GCD sums from Poisson integrals and systems of dilated functions

Upper bounds for GCD sums of the form (Formula Presented) are established, where (nk)1≤k≤N is any sequence of distinct positive integers and 0 1/2, a result that in turn settles two longstanding problems on the a.e. behavior of systems of dilated functions: the a.e. growth of sums of the form (Formula Presented)=1 f(nkx) and the a.e. convergence of (Formula Presented)=1 ckf(nkx) when f is 1-periodic and of bounded variation or in Lip1/2. © European Mathematical Society 2015

What does a strongly excited 't Hooft-Polyakov magnetic monopole do?

The time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield (BPS) magnetic monopoles in Minkowski spacetime is investigated by means of numerical simulations based on the technique of conformal compactification and on the use of hyperboloidal initial value problem. It is found that an initially static monopole does not radiate the entire energy of the exciting pulse toward future null infinity. Rather, a long-lasting quasi-stable `breathing state' develops in the central region and certain expanding shell structures -- built up by very high frequency oscillations -- are formed in the far away region.Comment: 4 pages, 6 figure

Hypertriglyceridaemia kezelese plazmaferezissel.

The authors present the case of a 38-year-old woman with severe hypertriglyceridemia-induced acute recurrent pancreatitis (triglyceride 16 761 mg/dl, 189.4 mmol/l). According to the knowledge of the authors, such a high triglyceride has not been previously reported in Hungarian and international scientific literature. The patient received conventional treatment (fluid replacement, analgesic, antibiotics, discontinuation of oral intake) and plasmapheresis too. After two sessions of plasmapheresis with one month interval the clinical and laboratory parameters greatly improved. Severe hypertriglyceridemia (triglyceride level more than 1000 mg/dl, approximately 11.3 mmol/l) is an independent risk factor for acute pancreatitis. Plasmapheresis seems to be safe and effective to rapidly decrease triglyceride levels and to remove the causative agent for pancreatitis in a patient with severe hypertriglyceridemia. Orv. Hetil., 2014, 155(30), 1203-1206