In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in form
d
s
2
=
g
a
b
(
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I would like to understand the first section of a paper titled: "More on Convolution of Riemannian Manifolds," by Bang-Yen Chen. Michigan State University.
http://emis.impa.br/EMIS/journals/BAG/vol.44/no.1/b44h1chn.pdf (first two pages).
The notion of convolution products is defined as follows:...
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The point is that
$$
-\frac{1}{\omega_0}\le \frac{\sin(2 \omega_0 T) \cos(2 \theta)}{\omega_0} \le \frac{1}{\omega_0},
$$
and this is true for all values of $T$. Therefore
$$
\lim_{T\rightarrow \infty} 2 T+\frac{\sin(2 \omega_0 T) \cos(2 \theta)}{\omega_0}=\lim_{T\rightarrow \infty} 2 T
$$
and
$...
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
Polynomial rings occur in many parts of mathematics, and the study of their properties was among the main motivations for the development of commutative algebra and ring theory. Polynomial rings and their ideals are fundamental in algebraic geometry. Many classes of rings, such as unique factorization domains...
