Joint uncertainty decoding has recently achieved promising results by using front-end uncertainty in the back-end in a mathematically consistent framework. One drawback of the method is that it relies on stereo-data or numerical algorithms, such as DPMC, which have high computational complexity and are difficult to deploy in real applications. We propose a Vector Taylor Series (VTS) approach to...

Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced. Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described. As an application, convexity of joint numerical ranges of 2×2 hermitian matrices is characterized. Another application involves existence of...

The q-numerical range (0 ≤ q ≤ 1) of an n × n matrix polynomial P (λ) = Amλ m + · · ·+ A1λ + A0 is defined by Wq(P ) = {λ ∈ C : y∗P (λ)x = 0, x, y ∈ C, x∗x = y∗y = 1, y∗x = q}. In this paper, we investigate the boundary and the shape of Wq(P ), using the notion of local dimension. We also obtain that the q-numerical range of first order matrix polynomials is always simply connected. Moreover, t...

Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced. Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described. As an application, convexity of joint numerical ranges of 2×2 hermitian matrices is characterized. Another application involves existence of...

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for > 0, the notion of Birkhoff-James approximate orthogonality sets for −higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural general...

For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint higher rank numerical ranges are obtained and their implications to quantum computing are discussed. It is shown that if the dimension of the underlying Hilbert ...

Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that and transform have the same joint essential spectrum. Further, it shown spectrum contained in numerical range

background:  the glenohumeral joint becomes dislocated more than any other major joint because it maintains a wide range of motion and its stability is inherently weak. the most common complication following acute initial shoulder dislocation is recurrent dislocation or chronic instability. imbalance of strength and range of motion in individuals with anterior dislocation can be a contributing ...