Annihilators of principal ideals in the exterior algebra

Koç, Cemal (Dogus Author) -- Esin, Songül (Dogus Author)In this paper we describe annihilators of principal ideals of exterior algebras. For odd elements we establish formulae for dimensions of their principal ideals and their annihilators. For even elements we exhibit (multiplicative) generators for annihilator ideals

A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are exactly the field K. All such finite dimensional semisimple algebras arise as a finite dimensional Leavitt path algebra. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely detemined specific graph - which we name as a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant {\kappa}(A) for A and count the number of isomorphism classes of Leavitt path algebras with {\kappa}(A)=n. Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras of possible trees with a given number of vertices and determine the number of distinct Leavitt path algebras of a line graph with a given number of vertices.Comment: 10 pages, 5 figure

A combinatorial discussion on finite dimensional leavitt path algebras

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant kappa(A) for A and count the number of isomorphism classes of Leavitt path algebras with the same fixed value of kappa(A).Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras. of possible trees with a given number of vertices and we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices

Severe 25-OH vitamin D deficiency as a reason for adverse pregnancy outcomes

Objective: There is a growing concern about the unfavorable effects of vitamin D deficiency in general population, including pregnant women, worldwide. The aim of this study is to evaluate the effect of severe maternal serum 25-OH vitamin D levels on adverse pregnancy outcomes in first trimester. Material and methods: Serum samples of 86 pregnant women in first trimester were collected prospectively from May 2017 to June 2017. Serum 25-OH vitamin D levels were analyzed by enzyme immunoassay method. Patients were classified according to maternal serum 25-OH vitamin D levels as group 1 (n¼34) 10ng/ml. The two groups were compared in terms of adverse pregnancy outcomes. Results: The mean 25-OH vitamin D levels of the total 86 pregnant women were 13.83 (6–48) ng/ml. 40% of the pregnant women had low level of 25-OH vitamin D levels (<10ng/ml). The adverse pregnancy outcomes were significantly increased in group 1 (p<.018). Conclusions: Maternal serum 25-OH vitamin D levels <10ng/ml is a risk factor for adverse pregnancy outcomes. 25-OH vitamin D levels should be screened in high-risk pregnant women and treated in case of deficiency

Myo-inositol oxygenese activity in second trimester of pregnancy: altered myoinositol catabolism in gestational diabetes mellitus

Objective: We aimed to determine myo-inositol oxygenase (MIOX) activity in gestational diabetes mellitus (GDM). Material and Methods: The insulin, HbA1c, and MIOX levels of 80 pregnant women were analysed after 75 g OGTT. Group I included patients with no risk factor for GDM, Group II: patients with high risk for GDM, and Group III: GDM patients. Results: Fasting plasma glucose and Homeostatic Model Assessment for Insulin Resistance index were significantly higher in GDM cases (Group 3). Regarding the MIOX levels, significantly higher levels were recorded at 0-h in Group 3 compared to Groups 1 and 2. Significant alteration in MIOX activity was found between 0- and 2-h in Group 3 compared to Groups 1 and 2 (p < .029). Conclusions: MIOX levels were higher in GDM cases so, it may be have a role in myo-inositol catabolism

An observational, multicenter, registry-based cohort study of Turkish Neonatal Society in neonates with Hypoxic ischemic encephalopathy

BACKGROUND: Hypoxic ischemic encephalopathy (HIE) is a significant cause of mortality and short- and long-term morbidities. Therapeutic hypothermia (TH) has been shown to be the standard care for HIE of infants ≥36 weeks gestational age (GA), as it has been demonstrated to reduce the rates of mortality, and adverse neurodevelopmental outcomes. This study aims to determine the incidence of HIE in our country, to assess the TH management in infants with HIE, and present short-term outcomes of these infants. METHODS: The Turkish Hypoxic Ischemic Encephalopathy Online Registry database was established for this multicenter, prospective, observational, nationally-based cohort study to evaluate the data of infants born at ≥34 weeks GA who displayed evidence of neonatal encephalopathy (NE) between March, 2020 and April 2022. RESULTS: The incidence of HIE among infants born at ≥36 weeks GA (n = 965) was 2.13 per 1000 live births (517:242440), and accounting for 1.55% (965:62062) of all neonatal intensive care unit admissions. The rates of mild, moderate and severe HİE were 25.5% (n = 246), 58.9% (n = 568), and 15.6% (n = 151), respectively. Infants with severe HIE had higher rates of abnormal magnetic resonance imaging (MRI) findings, and mortality (p0.05). TH was administered to 85 (34.5%) infants with mild HIE, and of those born of 34-35 weeks of GA, 67.4% (n = 31) received TH. A total of 58 (6%) deaths were reported with a higher mortality rate in infants born at 34-35 weeks of GA (OR 3.941, 95% Cl 1.446-10.7422, p = 0.007). CONCLUSION: The incidence of HIE remained similar over time with a reduction in mortality rate. The timing of TH initiation, whether [removed

Annihilators of principal ideals in the Grassmann algebra

Conference: Conference on Applied Geometric Algebras in Computer Science and Engineering Location: UNIV CAMBRIDGE, ENGN DEPT, CAMBRIDGE, ENGLAND Date: JUL 09-13, 2001It is well known that every Frobenius algebra is quasi-Frobenius, that is to say, if a finite dimensional algebra A over a field F has a nondegenerate bilinear form B such that B(xy, z) = B(x, yz) for all x, y, z ∊ A, then the maps L → Ann r (L) and R → Ann l (R) give inclusion preserving bijections between lattices of left and right ideals of A satisfying (a) Ann r (L 1 + L 2) = Ann r (L 1) ⋂ Ann r (L 2), Ann r (L 1 ⋂ L 2) = Ann r (L 1) + Ann r (L 2) (b) Ann l (R 1 + R 2) = Ann l (R 1) ⋂ Ann l (R 2), Ann l (R 1 ⋂ R 2) = Ann l (R 1) + Ann l (R 2) (c) Ann l(Ann r (L)) = LandAnn r (Ann l (R)) = R. (For example see [2].