Rigidness and extended Armendariz property

Muhittin Ba[문자]er,Fatma Kaynarca,곽태근 대한수학회 2011 대한수학회보 Vol.48 No.1

For a ring endomorphism α of a ring R, Krempa called α a rigid endomorphism if aα(a)=0 implies a=0 for a∈ R, and Hong et al. called R an α- rigid ring if there exists a rigid endomorphism α. Due to Rege and Chhawchharia, a ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. The Armendariz property of polynomials was extended to one of skew polynomials (i.e.,α-Armendariz rings and α-skew Armendariz rings) by Hong et al. In this paper, we study the relationship between α-rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an α-rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.

Papillary Fibroelastoma of the Mitral Valve: an Unusual Cause of Mitral Valve Obstruction

Muhittin Demirel,Emrah Acar,Cüneyt Toprak,Servet İzci,Lütfi Öcal 대한심장학회 2017 Korean Circulation Journal Vol.47 No.2

Generalized semicommutative rings and their extensions

Muhittin Baser,Abdullah Harmanci,곽태근 대한수학회 2008 대한수학회보 Vol.45 No.2

For an endomorphism α of a ring R, the endomorphism α is called semicommutative if ab = 0 implies aRα (b) = 0 for a ∈ R. A ring R is called α-semicommutative if there exists a semicommutative endomor-phism α of R. In this paper, various results of semicommutative ringsare extended to α-semicommutative rings. In addition, we introduce thenotion of an α-skew power series Armendariz ring which is an extensionof Armendariz property in a ring R by considering the polynomials in theskew power series ring R[[x;α]]. We show that a number of interestingproperties of a ringR transfer to its the skew power series ringR[[x;α]]and vice-versa such as the Baer property and the p.p.-property, when R is α-skew power series Armendariz. Several known results relating to α-rigid rings can be obtained as corollaries of our results.

INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS

Muhittin Baser,Begum Hicyilmaz,Fatma Kaynarca,곽태근,이양 대한수학회 2015 대한수학회지 Vol.52 No.6

In this paper, we investigate the insertion-of-factors-proper- ty (simply, IFP) on skew polynomial rings, introducing the concept of strongly σ-IFP for a ring endomorphism σ. A ring R is said to have strongly σ-IFP if the skew polynomial ring R[x; σ] has IFP. We examine some characterizations and extensions of strongly σ-IFP rings in relation with several ring theoretic properties which have important roles in ring theory. We also extend many of related basic results to the wider classes, and so several known results follow as consequences of our results.

Constant curvature factorable surfaces in 3-dimensional isotropic space

Muhittin Evren Aydin 대한수학회 2018 대한수학회지 Vol.55 No.1

In the present paper, we study and classify factorable surfaces in a 3-dimensional isotropic space with constant isotropic Gaussian $(K)$ and mean curvature $(H)$. We provide a non-existence result relating to such surfaces satisfying $\frac{H}{K}=const.$ Several examples are also illustrated.

Singular minimal translation graphs in Euclidean spaces

Muhittin Evren Aydin,Ayla Erdur,Mahmut Erg\"ut 대한수학회 2021 대한수학회지 Vol.58 No.1

In this paper, we consider the problem of finding the hypersurface $M^{n}$ in the Euclidean $\left( n+1\right)$-space $\mathbb{R}^{n+1}$ that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper halfspace $\mathbb{R}_{+}^{3}\left( \mathbf{u} \right) $ with lowest gravity center, for a fixed unit vector $\mathbf{u}\in \mathbb{R}^{3}$. We first state that a singular minimal cylinder $M^{n}$ in $\mathbb{R}^{n+1}$ is either a hyperplane or a $\alpha $-catenary cylinder. It is also shown that this result remains true when $M^{n}$ is a translation hypersurface and $\mathbf{u}$ is a horizantal vector. As a further application, we prove that a singular minimal translation graph in $\mathbb{R }^{3}$ of the form $z=f(x)+g(y+cx),$ $c\in \mathbb{R-\{}0\},$ with respect to a certain horizantal vector $\mathbf{u}$ is either a plane or a $\alpha $- catenary cylinder.

Axisymmetric analysis of a functionally graded layer resting on elastic substrate

Muhittin Turan,Gokhan Adiyaman,Volkan Kahya,Ahmet Birinci 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.58 No.3

This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel’s transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.

GENERALIZED SEMI COMMUTATIVE RINGS AND THEIR EXTENSIONS

Baser, Muhittin,Harmanci, Abdullah,Kwak, Tai-Keun Korean Mathematical Society 2008 대한수학회보 Vol.45 No.2

For an endomorphism ${\alpha}$ of a ring R, the endomorphism ${\alpha}$ is called semicommutative if ab=0 implies $aR{\alpha}(b)$=0 for a ${\in}$ R. A ring R is called ${\alpha}$-semicommutative if there exists a semicommutative endomorphism ${\alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${\alpha}$-semicommutative rings. In addition, we introduce the notion of an ${\alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;\;{\alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;\;{\alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${\alpha}$-skew power series Armendariz. Several known results relating to ${\alpha}$-rigid rings can be obtained as corollaries of our results.

