the influence of social conditions on literature is an issue that many critics and scholars confirm and prove it; as duality is one of the manifestations of the influence of social conditions on the poet. it means that whenever the ambitions and beliefs of poet opposes the social facts, the duality will manifests in his poetry. the reality that the contemporary poets live in, imposes strong con...

• The dual problem is always convex no matter if the primal problem is convex, i.e., g is always concave. • The primal and dual optimal values, f∗ and g∗, always satisfy weak duality: f∗ ≥ g∗. • Slater’s condition: for convex primal, if there is an x such that h1(x) < 0, · · · , hm(x) < 0 and l1(x) = 0, · · · , lr(x) = 0 (12.5) then strong duality holds: f∗ = g∗. Note that the condition can be ...

Loosely speaking, a stationary time series is one whose statistical properties remain constant over time, whereas the statistical properties of locally stationary (LS) time series change slowly over time. As a consequence, LS series can appear stationary when examined close up, but appear nonstationary when examined on a larger scale. Priestley (1983) and Nason and von Sachs (1999) review local...