D be a positive definite quaternion algebra over a totally real number field K, F (X, Y ) a hermitian form in 2N variables over D, and Z a right D-vector space which is isotropic with respect to F . We prove the existence of a small-height basis for Z over D, such that F (X, X) vanishes at each of the basis vectors. This constitutes a non-commutative analogue of a theorem of Vaaler [19], an...
متن کاملOn the Perimeter of an Ellipse
Computing accurate approximations to the perimeter of an ellipse is a favourite problem of mathematicians, attracting luminaries such as Ramanujan [1, 2, 3]. As is well known, the perimeter, , of an ellipse with semimajor axis a and semiminor axis b can be expressed exactly as a complete elliptic integral of the second kind, which can also be written as a Gaussian hypergeometric function, (1) ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2012
ISSN: 0019-2082
DOI: 10.1215/ijm/1380287468