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

Raman and Infrared-Active Phonons in Hexagonal HoMnO3_3 Single Crystals: Magnetic Ordering Effects

Polarized Raman scattering and infrared reflection spectra of hexagonal HoMnO$_3$ single crystals in the temperature range 10-300 K are reported. Group-theoretical analysis is performed and scattering selection rules for the second order scattering processes are presented. Based on the results of lattice dynamics calculations, performed within the shell model, the observed lines in the spectra are assigned to definite lattice vibrations. The magnetic ordering of Mn ions, which occurs below T$_N$=76 K, is shown to effect both Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and, consequently, Mn exchange interaction.Comment: 8 pages, 6 figure

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

On metric-connection compatibility and the signature change of space-time

We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are require

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

CCD photometric search for peculiar stars in open clusters. VIII. King 21, NGC 3293, NGC 5999, NGC 6802, NGC 6830, Ruprecht 44, Ruprecht 115, and Ruprecht 120

We continue our survey for magnetic chemically peculiar (CP2) stars in galactic open clusters to shed more light on their origin and evolution. To study the group of CP2 stars, it is essential to find these objects in different galactic environments and at a wide range of evolutionary stages. The knowledge of open clusters ages and metallicities can help to find a correlation of these parameters with the (non-)presence of peculiarities which has to be taken into account in stellar evolution models. The intermediate band Delta a photometric system samples the depth of the 5200A flux depression by comparing the flux at the center with the adjacent regions with bandwidths of 110A to 230A. It is capable to detect magnetic CP2 and CP4 stars with high efficiency, but also the groups of (metal-weak) lambda Bootis, as well as classical Be/shell stars can be successfully investigated. In addition, it allows to determine the age, reddening and distance modulus with an appropriate accuracy by fitting isochrones. From the 1677 observed members of the eight open clusters, twenty five CP2 and one Ae stars were identified. Further nineteen deviating stars are designated as questionable due to several reasons. The estimated age, reddening and distance for the programme clusters were compared with published vales of the literature and discussed in this context. The current paper shows that CP2 stars are present continuously in very young (7Myr) to intermediate age (500Myr) open clusters at distances larger than 2kpc from the Sun

Deroofing - a method of choice in the treatment of suppurative perineal hidradenitis

Purpose: Suppurative hidradenitis is a chronic relapsing inflammatory disease that affects the apocrine sweat glands. Therefore, it is most often located in the axilla, groin and perianal area. Usually, people of working age affected. Perineal and perianal locations cover about 37% of the total morbidity rate and are more common in males. The objective of this study was to share our experience with the application of deroofing for the treatment of purulent perineal hidradenitis.Material and methods: This prospective interventional study covered 13 patients with suppurative fistulasing hidradenitis of perineum treated in Division of Coloproctology and Septic Surgery, Georgi Stranski University Hospital of Pleven for the period from 2008 till 2013.Results: The interval between the occurrence of disease and its surgical treatment was very long - from two to 36 years (average of 9,2 years). It resulted from the progression of the disease with enlarged soft tissue involvement. Sometimes, the disease was complicated by chroniosepsis. The average hospital stay was 13,5-day long. Operative wounds healed secondarily at an average of about 30 days. The patients were followedup for six months, one year and two years. Two patients with relapses on the sixth postoperative month were hospitalized again. The surgical intervention warranted good results.Conclusion: Treatment of suppurative hidradenitis of the perineum is complex, both in terms of local status and systematic violations resulting in chronic infection. There are numerous surgical techniques for treating this pathology. The advantages of deroofing are the following: minimal trauma to the patient, application by using local anesthesia at the early stage in order to minimize hospital stay, no need of special equipment, a lower recurrence rate than the other methods and formation of aesthetically acceptable scar