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Question: Suppose $$0 = - \Delta u+u~~\text{in}~U,$$
where $U$ is open connected bounded set and $u(x)$ is $C^2(U)$ and $C(\partial U)$. and that $max _{\partial U}$$u$ $>0$
a) Prove that $max _{\partial U}$$u$ = $max_{\bar U}$
b) THere does NOT exist $x_0$ $\in$ U such that $u(x_0)=max_{\bar U}$...
Projected area is the two
dimensional area measurement of a three-dimensional object by projecting its shape on to an arbitrary plane. This is often used in mechanical engineering and architectural engineering related fields, specifically hardness testing, axial stress, wind pressures, and terminal velocity.
The geometrical definition of a projected area is: "the rectilinear parallel projection of a surface of any shape onto a plane". This translates into the equation:
A
projected
=
∫...
The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, smallest enclosing circle problem) is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in n-dimensional space, the smallest bounding sphere problem, is to compute the smallest n-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857.The smallest-circle problem in the plane is an example of a...
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