t-Generalized Supplemented Modules

In the present paper, t-generalized supplemented modules are defined starting from the generalized ⨁-supplemented modules. In addition, we present examples separating the t-generalized supplemented modules, supplemented modules, and generalized ⨁-supplemented modules and also show the equality of these modules for projective and finitely generated modules. Moreover, we define cofinitely t-generalized supplemented modules and give the characterization of these modules. Furthermore, for any ring R, we show that any finite direct sum of t-generalized supplemented R-modules is t-generalized supplemented and that any direct sum of cofinitely t-generalized supplemented R-modules is a cofinitely t-generalized supplemented module.Доведено, що t-узагальнені доповнені модулі визначені на основі узагальнених ⨁-доповнених модулів. Kpiм того, наведено приклади, що відокремлюють t-узагальнені доповнені модулі, доповнені модулі та узагальнені ⨁-доповнені модулі, а також доведено рівність цих модулів для проективних та скінченнопороджених модулів. Також визначено кофінітно t-узагальнені доповнені модулі та наведено характеристику цих модулів. Більш того, для кожного кільця R доведено, що будь-яка скінченна пряма сума t-узагальнених доповнених R-модулів є t-узагальненою доповненою, а також будь-яка пряма сума кофінітно t-узагальнених доповнених R-модулів є кофінітно t-узагальненим доповненим R-модулем

G-Supplemented Modules

Following the concept of generalized small submodule, we define g -supplemented modules and characterize some fundamental properties of these modules. Moreover, the generalized radical of a module is defined and the relationship between the generalized radical and the radical of a module is investigated. Finally, the definition of amply g -supplemented modules is given with some basic properties of these modules.Із застосуванням поняття узагальненого малого підмодуля визначено поняття g-доповнених модулів та охарактеризовано дєякі фундаментальні властивості цих модулів. Крім того, визначено поняття узагальненого радикала модуля та вивчено співвідношення між узагальненим радикалом та радикалом модуля. Насамкінець наведено визначення поняття рясно g-доповнених модулів та вивчено основні властивості цих модулів

The incidence of pneumatised inferior turbinate and relation to close anatomic structures

Background: Pneumatisation of the inferior turbinate (PIT) is a rare abnormality of the paranasal sinus. It is very difficult to differentiate from the hypertrophia of the inferior turbinate clinically. Thus, it is important to be considered, especially in cases with no response to medical treatments. We aimed to investigate the presence and the frequency of PIT by computed tomography (CT). Materials and methods: A total of 2905 cases (1381 female, 1524 male) with an age range between 16 and 84 were included. Results: The pneumatisation of the inferior turbinate was observed in 1.72% of the cases with a percentage of 1.88% in women and 1.57% in men. In PIT (+) cases the bilaterality was found in 54% of them. According to the subtypes, 70% was lamellar, 28% was bullous and 2% was extensive. No statistically significant difference was found for age distribution. The most commonly associated variations were the pneumatisation of the middle and upper turbinate and the septal deviation. Conclusions: The pneumatisation of the inferior turbinate is a rare variation with a similar frequency among men and women. It is diagnosed by CT and when symptomatic, the optimal treatment is surgery

Investigation of Single Air Bubble Dynamics and the Effect of Nanoparticles in Rectangular Minichannels

Bubble dynamics and understanding related mechanisms based on force analysis are necessary for better understanding two-phase flow phenomena in small channels. To address this subject, experiments were conducted with injected single air bubbles into rectangular minichannels containing flows of pure water, pure ethanol and TiO2-nanoparticle-based nanofluids, which had a nanoparticle mass fraction of 0.005 wt% for both water and ethanol base fluids. For a range of fluid flow rates, bubble movement and temperature profiles were captured along the channel using high-speed and infrared (IR) cameras, respectively. Upon heating, when using nanofluids, deposition of TiO2 nanoparticles occurred. The results in the channels with cross sectional dimensions of 2 mm × 4 mm and heated length of 7 cm were compared with their counterparts on plain surfaces. Heat fluxes were applied by means of a tantalum film heater on the outer surface of the channel. Bubble dynamics and forces acting on the bubbles were quantitatively analyzed in relation to the fluid type, heat flux, flow rate and deposition. This study highlights the effects of TiO2-nanoparticles (dispersed in two different base fluids) on single-bubble dynamics in minichannels. The nanoparticle deposition was found to have a retarding effect on the bubble movement and led to a more elliptical shape rather than a spherical bubble shape. The bubble behavior is comprehensively assessed in the light of the visualization data and acting forces

