in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily exte...

Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixedjump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by i...

We propose a simple inter-symbol interference (ISI) and inter-block interference (IBI) cancellation scheme for single carrier block transmission with cyclic prefix (SCCP) systems with insufficient guard interval (GI). In the SC-CP system, the equalization and demodulation processing is conducted in a block-by-block manner, therefore, the IBI can be reduced by using previously detected data sign...

The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium voltage distribution systems. Inherent balance submodule (SM) capacitor voltages is considered as an ideal property which avoids complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This paper extends the inherent concept previously shown square-wave modulati...

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The n 2 th column of our circulant preconditioner Sn is equal to the n 2 th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be deened as (S n Sn)...

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

A k x k matrix A = [aU lover a field F is called circulant if aij = a (j-i) mod k' A [2k ,k l linear code over F = GF (q) is called double-circulant if it is generated by a matrix of the fonn [I A l, where A is a circulant matrix. In this work we ftrst employ the Fourier transform techJ nique to analyze and construct se:veral families of double-circulant codes. The minimum distance of the resul...