A skew generalized power series ring R[[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are...

Abstract: In this paper, we consider the skew circulant and skew left circulant matrices with the Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices are also discussed. We obtain the determ...

The generalization of the maximum-likelihood-like estimator for clock skew by Leng and Wu in the above paper is erroneous because the correlation of the noise components in the model is not taken into account in the derivation of the maximum likelihood estimator, its performance bound, and the optimal selection of the gap between two subtracting time stamps. This comment investigates the issue ...

Let k be a positive integer. A hypergraphH is k-partition-connected if for every partition P of V (H), there are at least k(|P |−1) hyperedges intersecting at least two classes of P . In this paper, we determine the minimum number of hyperedges in a hypergraph whose addition makes the resulting hypergraph k-partition-connected. We also characterize the hyperedges of a k-partition-connected hype...

Variation has an increasingly negative impact on key interconnect applications, including clock skew and signal line delay. Here we consider both random and systematic variation in interconnect and device parameters as technology scales from 180nm to 50nm. For the case considered, we show that (1) clock skew increases from about 15% to 30% of the clock cycle, and (2) modeling systematic variati...

We establish the existence of a nontrivial solution for systems with an arbitrary number of coupled Poisson equations with critical growth in punctured unbounded domains. The proof depends on a generalized linking theorem due to Krysewski and Szulkin, and on a concentration-compactness argument, proved by Frigon and the author. Applications to reaction-diffusion systems with skew gradient struc...

In this paper, skew cyclic and skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv=vu=0 are studied. We show that Gray image of a skew cyclic code of length n over R is a skew quasi-cyclic code of length 3n over F_q of index 3. Structural properties of skew cyclic and skew constacyclic over R are obtained. Further, gener...

Turbulent stress is the fundamental quantity in the filtered equation for large-scale velocity that reflects its interactions with small-scale velocity modes. We develop an expansion of the turbulent stress tensor into a double series of contributions from different scales of motion and different orders of space-derivatives of velocity, a Multi-Scale Gradient (MSG) expansion. We compare our met...