Second order perturbation analyses are presented of the order three superharmonic resonance in a Duffing oscillator, ü+δu˙+u3 = P cos ϯt and of the primary resonance in a Duffing oscillator with softening non-linearity, ü+δu˙-u3 = P cos ϯt.
There were self-deprecatory references to losing his parliamentary seat after 13 years, allusions to the Cheeky Girls and corruption in parliament, a duff anecdote about his name – almost an anagram of "I like to be MP", he told us – and a small section about the Daily Mail, which had quoted the event's promoter, Robert Meakin, on the likelihood of Opik being bottled off the stage.
Root, who is 141 not out overnight after the first day at Old Trafford, is two matches into his new position at No3 and revealed his dismissals in the first Test – a top edge when sweeping Yasir Shah in the first innings, before a duffed pull off the seamer Rahat Ali in the second – have prompted a rethink.
"The funding is in place for the club to operate normally until the sale is complete, which should be in July," said a Duff & Phelps spokesman.
Finally, we perform numerical simulations of an acoustic rectification device in which a Duffing oscillator is attached to the end of a tri-atomic mass spring chain.
As the first half draws to a close, City are leading 2-1 and banging on the door to add more — a Villa back-heel deep on the left-wing starts a gorgeous, flowing move that nearly results in a tap-in for Duff, and Duff curls a ball just outside Coe's far post.
At the Court of Session in Edinburgh, Lord Hodge approved a Duff and Phelps motion to hand over what remains of the old club to liquidators BDO.
Duff put in a lovely low cross from the left and Doyle, attempting a slinky back-hell, completely missed it.
Ryan's show-business career started when she landed a bit part in a Hilary Duff video (playing Marilyn Monroe) as a result of her first audition, while still living in Victorville.
