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REMARKS ON GENERALIZED JORDAN (α, β)<sup>*</sup>-DERIVATIONS OF SEMIPRIME RINGS WITH INVOLUTION
Hongan, Motoshi,Rehman, Nadeem ur Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1
Let R be an associative ring with involution * and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an $({\alpha},{\beta})^*$-derivation of R if $d(xy)=d(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $F:R{\rightarrow}R$ is called a generalized $({\alpha},{\beta})^*$-derivation of R associated with an $({\alpha},{\beta})^*$-derivation d if $F(xy)=F(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [12], and a theorem of Daif and El-Sayiad [6], moreover, we generalize a theorem of Ali et al. [4] and a theorem of Huang and Koc [9] related to generalized Jordan triple $({\alpha},{\beta})^*$-derivations.
ON GENERALIZED (α, β)-DERIVATIONS IN BCI-ALGEBRAS
Al-Roqi, Abdullah M. The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.1
The notion of generalized (regular) (${\alpha},\;{\beta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${\alpha},\;{\beta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${\alpha},\;{\beta}$)-derivation and ${\alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${\alpha},\;{\beta}$)-derivations are proved.
Multiplicative (generalized) (\alpha, \beta)-derivations on left ideals in prime rings
Faiza Shujat 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.1
A mapping T:R\to R (not necessarily additive) is called multiplicative left \alpha-centralizer if T(xy)=T(x)\alpha(y) for all x,y\in R. A mapping F:R\to R (not necessarily additive) is called multiplicative (generalized) (\alpha, \beta)-derivation if there exists a map (neither necessarily additive nor derivation) f:R\to R such that F(xy)=F(x)\alpha(y)+\beta(x)f(y) for all x,y\in R, where \alpha and \beta are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (\alpha, \beta)-derivations and multiplicative left \alpha-centralizer on the left ideal of a prime ring R.
REMARKS ON GENERALIZED (α, β)-DERIVATIONS IN SEMIPRIME RINGS
Hongan, Motoshi,ur Rehman, Nadeem Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].
REGIONS OF VARIABILITY FOR GENERALIZED α-CONVEX AND β-STARLIKE FUNCTIONS, AND THEIR EXTREME POINTS
Chen, Shaolin,Huang, Aiwu Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.4
Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.
만성 C형 간염환자에서 Interferon Alpha-2b와 Ribavirin 치료 중 발생한 범발성 습진 양상의 발진
권연숙 ( Yeon Sook Kwon ),김대석 ( Dae Suk Kim ),류동진 ( Dong Jin Ryu ),오상호 ( Sang Ho Oh ),이광훈 ( Kwang Hoon Lee ) 대한피부과학회 2008 대한피부과학회지 Vol.46 No.7
The combination of interferon alpha with ribavirin is currently recommended in the treatment of hepatitis C virus (HCV) infection. Commonly reported cutaneous reactions include localized reactions such as injection site inflammation and necrosis and worsening of other skin disorders, including psoriasis, lichen planus, vitiligo, or systemic lupus erythematosus. However, generalized eczematous reactions have been reported to occur uncommonly in patients treated with interferon and ribavirin, however such a case has not been described in the Korean literature. Herein, we describe a 49-year old female showing generalized eczema-like eruption after treatment of interferon alpha-2b and ribavirin for chronic HCV infection. (Korean J Dermatol 2008;46(7):915~918)
Cytotoxicity Evaluation of Essential Oil and its Component from Zingiber officinale Roscoe
Lee, Yongkyu Korean Society of ToxicologyKorea Environmental Mu 2016 Toxicological Research Vol.32 No.3
Zingiber officinale Roscoe has been widely used as a folk medicine to treat various diseases, including cancer. This study aims to re-examine the therapeutic potential of co-administration of natural products and cancer chemotherapeutics. Candidate material for this project, ${\alpha}$-zingiberene, was extracted from Zingiber officinale Roscoe, and ${\alpha}$-zingiberene makes up $35.02{\pm}0.30%$ of its total essential oil. ${\alpha}$-Zingiberene showed low $IC_{50}$ values, $60.6{\pm}3.6$, $46.2{\pm}0.6$, $172.0{\pm}6.6$, $80.3{\pm}6.6$ (${\mu}g/mL$) in HeLa, SiHa, MCF-7 and HL-60 cells each. These values are a little bit higher than $IC_{50}$ values of general essential oil in those cells. The treatment of ${\alpha}$-zingiberene produced nucleosomal DNA fragmentation in SiHa cells, and the percentage of sub-diploid cells increased in a concentration-dependent manner in SiHa cells, hallmark features of apoptosis. Mitochondrial cytochrome c activation and an in vitro caspase-3 activity assay demonstrated that the activation of caspases accompanies the apoptotic effect of ${\alpha}$-zingiberene, which mediates cell death. These results suggest that the apoptotic effect of ${\alpha}$-zingiberene on SiHa cells may converge caspase-3 activation through the release of mitochondrial cytochrome c into cytoplasm. It is considered that anti-proliferative effect of ${\alpha}$-zingiberene is a result of apoptotic effects, and ${\alpha}$-zingiberene is worth furthermore study to develop it as cancer chemotherapeutics.
Geometry of locally projectively flat finsler space with certain (\alpha, \beta)-metric
Ajaykumar Abbaniramakrishnappa,Pradeep Kumar 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.1
In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special $(\alpha, \beta)$-metric and the generalised first approximate Matsumoto $(\alpha, \beta)$-metric, where $\alpha$ is a Riemannian metric and $\beta$ is a differential one-form. Further, we concluded that $\alpha$ is locally Projectively flat and have $\beta$ is parallel with respect to $\alpha$ for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.
ON GENERALIZED RICCI-RECURRENT TRANS-SASAKIAN MANIFOLDS
Kim, Jeong-Sik,Prasad, Rajendra,Tripathi, Mukut-Mani Korean Mathematical Society 2002 대한수학회지 Vol.39 No.6
Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.
Wu, Xinxing,Zhu, Peiyong Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.4
Similarly to Tychonoff product, we introduce the concept of generalized product topology which is different from the notion of product of generalized topologies in [$\acute{A}$. $Cs\acute{a}sz\acute{a}r$, Acta Math. Hungar. 123 (2009), 127-132] for generalized topology and obtain some properties about it. Besides, we prove that connectedness, ${\sigma}$-connectedness and ${\alpha}$-connectedness are all preserved under this product.