A 3-year retrospective study of clinical durability of bulk-filled resin composite restorations

Ugurlu Muhittin,Sari Fatmanur 대한치과보존학회 2022 Restorative Dentistry & Endodontics Vol.47 No.1

Objectives This study aimed to assess the clinical longevity of a bulk-fill resin composite in Class II restorations for 3-year. Materials and Methods Patient record files acquired from the 40 patients who were treated due to needed 2 similar sizes Class II composite restorations were used for this retrospective study. In the experimental cavity, the flowable resin composite SDR was inserted in the dentinal part as a 4 mm intermediate layer. A 2 mm coverage layer with a nano-hybrid resin composite (CeramX) was placed on SDR. The control restoration was performed by an incremental technique of 2 mm using the nano-hybrid resin composite. The restorations were blindly assessed by 2 calibrated examiners using modified United States Public Health Service criteria at baseline and 1, 2, and 3 years. The data were analyzed using non-parametric tests (p = 0.05). Results Eighty Class II restorations were evaluated. After 3-years, 4 restorations (5%) failed, 1 SDR + CeramX, and 3 CeramX restorations. The annual failure rate (AFR) of the restorations was 1.7%. The SDR + CeramX group revealed an AFR of 0.8%, and the CeramX group an AFR of 2.5% (p > 0.05). Regarding anatomical form and marginal adaptation, significant alterations were observed in the CeramX group after 3-years (p < 0.05). The changes in the color match were observed in each group over time (p < 0.05). Conclusions The use of SDR demonstrated good clinical durability in deep Class II resin composite restorations. Objectives This study aimed to assess the clinical longevity of a bulk-fill resin composite in Class II restorations for 3-year. Materials and Methods Patient record files acquired from the 40 patients who were treated due to needed 2 similar sizes Class II composite restorations were used for this retrospective study. In the experimental cavity, the flowable resin composite SDR was inserted in the dentinal part as a 4 mm intermediate layer. A 2 mm coverage layer with a nano-hybrid resin composite (CeramX) was placed on SDR. The control restoration was performed by an incremental technique of 2 mm using the nano-hybrid resin composite. The restorations were blindly assessed by 2 calibrated examiners using modified United States Public Health Service criteria at baseline and 1, 2, and 3 years. The data were analyzed using non-parametric tests (p = 0.05). Results Eighty Class II restorations were evaluated. After 3-years, 4 restorations (5%) failed, 1 SDR + CeramX, and 3 CeramX restorations. The annual failure rate (AFR) of the restorations was 1.7%. The SDR + CeramX group revealed an AFR of 0.8%, and the CeramX group an AFR of 2.5% (p > 0.05). Regarding anatomical form and marginal adaptation, significant alterations were observed in the CeramX group after 3-years (p < 0.05). The changes in the color match were observed in each group over time (p < 0.05). Conclusions The use of SDR demonstrated good clinical durability in deep Class II resin composite restorations.

Bonding of a resin-modified glass ionomer cement to dentin using universal adhesives

Ugurlu, Muhittin The Korean Academy of Conservative Dentistry 2020 Restorative Dentistry & Endodontics Vol.45 No.3

Objectives: This study aims to assess the effect of universal adhesives pretreatment on the bond strength of resin-modified glass ionomer cement to dentin. Materials and Methods: Fifty caries-free human third molars were employed. The teeth were randomly assigned into five groups (n = 10) based on dentin surface pretreatments: Single Bond Universal (3M Oral Care), Gluma Bond Universal (Heraeus Kulzer), Prime&Bond Elect (Dentsply), Cavity Conditioner (GC) and control (no surface treatment). After Fuji II LC (GC) was bonded to the dentin surfaces, the specimens were stored for 7 days at 37℃. The specimens were segmented into microspecimens, and the microspecimens were subjugated to microtensile bond strength testing (1.0 mm/min). The modes of failure analyzed using a stereomicroscope and scanning electron microscopy. Data were statistically analyzed with one-way analysis of variance and Duncan tests (p = 0.05). Results: The surface pretreatments with the universal adhesives and conditioner increased the bond strength of Fuji II LC to dentin (p < 0.05). Single Bond Universal and Gluma Bond Universal provided higher bond strength to Fuji II LC than Cavity Conditioner (p < 0.05). The bond strengths obtained from Prime&Bond Elect and Cavity Conditioner were not statistically different (p > 0.05). Conclusions: The universal adhesives and polyacrylic acid conditioner could increase the bond strength of resin-modified glass ionomer cement (RMGIC) to dentin. The use of universal adhesives before the application of RMGIC may be more beneficial in improving bond strength.