On Arf rings

Ankara : The Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, c1994.Thesis (Master's) -- Bilkent University, 1994.Includes bibliographical references leaves 63-64In this thesis, we worked with curves which have cusp type singularities. We described the Arf theory, which solves the problem of understanding and finding the multiplicity sequence of a curve branch algebraically. We proposed an algorithm for finding the Arf characters of a given curve branch. We also faced the problem of Frobenius, and proposed an algorithm for the solution of problem of Frobenius in the most general case.Arslan, Sefa FezaM.S

Monomial curves and the Cohen-Macaulayness of their tangent cones

Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 1999.Thesis (Ph. D.) -- Bilkent University, 1999.Includes bibliographical references leaves 48-50.In this thesis, we show that in affine /-space with / > 4, there are monomial curves with arbitrarily large minimal number of generators of the tangent cone and still having Cohen-Macaulay tangent cone. In order to prove this result, we give complete descriptions of the defining ideals of infinitely many families of monomial curves. We determine the tangent cones of these families of curves and check the Cohen-Macaulayness of their tangent cones by using Grobner theory. Also, we compute the Hilbert functions of these families of monomial curves. Finally, we make some genus computations by using the Hilbert polynomials for complete intersections in projective case and by using Riemann-Hurwitz formula for complete intersection curves of superelliptic type.Arslan, Sefa FezaPh.D

Hilbert functions of Gorenstein monomial curves

It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their de. ning ideals in the non-complete intersection case. In order to obtain this result, we determine the generators of their tangent cones explicitly by using standard basis computations under these arithmetic assumptions and show that the tangent cones are Cohen-Macaulay. In the complete intersection case, by characterizing certain families of complete intersection numerical semigroups, we give an inductive method to obtain large families of complete intersection local rings with arbitrary embedding dimension having non- decreasing Hilbert functions

Cebir II

Bu lisans dersi, Cebir I dersinin devamıdır. Konular grup temsilleri, halkalar, idealler, cisimler, polinom halkaları, modüller, çarpanlara ayırma, kuadratik sayı cisimlerindeki tamsayılar, cisim genişlemeleri ve Galois teorisini içerir.Bu ders TÜBA Açıkders Malzemeleri Projesi kapsamında hazırlanmıştır ve TÜBA Ulusal Açıkders Malzemeleri Portalinde (http://www.acikders.org.tr) de yayınlanmaktadır

Monomial curve families supporting Rossi's conjecture

In this article, we give a constructive method to form infinitely many families of monomial curves in affine 4-space with corresponding Gorenstein local rings in embedding dimension 4 supporting Rossi's conjecture. Starting with any monomial curve in affine 2-space, we obtain large families of Gorenstein local rings with embedding dimension 4, having non-decreasing Hilbert functions, although their associated graded rings are not Cohen-Macaulay

GLUING AND HILBERT FUNCTIONS OF MONOMIAL CURVES

In this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique for constructing large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has a non-decreasing Hilbert function

Deceased-donor transplantation activities in Turkey.

Int Soc Organ Donat & Procuremen

Deceased-donor transplantation activities at Baskent University.

Int Soc Organ Donat & Procuremen

Can we predict patients that will not benefit from invasive mechanical ventilation? A novel scoring system in intensive care: the IMV mortality prediction score (IMPRES)

KUCUK, Ahmet Oguzhan/0000-0002-6993-0519; Kirakli, Cenk/0000-0001-6013-7330; KUCUK, Mehtap PEHLIVANLAR/0000-0003-2247-4074; Aksoy, Iskender/0000-0002-4426-3342WOS: 000504051300010PubMed: 31655511Background/aim: The present study aimed to define the clinical and laboratory criteria for predicting patients that will not benefit from invasive mechanical ventilation (IMV) treatment and determine the prediction of mortality and prognosis of these critical ill patients. Materials and methods: The study was designed as an observational, multicenter, prospective, and cross-sectional clinical study. It was conducted by 75 researchers at 41 centers in intensive care units (ICUs) located in various geographical areas of Turkey. It included a total of 1463 ICU patients who were receiving invasive mechanical ventilation (IMV) treatment. A total of 158 parameters were examined via logistic regression analysis to identify independent risk factors for mortality; using these data, the IMV Mortality Prediction Score (IMPRES) scoring system was developed. Results: The following cut-off scores were used to indicate mortality risk: 8, very high risk. There was a 26.8% mortality rate among the 254 patients who had a total IMPRES score of lower than 2. The mortality rate was 93.3% for patients with total 1M PRES scores of greater than 8 (P < 0.001). Conclusion: The present study included a large number of patients from various geographical areas of the country who were admitted to various types of ICUs, had diverse diagnoses and comorbidities, were intubated with various indications in either urgent or elective settings, and were followed by physicians from various specialties. Therefore, our data are more general and can be applied to a broader population. This study devised a new scoring system for decision-making for critically ill patients as to whether they need to be intubated or not and presents a rapid and accurate prediction of mortality and prognosis prior to ICU admission using simple clinical data