correction has been developed by Shen et al. [ 9 , 10 ]. Besides, the non-linearization of the chord and twist angle of the BEM theory poses problems in the manufacturing of the wind turbine blade. Several researchers have worked on the linearization of the
 Arens , R . Operational calculus of linear relations . Pacific J. Math . 11 , 1 ( 1961 ), 9 – 23 .  Kato , T . Trotter’s product formula for an arbitrary pair of self-adjoint contraction semigroups . In Topics in Functional
REFERENCES  Alvarez , T . On regular linear relations . Acta. Math. Sini. (English Ser.) 28 , 2 , ( 2012 ), 183 – 194 .  Bouaniza , H . and Mnif , M . On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation
model as an observer in anti-sway control of cranes, but it may leads to inaccuracy in state space variables. In this paper nonlinear and linear dynamical models of an overhead crane with chains will be formulated and analyzed. In addition to the payload
the type of air distributors and their geometric shapes, the initial velocities and temperatures of the jet, as well as on the interaction with natural convection and exhaust air flows. An effective air distributor is a linear diffuser - an ordinary
In this paper, we argue for the existence of two local domains (phases, cf. Chomsky 2001; 2009; Legate 2003, among others) inside the DP: the n*-phase, parallel to the vP (as in Svenonius 2004), and the d*-phase, parallel to the CP. Two acknowledged phasal properties are discussed. (i) The n*/d*-phases define their own peripheries: peripheries are essentially modal-quantificational spaces, as shown by the decomposition of Topic—Focus features recently proposed (Butler 2004; McNay 2005; 2006). (ii) Phases are assumed to be domains of linearization: after (internal or external) merge, syntactic objects are hierarchical, but not linear, so phases must be linearized before they are sent to PF. The distribution and interpretation of DP-internal adjectives is taken to be indicative of these two domains.
We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.