Our choice of normalization factor ensures that F is unitary: F† ◦F = I , where I is the identity transformation, and F† is the Hermitian conjugate of F, that is, (F†) jk = Fk j . Also recall that the exponential of a matrix M is given by the infinite series (M) . = ∑∞ p=0(1/p!)M (provided it converges). Thus a complex-linear map f : Cn→Cn is a logarithm for F if F = exp ( f ), and we write f =...

We consider the complexity of the emptiness problem for various classes of graph languages deened by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for connuent and boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, NL-complete for d...

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead ...

The single-pushout approach to graph transformation interprets a double-pushout transformation rule of the classical algebraic approach which consists of two rotul graph morphisms as a single particll morphism from the left-to the right-hand side. The notion of a double-pushout diagram for the transformation process can then be substituted by a single-pushout diagram in an appropriate category ...

We characterize the pairs of partial homomorphisms of total Σ-algebras that have a pushout in the corresponding category, for an arbitrary signature Σ. This characterization provides the application condition for the single-pushout approach to the transformation of total algebras.

Dickenstein, A., N. Fitchas, M. Giusti and C. Sessa, The membership problem for unmixed polynomial ideals is solvable in single exponential time, Discrete Applied Mathematics 33 (1991) 73-94. Deciding membership for polynomial ideals represents a classical problem of computational commutative algebra which is exponential space hard. This means that the usual al membership problem which are base...