A well–known theorem of Schoenberg states that if f(z) generates a PFr sequence then 1/f(−z) generates a PFr sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if f(z) generates a PF sequence then 1/f(−z) generates a PF sequence.

We consider an asset-liability management (ALM) problem for a defined benefit pension fund (PF). The PF manager is assumed to follow a maximal fund valuation problem facing an extended set of risk factors:  due to the longevity of the    PF members, the inflation affecting salaries in real terms and future incomes, interest rates and market factors affecting jointly the PF liability and asset p...

The impact of phenylphthalamic acid (PPA) rates including 0 (PPA0), 1000 (PPA1000), 2000 (PPA2000) or 3000 (PPA3000) mg L-1 and perfect fertilizer rates including 0 (PF0), 100 (PF100), 200 (PF200) and 300 (PF300) mg L-1 was studied on vegetative and reproductive growth of ornamental pep...

For a semigroup S the finitary power semigroup of S, denoted Pf (S), consists of all finite subsets of S under the usual multiplication. The main result of this paper asserts that Pf (G) is not finitely generated for any infinite group G.

Palynological and Palynofacies analysis combined with sedimentological studies have been performed on Dalichai Formation, northeast of Semnan, in order to define its paleoenviromental interpretation. Based on petrographic studies of organic matter, three palynofacies types were recognized as PF-1, PF-2, and PF-3. PF-1 is a characteristic of proximal shelf settings or basin. This palynofacies in...

The study aimed to uncover the risk factors for the new defined pancreatic fistula (PF) and clinical related PF (CR-PF) after pancreaticoduodenectomy (PD) surgery and to evaluate the medico-economic effect of patients. A total of 412 patients were classified into two groups according to different criteria, PF and NOPF according to PF occurrence: CR-PF (grades B and C) and NOCR-PF (grade A) base...

Patellofemoral (PF) osteoarthritis (OA) is a somewhat predominant illness, affecting up to 24% of women and 11% ofmen over the age of 55 years who suffer from symptomatic knee OA. The purposes of this narrative overview are tosummarize the present situation of patellofemoral arthroplasty (PFA) in the treatment of solitary PF-OA, and to givean account of the clinical results of...

Low toxicity, environmentally friendly and sustainable bio-based phenol–formaldehyde (PF) resins are the primary factors health goals that researchers need to consider when modifying PF resins. Two novel biomass-modified were synthesized using two flavonoid phenols of daidzein naringenin with rigid backbone structures. The results show compared ordinary PF, introduction during synthesis N-PF D-...