Synthesis, spectroscopic characterizations and quantum chemical computational studies of (Z)-4-[(E)-p-tolyldiazenyl]-6-[(2-hydroxyphenylamino) methylene]-2-methoxycyclohexa-2,4-dienone

In this study, the molecular structure and spectroscopic properties of title compound were characterized by X-ray diffraction, FT-IR and UV-vis spectroscopies. These properties of title compound were also investigated from calculative point of view. The X-ray diffraction and FT-IR analyses reveal the existence of keto form in the solid state. UV-vis spectra were recorded in different organic solvents. The results show that title compound exists in both keto and enol forms in DMSO, EtOH but it exists in enol form in benzene. In addition, the title compound in DMSO showed new absorption band at 436 nm due to the high ionizing effect of this solvent. The geometry optimization of title compound in gas phase was performed using DFT method with B3LYP applying 6-311G(d,p) basis set. TD-DFT calculations starting from optimized geometry were carried out in gas phase to calculate excitation energies of title compound. The non-linear optical properties were computed with the same level of theory and title compound showed a good second order nonlinear optical property. In addition, thermodynamic properties were obtained in the range of 100-500 K. © 2012 Elsevier B.V. All rights reserved

Synthesis, spectroscopic characterizations and quantum chemical computational studies of (Z)-4-[(E)-p-tolyldiazenyl]-6-[(2-hydroxyphenylamino)methylene]-2-methoxycyclohexa-2,4-dienone.

In this study, the molecular structure and spectroscopic properties of title compound were characterized by X-ray diffraction, FT-IR and UV-vis spectroscopies. These properties of title compound were also investigated from calculative point of view. The X-ray diffraction and FT-IR analyses reveal the existence of keto form in the solid state. UV-vis spectra were recorded in different organic solvents. The results show that title compound exists in both keto and enol forms in DMSO, EtOH but it exists in enol form in benzene. In addition, the title compound in DMSO showed new absorption band at 436 nm due to the high ionizing effect of this solvent. The geometry optimization of title compound in gas phase was performed using DFT method with B3LYP applying 6-311G(d,p) basis set. TD-DFT calculations starting from optimized geometry were carried out in gas phase to calculate excitation energies of title compound. The non-linear optical properties were computed with the same level of theory and title compound showed a good second order nonlinear optical property. In addition, thermodynamic properties were obtained in the range of 100-500 K

(E)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol: X-ray and DFT-calculated structures

The crystal structure of (E)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol is determined by using X-ray diffraction and then the molecular structure is investigated with density functional theory (DFT). X-Ray study shows that the title compound has a strong intramolecular O-H⋯N hydrogen bond and three dimensional crystal structure is primarily determined by C-H⋯π and weak van der Waals interactions. The strong O-H⋯N bond is an evidence of the preference for the phenol-imine tautomeric form in the solid state. Optimized molecular geometry is calculated with DFT at the B3LYP/6-31G(d,p) level. The IR spectra of compound were recorded experimentally and calculated to compare with each other. The results from both experiment and theoretical calculations are compared in this study. © 2010 Pleiades Publishing, Ltd

Antioxidant activity and phenolic composition of sumac (Rhus coriaria L.) extracts

Antioxidant activity and phenolic compounds of sumac extracts were investigated. Sumac was extracted in methanol and subjected to solvent-solvent partitioning to yield two fractions as ethyl acetate and aqueous. Methanol extract was further fractioned over Sephadex LH-20 column. Antioxidant activity of extracts and fractions were screened using ferric thiocyanate and DPPH radical scavenging methods. Phenolic composition of active fraction(s) was determined by HPLC-MS systems. Those fractions which exhibited strong antioxidant activity were rich in anthocyanins and hydrolysable tannins. While gallic acid was the main phenolic acid in the extracts, anthocyanin fraction contained cyanidin, peonidin, pelargonidin, petunidin, and delphinidin glucosides and coumarates. Pentagalloyl glucose was abundant in the hydrolysable tannin fraction. Effective scavenging concentration (EC50) on DPPH radical was 0.70 mu g/mL both in ethyl acetate and tannin fractions, and 5.33 mu g/mL in anthocyanin rich fraction. Same extracts and fractions showed moderate lipid peroxidation inhibition effect compared with the synthetic antioxidants. The findings demonstrate that sumac can be used as a natural antioxidant. (c) 2006 Elsevier Ltd. All rights reserved