On a single-input-single-out (SISO) interference channel (IC), conventional non-cooperative strategies encourage players selfishly maximizing their transmit data rates, neglecting the deficit of performance caused by and to other players. In the case of proper complex Gaussian noise, the maximum entropy theorem shows that the best-response strategy is to transmit with proper signals (symmetric ...

For each unital $C^*$-algebra $A$, we denote $cel_{CU}(A)=\sup\{cel(u):u\in CU(A)\}$, where $cel(u)$ is the exponential length of $u$ and $CU(A)$ closure commutator subgroup $U_0(A)$. In this paper, prove that $cel_{CU}(A)=2\pi$ provided $A$ an $AH$ algebras with slow dimension growth whose real rank not zero. On other hand, $cel_{CU}(A)\leq 2\pi$ when algebra ideal property no (if further assu...

The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank amon...

In this paper we present new structural information about the multiplier algebra M(A) of a σ-unital purely infinite simple C∗-algebra A, by characterizing the positive elements A ∈ M(A) that are strict sums of projections belonging to A. If A 6∈ A and A itself is not a projection, then the necessary and sufficient condition for A to be a strict sum of projections belonging to A is that ‖A‖ > 1 ...

This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for characterizing nonlinear dynamical systems in an equation-free manner by decomposing the state of the system into low-rank terms whose Fourier components in ...