Numerical range of a weighted shift with periodic weights

The numerical radius of a weighted shift operator with geometric weights

Let T be a weighted shift operator T on the Hilbert space 2(N) with geometric weights. Then the numerical range of T is a closed disk about the origin, and its numerical radius is determined in terms of the reciprocal of the minimum positive root of a hypergeometric function. This function is related to two Rogers-Ramanujan identities.

Entropy of Weighted Graphs with Randi'c Weights

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös,...

Mean Shift Algorithm with Heterogeneous Node Weights∗

The conventional mean shift algorithm has been known to be sensitive to selecting a bandwidth. We present a robust mean shift algorithm with heterogeneous node weights that come from a geometric structure of a given data set. Before running MS procedure, we reconstruct un-normalized weights (a rough surface of data points) from the Delaunay Triangulation. The un-normalized weights help MS to av...

Spatial Numerical Range of Operators on Weighted Hardy Spaces

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.