Index of elliptic operators for a diffeomorphism

We develop elliptic theory of operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and of the symbol of the operator. The symbol in this situation is an element of a certain crossed product. We express the index as the pairing of the class in K-theory defined by the symbol and the Todd class in periodic cyclic cohomology of the crossed product.Comment: 37 page

Discrete breathers assist energy transfer to ac driven nonlinear chains

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $\omega$ within the linear phonon band. The results for the on-site potentials with hard and soft nonlinearity types are compared. For the hard-type nonlinearity, it is shown that when the driving frequency is close to (far from) the {\em upper} edge of the phonon band, the power of the energy source normalized to $A^2$ increases (decreases) with increasing $A$. In contrast, for the soft-type nonlinearity, the normalized power of the energy source increases (decreases) with increasing $A$ when the driving frequency is close to (far from) the {\em lower} edge of the phonon band. Our further demonstrations indicate that, in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasi-periodically emitting moving DBs in the regime with driving frequency close to the DBs frequency, that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.Comment: 11 pages, 13 figure

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande

Classical approach in duodenopancreatectomy - the key to success of a controversial intervention

Secția IV Chirurgie, Secția Radiologie, Secția Gastoenterologie, Spital ”Sf. Spiridon”, U.M.F. “Grigore T. Popa”, Iași, România, Al XIII-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” și al III-lea Congres al Societății de Endoscopie, Chirurgie miniminvazivă și Ultrasonografie ”V.M.Guțu” din Republica MoldovaIntroducere: Duodenopancreatectomia cefalică (DPC) este considerată tratamentul standard pentru tumorile periampulare. În pofida evoluției în chirurgia pancreatică, morbiditatea postoperatorie după DPC rămâne crescută. În timp ce rata mortalității asociate intervenției chirurgicale a scăzut la mai puțin de 4%, morbiditatea postoperatorie se menține la mai mult de 50%, datorate în special anastomozei pancreaticojejunale, principala vulnerabilitate a chirurgiei pancreatice. Material și metode: Autorii prezintă un studiu pe 5 ani, între ianuarie 2014 și aprilie 2019, pe un lot de 17 pacienți la care s-a practicat DPC cu reconstrucție clasică tip Whipple Child, cu 2 variante de anastomoză pancretico-jejunală. Media de vârstă a fost de 58,5. Rezultate: Mortalitatea imediat postoperatorie în lotul studiat a fost de 0%, iar morbiditatea a fost reprezentată de 1 caz de fistulă pancreatică și 2 cazuri de hemoragii postoperatorii. Supraviețuirea la 1 an a fost de 64,7%, 5 pacienți fiind pierduți din supraveghere și 1 deces. Concluzii: Fistula pancreatică, prin complicațiile cu pericol vital ca de exemplu hemoargia și peritonita, este principala cauză de morbiditate și mortalitate după duodenopancreatectomie cefalică. Factorii care contribuie la această complicație sunt reprezentați de textura moale a țesutului pancratic și de diametrul subțire al ductului pancreatic.Introduction: Pancreaticoduodenectomy (PD) is considered the standard treatment for periampullary tumors. Despite progresses in pancreatic surgery, the postoperative morbidity after PD remains high. While the operation-associated mortality rate of pancreatic surgery has decreased to less than 4%, the postoperative morbidity rate is reported to be as high as 50%, largely due to the pancreaticojejunal anastomosis, the major vulnerability of pancreatic surgery. Material and methods: The authors present a study between January 2014 and April 2019, on a series of 17 patients with PD with classical reconstruction type Whipple Child, with 2 types of pancreaticojejunal anatomosis. The median age was 58,5. Results: Postoperative mortality in the study was 0%, and morbidity was 1 case of pancreatic fistula and 2 postoperative bleeding. The survival at 1 year was about 64,7%, 5 patients were lost under surveillance and one death. Conclusions: Pancreatic fistula, with life-threatening complications, such as postoperative hemorrhage and peritonitis, is the most important cause of morbidity and mortality in PD. Factors contributing to this complication are: soft pancreatic tissue texture and small pancreatic duct diameter

Penilaian Kinerja Keuangan Koperasi di Kabupaten Pelalawan

This paper describe development and financial performance of cooperative in District Pelalawan among 2007 - 2008. Studies on primary and secondary cooperative in 12 sub-districts. Method in this stady use performance measuring of productivity, efficiency, growth, liquidity, and solvability of cooperative. Productivity of cooperative in Pelalawan was highly but efficiency still low. Profit and income were highly, even liquidity of cooperative very high, and solvability was good