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

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

Mode identification in the high-amplitude {\delta} Scuti star V2367 Cyg

We report on a multi-site photometric campaign on the high-amplitude $\delta$ Scuti star V2367 Cyg in order to determine the pulsation modes. We also used high-dispersion spectroscopy to estimate the stellar parameters and projected rotational velocity. Time series multicolour photometry was obtained during a 98-d interval from five different sites. These data were used together with model atmospheres and non-adiabatic pulsation models to identify the spherical harmonic degree of the three independent frequencies of highest amplitude as well as the first two harmonics of the dominant mode. This was accomplished by matching the observed relative light amplitudes and phases in different wavebands with those computed by the models. In general, our results support the assumed mode identifications in a previous analysis of Kepler data.Comment: 9 pages, 5 figures, 4 tables. Accepted for publication in MNRA