We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...

We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...

In this paper, we study the linear structure of sets A ⊂ Fn2 with doubling constant σ(A) < 2, where σ(A) := |A+A| |A| . In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with |V | ≤ |A|. Finally, we classify all binary sets with small doubling constant.

We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν, where the Borel measure ν satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When ν = f dx, this condition, which we call D , admits the possibility of f vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when 0 < ...

OBJECTIVE To compare the effects of deep breathing exercises (DBE) and the flow-oriented incentive spirometry (IS) in patients undergone coronary artery bypass grafting (CABG) through the following variables: forced vital capacity - FVC, forced expiratory volume in 1 second - FEV(1), maximal respiratory pressures and oxygen saturation. METHODS Thirty six patients in CABG postoperative period ...

â  upper gastrointestinal tract (gastroduodenal) crohn’s disease (cd) is an uncommon condition, occurring in about 1-5% of all cd cases. our case was an extremely rare manifestation of cd, who presented with distal duodenal obstruction. as preoperative diagnosis was not estabâ­lished he underwent segmental resection and end-to-end anastomosis. postoperative small bowel fistulae were not obser...

PURPOSE To evaluate changes occurring in central corneal thickness (CCT) immediately after uneventful cataract surgery. METHODS Thirteen consecutive patients who had uneventful phacoemulsification surgery by the same experienced surgeon were prospectively evaluated for CCT measurements 1 hour preoperatively and 1 hour, 1 day, and 1 week postoperatively. The unoperated eye also had CCT measure...

The aim of our study was to investigate the main characteristics peripheral blood NKT cell phenotype in patients with disseminated purulent peritonitis (DPP) dynamics postoperative period, depending on disease outcome. Fifty-two acute surgical diseases and injuries abdominal organs complicated by DPP, 68 healthy individuals control group, were examined. Blood sampling performed before surgery (...

UNLABELLED The introduction of markers which help in the identification of patients prone to suffer from postoperative complications enables to recognize them more easily and thus, treat them more effectively. THE AIM OF THE STUDY was to evaluate complete blood count indicators, as well as preoperative results obtained on the basis of the POSSUM and P-POSSUM scoring systems, considering the pre...

Mesenchymal hamartoma and hepatoblastoma are common causes of hepatic masses in pediatric population; they have similar radiologic and pathologic features. Herein, we present a case of mesenchymal hamartoma that was preoperatively diagnosed as hepatoblastoma. The mass was completely resected instead of being treated with preoperative chemotherapy. Postoperative pathological evaluation revealed ...