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ON COFINITELY CLOSED WEAK δ-SUPPLEMENTED MODULES
( Esra Öztürk Sözen ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
A module M is called cofinitely closed weak δ-supplemented (briey δ-ccws-module) if for any cofinite closed submodule N of M has a weak δ-supplement in M: In this paper we investigate the basic properties of δ-ccws modules. In the light of this study, we can list the main facts obtained as following: (1) Any cofinite closed direct summand of a δ-ccws module is also a δ-ccws module; (2) Let R be a left δ-V -ring. Then R is a δ-ccws module iff R is a ccws-module iff R is extending; (3) Any nonsingular homomorphic image of a δ-ccws-module is also a δ-ccws-module; (4) We characterize nonsingular δ-V -rings in which all nonsingular modules are δ-ccws.
A RECENT GENERALIZATION OF COFINITELY INJECTIVE MODULES
( Esra Öztürk Sözen ) 호남수학회 2023 호남수학학술지 Vol.45 No.3
Let R be an associative ring with identity and M be a left R-module. In this paper, we define modules that have the property (δ- CE) ((δ-CEE)), these are modules that have a δ-supplement (ample δ- supplements) in every cofinite extension which are generalized version of modules that have the properties (CE) and (CEE) introduced in [6] and so a generalization of Zöschinger’s modules with the properties (E) and (EE) given in [23]. We investigate various properties of these modules along with examples. In particular we prove these: (1) a module M has the property (δ-CEE) if and only if every submodule of M has the property (δ-CE); (2) direct summands of a module that has the property (δ-CE) also have the property (δ-CE); (3) each factor module of a module that has the property (δ-CE) also has the property (δ-CE) under a special condition; (4) every module with composition series has the property (δ- CE); (5) over a δ-V -ring a module M has the property (δ-CE) if and only if M is cofinitely injective; (6) a ring R is δ-semiperfect if and only if every left R-module has the property (δ-CE).
Esra Akyüz Özkan,Allahverdi Sadigov,Osman Öztürk 한국임상영양학회 2022 Clinical Nutrition Research Vol.11 No.3
To investigate adipokines (vaspin, omentin-1, adiponectin and leptin) and their correlation with hepatosteatosis degree in obese/overweight (O/O) children. We analyzed adipokine levels of 81 children (49 O/O, [body mass index (BMI) > 95th] and 32 non-obese (BMI = 5-85th) admitted to the pediatric outpatient clinic. Serum triglyceride, glucose, low density lipoprotein-cholesterol, total cholesterol, high density lipoprotein-cholesterol, alanine aminotransferase, aspartate aminotransferase (AST), insulin, HbA1c levels and leptin, omentin-1, vaspin, adiponectin levels were studied. O/O children with hepatosteatosis were divided into grades 1, 2 and 3 according to the degree of hepatosteatosis determined by ultrasonography. While AST (p = 0.001), triglyceride (p = 0.006), BMI percentile (p = 0.000), HOMA index (p = 0.002), systolic blood pressure (p = 0.02), leptin (p = 0.001), omentin-1 (p = 0.001), adiponectin (p = 0.001) levels were higher, vaspin level was lower (p = 0.008) in the (O/O) group compared to the controls. There was a positive correlation between HDL and vaspin, and a negative correlation between HDL and omentin-1 in the O/O group. Also it was observed that as the degree of hepatosteotosis increased, leptin (p = 0.004), omentin-1 (p = 0.001) levels were increased. There was no significant change in vaspin level (p = 0.128). The high levels of omentin-1, leptin and adiponectin have an association with the development of hepatosteatosis in O/O children.
Experimental Determination of Interfacial Energies for Solid Sn in Equilibrium with Sn-Mg-Zn Liquid
Yemliha Altıntas,Esra Öztürk,Sezen Aksöz,Kâzım Keşlioğlu,Necmettin Maraşlı 대한금속·재료학회 2015 METALS AND MATERIALS International Vol.21 No.2
The equilibrated grain boundary groove shapes of solid Sn in equilibrium with Sn-Mg-Zn liquid were observedfrom a quenched sample by using a radial heat flow apparatus. The Gibbs-Thomson coefficient, solid-liquidinterfacial energy and grain boundary energy of solid Sn were determined from the observed grain boundarygroove shapes. The thermal conductivity of the eutectic solid phase for Sn-8.12 at% Mg-4.97 at% Zn alloy and thethermal conductivity ratio of the liquid phase to the solid phase for Sn-8.12 at% Mg-4.97 at% Zn alloy at eutectictemperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus,respectively. The Gibbs-Thomson coefficient, solid-liquid interfacial energy and grain boundary energy of solidSn in equilibrium with Sn-Mg-Zn liquid were determined to be (8.3 ± 0.6)×10-8 Km, (118.5 ± 14.2)×10-3 Jm-2and (225.1 ± 29.3)×10-3 J m-2 respectively from observed grain boundary groove shapes. A comparison ofpresent results for solid Sn in the Sn-8.12 at% Mg-4.97 at% Zn alloy with the results obtained in previous worksfor similar solid Sn in equilibrium with different binary or ternary liquid was made.