Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

Frames of reference in spaces with affine connections and metrics

A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to the vector field sub space, (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed. On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution. PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2

Mixing and Accretion in lambda Bootis Stars

Strong evidence for deep mixing has been uncovered for slowly rotating F, and A stars of the main sequence. As the accretion/diffusion model for the formation of lboo stars is heavily dependent on mixing in superficial regions, such deep mixing may have important repercussions on our understanding of these stars. It is shown that deep mixing at a level similar to that of FmAm stars increases the amount of matter that needs to be accreted by the stars with respect with the standard models by some three orders of magnitude. It is also shown that significantly larger accretion rates have to be maintained, as high as $10^{-11}$~M_\sun yr^{-1}, to prevent meridional circulation from canceling the effect of accretion. The existence of old ($\approx 1$~Gyr) is not a likely outcome of the present models for accretion/diffusion with or without deep mixing. It is argued that lboo stars are potentially very good diagnostics of mixing mechanisms in moderately fast rotators.Comment: To appear in Astrophysical Journal Letters. 4 pages, 2 fgure

Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. Its evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present first part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests. We show that the evolution of pure quantum-mechanical states can be described as a suitable linear transport along paths, called evolution transport, of the state sections in the Hilbert fibre bundle of states of a considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: new material, references, and comments are added. Minor style chages. Continuation of quan-ph/9803083. For continuation of the this series see http://www.inrne.bas.bg/mathmod/bozhome

Changes in the function of the anal sphincter complex and generated anal pressure at different anatomical levels after elastic ligature application in patients with anal fistula

Purpose: The purpose of the present study was to measure by means of especially developed apparatus the anal and intrarectal pressure before and after different operations for perianal fistulas as well as to correlate the degree of incontinence evaluated by Fecal Incontinence Severity Index (FISI) with changes in the measured pressures and type of operation used.Material and methods: The study covered 311 patients with perianal fistulas who were operated with several methods. Anal canal pressures at 5 different levels were measured by the especially developed apparatus at rest, squeezing and cough, before and after 6 months of operation. FISI form was used for incontinence detection.Results: Resting, squeezing and cough pressures were higher in men before and after operations. Average reduction of anal rest pressure by 10-15%, at contraction by 20-25% and at cough by 5-10% resulted in mild incontinence according to FISI score. Average reduction of anal rest pressure by 20-25%, at contraction by 30-40% and at cough by 20-25% correlated with postoperative moderate degree of incontinence according to FISI score. No severe incontinence was registered by FISI examination. Usage of the method of elastic ligation of perianal fistulas, i.e. the method of Hippocrates-Thoma Junescu caused the highest percentage of postoperative mild degree incontinence (15,9%) and moderate one (4,3%) by FISI. No patients presented with severe degree of incontinence.Conclusion: The method of anal sphincter tonometry demonstrated a significant reduction of anal pressure after surgery for anal fistulas. This objective decrease of anal sphincter tone correlated with the higher FISI score arguing of postoperative incontinence. The method of Hippocrates-Thoma-Junescu resulted in the highest rate of incontinence (around 20%) and anal pressure reduction

The 2003 eclipse of EE Cep is coming. A review of past eclipses

EE Cep is an eclipsing binary with a period of 5.6 years. The next eclipse will occur soon, in May-June 2003, and all available past eclipses were collected and briefly analysed. EE Cep shows very large changes of the shape and the depth of minima during different eclipses, however it is possible to single out some persistent features. The analysis suggests that the eclipsing body should be a long object surrounded by an extended semi-transparent envelope. As an explanation, a model of a precessing optically thick disc, inclined to the plane of the binary orbit, is invoked. The changes of its spatial orientation, which is defined by the inclination of the disc and the tilt, induced most probably by precession of the disc spin axis with a period of about 50 years, produce strange photometric behaviour of this star. The H_alpha emission, and possibly the NaI absorptions, show significant changes during several months outside of the eclipse phase.Comment: 7 pages, 7 figures, LaTeX2e, accepted by A&

Open lateral sphincterotomy - A method of choice in the treatment of chronic anal fissure. Indications and results

Aim: The key to the treatment of chronic anal fissures is the reduction of the abnormal values of anal resting pressure. The aim of the surgical treatment is to reduce the activity of the internal anal sphincter and to provide proper conditions for the fissure to cure, which can be achieved by internal sphincterotomy. In the modern surgical practice the internal sphincterotomy is performed away from the fissure, lateral of the last, using open or closed technique.Methods: In our study we performed open lateral internal sphincterotomy (OLST) of 82 patients with chronic anal fissure, compared to a control group of 231 patients, treated with different methods. Results: We didn`t register any recurrences in the sixth post-operative moth after OLST. 11% of patients with OLST were with registered incontinence after the sixth post-operative month compared with 4.4% in non-OLST patients. The data was statistically significant (p=0.032)Conclusion: Choosing an OLST as a method for treatment of chronic anal fissure requires careful selection of patients. It is not recommended for patients with a risk of incontinence like those with a previous birth trauma, age beyond 60 years, previous ano-rectal operations, neurological diseases and low values in anal resting pressure.Aim: The key to the treatment of chronic anal fissures is the reduction of the abnormal values of anal resting pressure. The aim of the surgical treatment is to reduce the activity of the internal anal sphincter and to provide proper conditions for the fissure to cure, which can be achieved by internal sphincterotomy. In the modern surgical practice the internal sphincterotomy is performed away from the fissure, lateral of the last, using open or closed technique.Methods: In our study we performed open lateral internal sphincterotomy (OLST) of 82 patients with chronic anal fissure, compared to a control group of 231 patients, treated with different methods. Results: We didn`t register any recurrences in the sixth post-operative moth after OLST. 11% of patients with OLST were with registered incontinence after the sixth post-operative month compared with 4.4% in non-OLST patients. The data was statistically significant (p=0.032)Conclusion: Choosing an OLST as a method for treatment of chronic anal fissure requires careful selection of patients. It is not recommended for patients with a risk of incontinence like those with a previous birth trauma, age beyond 60 years, previous ano-rectal operations, neurological diseases and low values in anal resting pressure