The inverse problem for convex bodies

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The inverse moment problem for convex polytopes

We present a general and novel approach for the reconstruction of any convex d-dimensional polytope P , assuming knowledge of finitely many of its integral moments. In particular, we show that the vertices of an N-vertex convex polytope in R can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure of degree D), in d + 1 distinct directions in gener...

Nakajima’s Problem for General Convex Bodies

For a convex body K ⊂ Rn, the kth projection function of K assigns to any k-dimensional linear subspace of Rn the k-volume of the orthogonal projection of K to that subspace. Let K and K0 be convex bodies in Rn, let K0 be centrally symmetric and satisfy a weak regularity assumption. Let i, j ∈ N be such that 1 ≤ i < j ≤ n − 2 with (i, j) 6= (1, n−2). Assume that K and K0 have proportional ith p...

An Inverse Scattering Result for Several Convex Bodies

The use of inverse quadratic radial basis functions for the solution of an inverse heat problem

‎In this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎The method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...