Let G be a finite simple graph and J(G) denote its vertex cover ideal in polynomial ring over field. The k-th symbolic power of is denoted by \(J(G)^{(k)}\). In this paper, we give criterion for ideals decomposable graphs to have the property that all their powers are not componentwise linear. Also, necessary sufficient condition on so \(J(G)^{(k)}\) linear some (equivalently, all) \(k \ge 2\) ...

Abstract Sharing analysis is used to statically discover data structures which may overlap in object-oriented programs. Using the abstract interpretation framework, we show that sharing greatly benefits from linearity information. A variable linear a program state when different field paths starting it always reach objects. We propose graph-based domain can represent aliasing, linearity, and in...

A new linearization technique for a CMOS high frequency mixer will be presented. The reduction of the total harmonic distortion coefficient is achieved by replacing the simple differential amplifier from the basic multiplier circuit with a cross-connection differential amplifier, with the advantage of canceling the third-order harmonic from the output signal expression. The circuit was implemen...

We propose a new general framework for the security of multivariate quadratic (MQ) schemes with respect to attacks that exploit the existence of linear subspaces. We adopt linearity measures that have been used traditionally to estimate the security of symmetric cryptographic primitives, namely the nonlinearity measure for vectorial functions introduced by Nyberg at Eurocrypt ’92, and the (s, t...