Motivated by applications in quantum information and quantum control, a new type of C-numerical range, the relative C-numerical range denoted W K (C, A), is introduced. It arises upon replacing the unitary group U (N) in the definition of the classical C-numerical range by any of its compact and connected subgroups K ⊂ U (N). The geometric properties of the relative C-numerical range are analys...

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

The drops are used to control the descents,  stabilize the bed level, and control the upstream water level in sloping channels with less slope than the ground slope. The current study presents a numerical analysis of hydraulic characteristics in the vertical drop using computational fluid dynamics. At first, the laboratory models were used for verification and choosing the best model of turbule...

The higher rank numerical range is useful for constructing quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its rank-k numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that the higher rank numeri...

We present two new k-dimensional data structures, called the PKD-tree and the PKD-tree, respectively. They are explored for indexing combined text and point data, and evaluated experimentally for orthogonal range search (for 2 ≤ k ≤ 100 and n up to 1,000,000) using synthetic data and real data. We compared the range search performance of the PKD-tree with the PKD-tree, the k-d tree, the Pyramid...

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its higher rank numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that ...