Let p be an odd prime. In 2008 E. Mortenson proved van Hamme's following conjecture: (p−1)/2 k=0 (4k + 1) −1/2 k 3 ≡ (−1) (p−1)/2 p (mod p 3).

This paper proposes an implementation of a Euler/Venn reasoning system using directed acyclic graphs and shows that this implementation is correct with respect to a modified Shin/Hammer mathematical model of Euler/Venn Reasoning. In proving its correctness it will also be shown that the proposed implementation preserves or inherits the soundness and completeness properties of the mathematical m...

QUESTION UNDER STUDY To investigate the aetiology and long-term clinical outcomes of patients diagnosed with digital ischemia. METHOD Data of 36 consecutive patients presenting with digital ischemia were collected in July 2000 to June 2001 from a vascular referral centre. Demographic data, aetiology, medication and treatment were abstracted from the medical records. Clinical outcomes were ass...

In this paper, the robust design with an uncertain model of a vibro-impact electro-mechanical system is done. The electro-mechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists...