Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

A discrete slug population model determined by egg production

Slugs are significant pests in agriculture (as well as a nuisance to gardeners), and it is therefore important to understand their population dynamics for the construction of efficient and effective control measures. Differential equation models of slug populations require the inclusion of large (variable) temporal delays, and strong seasonal forcing results in a non-autonomous system. This renders such models open to only a limited amount of rigorous analysis. In this paper, we derive a novel batch model based purely upon the quantity of eggs produced at different times of the year. This model is open to considerable reduction; from the resulting two variable discrete-time system it is possible to reconstruct the dynamics of the full population across the year and give conditions for extinction or global stability and persistence. Furthermore, the steady state temporal population distribution displays qualitatively different behavior with only small changes in the survival probability of slugs. The model demonstrates how small variations in the favorability of different years may result in widely different slug population fluctuations between consecutive years, and is in good agreement with field data

Clinico-diagnostic peculiarities of dysplastic coxarthrosis of III-IV degree

CIinicodiagnostic researches included. 73 patients with dysplastic coxarthrosis who were examined and treated in orthopedic ward of Scientific Center of Reconstructive and. Restorative Surgery SB RAMS during 2001-2010 years. The aim. of the research is to specify clinic-radiologic criteria of hip joint with dysplastic changes at the arthrosis of III-IV degree. The diagnosis was set on the basis of clinicodiagnostic criteria. The main signs that characterize dysplastic joint were: anteversion of femoral neck; deflection of acetabulum anterior from sagittal plane; disorder of center of the head in horizontal plane; change of cervical-diaphyseal angle and. the angulation of acetabulum (more than 60°). Acetabulum becomes shallow and. head's embedding into it is Iess than 1/3 (1/2 as a norm). Main clinical manifestations of all examined patients were bending-adduction and rotation contractures of hip joints, shortening of extremities concerned with pathoIogic process, stabIe pain syndrome, gross Iimping with disorder of support function of extremity and Iocomotor act of waIking. In aII 73 patients we reveaIed. different disorders of anatomic interreIations of components of hip joint that are typicaI for grave forms of dyspIastic coxarthrosis. Ensuring of stabiIity of an impIant is extremeIy important at totaI hip joint repIacement. Prediction of measures of postoperative compIications prevention that allow to determine right tactics of operative treatment is the first to reaIize. If the indices of dyspIasia (ratio between thickness of acetabuIum's bottom and its depth) at dyspIastic coxarthrosis of III-IV degree is Iess than 0,6, it's possibIe to predict appearance of instabiIity of hip component of an impIant. VaIues of these indices can be used for forming impIant bed at the pIacing of impIant cup without additionaI ways of fixation

Staining method for coronary arteries

Detection of elastic and collagen fibers in the same histological section to determine their relationships and quantification is important for connective tissue investigations. The aim of the study was to assess the possibility of differentiated staining of elastic and collagen fibers with resorcin-fuchsin and fast green FCF in the same histological section and compare the result of this method with the results of the classical methods of staining connective tissue, performed according to standard protocols. Material and methods. We studied adult human hearts, obtained from patients who died from non-cardiac causes. We cut tissue sections from the anterior interventricular artery and the underlying myocardium. After formalin fixation, standard processing and embedding in paraffin of the material, histological sections were made. Histological sections were deparaffinized and immersed resorcin-fuchsin for 15 minutes, then stained with Weigert’s iron hematoxylin for 2 minutes, then for 2 minutes were applied to the preparation surface 0.1% solution of fast green FCF mixed with a saturated solution of picric acid immediately before staining in a ratio of 1:10, the histological sections were dehydrated, cleared and mounted in permanent mounting medium. Results. Elastic fibers were dyed in dark blue, and collagen fibers in different shades of green, which made it possible to differentiate them on the basis of color differences in one histological section. Conclusion. We have developed and tested the method of staining, which provides the possibility of simultaneous detection of elastic and collagen fibers with successive staining with solutions of resorcin-fuchsin and fast green FCF on one histological section