• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.451-459
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• 2019

Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2027-2034
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• 2013

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.589-597
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• 2018

For $A,B{\in}M_2(\mathbb{C})$, let the Jordan product be AB + BA and G(A) the eigenvalue inclusion set, the Gershgorin set of A. Characterization is obtained for maps ${\phi}:M_2(\mathbb{C}){\rightarrow}M_2(\mathbb{C})$ satisfying $$G[{\phi}(A){\phi}(B)+{\phi}(B){\phi}(A)]=G(AB+BA)$$ for all matrices A and B. In fact, it is shown that such a map has the form ${\phi}(A)={\pm}(PD)A(PD)^{-1}$, where P is a permutation matrix and D is a unitary diagonal matrix in $M_2(\mathbb{C})$.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-485
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• 2023

Let 𝓐 be a unital Banach *-algebra and 𝓜 be a unital *-𝓐-bimodule. If W is a left separating point of 𝓜, we show that every *-derivable mapping at W is a Jordan derivation, and every *-left derivable mapping at W is a Jordan left derivation under the condition W𝓐 = 𝓐W. Moreover we give a complete description of linear mappings 𝛿 and 𝜏 from 𝓐 into 𝓜 satisfying 𝛿(A)B^* + A𝜏(B)^* = 0 for any A, B ∈ 𝓐 with AB^* = 0 or 𝛿(A)◦B^* + A◦𝜏(B)^* = 0 for any A, B ∈ 𝓐 with A◦B^* = 0, where A◦B = AB + BA is the Jordan product.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.359-370
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• 2020

A graph G is called a well covered graph if every maximal independent set in G is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.5
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• pp.455-463
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• 2021

The main objective of this research was to analyze the influence of digital marketing on purchasing decisions. The research was guided by specific aims; to evaluate numerous digital marketing platforms in Jordan that can affect the purchasing decisions and identify product categories purchased by customers on digital media platforms. Furthermore, questionnaires were given based on a simple sampling technique and acquired in the Jordanian market. 300 questionnaires were distributed, and 220 available samples were gathered, except for incomplete questionnaires, resulting in a 73% response rate to all those who selected to participate. Descriptive analysis, reliability test, correlation test, and multiple regressions were used in this research. Moreover, this study's results demonstrated that digital marketing, such as social media marketing and mobile marketing, has a profound impact on consumer purchasing decisions. However, hypothesis testing demonstrated that there are many patronized digital media platforms in Jordan that affect student behavior. Jordanian students buy various product categories on digital media platforms, and digital marketing affects student decision-making. Finally, the results of this study suggest that firms should adopt strategies to leverage the digital world and technology, increase brand awareness through digital platforms to continue competing in today's commercial environment.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.563-574
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• 2017

Let $\mathcal{A}$ be a unital real standard Jordan operator algebra acting on a Hilbert space H of dimension at least 2. We show that every bijection ${\phi}$ on $\mathcal{A}$ satisfying ${\phi}(A^2{\circ}B)={\phi}(A)^2{\circ}{\phi}(B)$ is of the form ${\phi}={\varepsilon}{\psi}$ where ${\psi}$ is an automorphism on $\mathcal{A}$ and ${\varepsilon}{\in}\{-1,1\}$. As a consequence if $\mathcal{A}$ is the real algebra of all self-adjoint operators on a Hilbert space H, then there exists a unitary or conjugate unitary operator U on H such that ${\phi}(A)={\varepsilon}UAU^*$ for all $A{\in}\mathcal{A}$.

• Asian-Australasian Journal of Animal Sciences
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• v.25 no.8
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• pp.1132-1137
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• 2012

Objective of this experiment was to evaluate the effect of partial substitution of barley grain with bread by-product (BB) on performance of Awassi ewes and their lambs. Forty Awassi ewes rearing single lambs were randomly allotted into four experimental diets containing various levels of BB. The experimental diets contained 0 (BB0), 10 (BB10), 15 (BB15), and 20% (BB20) of BB on dietary dry matter (DM). The study lasted for eight weeks, in which the first week was used as an adaptation period and seven weeks of data collection. Ewes and their lambs were penned individually where they were fed their lactating diets ad libitum. Ewes and lambs body weights were measured at the beginning and at the end of the experiment. However, milk production and composition were evaluated biweekly. Feeding BB had no effect (p>0.05) on dry matter (DM), organic matter (OM), and crude protein (CP) intakes. However, neutral detergent fiber (NDF) intake was the lowest (p<0.05) for the BB20 and BB15 diets followed to BB10 diet (i.e., 640, 677, 772 g/d, respectively) while the highest NDF intake was for the BB0 diet (i.e., 825 g/d). Similarly, NDF intake decreased linearly (p<0.001) as the BB content increased. Acid detergent fiber (ADF) intake was highest (p<0.05) for the BB0 and BB10 diets (425 and 416 g/d, respectively) followed by the BB15 and BB20 diets (359 and 342 g/d, respectively). Moreover, a linear (p<0.001), quadratic (p = 0.04), and cubic (p = 0.04) effects were observed in ADF intake among diets. Nutrient digestibility was similar among different diets. Bread by-product had no effect (p>0.05) on ewes body weight change and on lamb performance (i.e., weaning body weight and average daily gain). Similarly, no differences (p>0.05) were observed either in milk production or composition by the BB substitution. Inclusion of BB reduced feed cost by 9, 14, and 18% for the BB10, BB15, and BB20 diets, respectively. No differences were observed in milk efficiency (DM intake: milk production; p>0.05) among diets. However, cost of milk production ($US/kg milk) was the lowest (p<0.05) in the diet containing BB20. Results of the present study indicate that feeding bread by-product up to 20% of the diet DM had no effect on performance of Awassi ewes and their lambs and reduced feed cost.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.359-367
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• 2009

The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.61-74
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• 2018

Let $\mathcal{A}$ and $\mathcal{B}$ be two prime ${\ast}$-algebras. Let ${\Phi}:\mathcal{A}{\rightarrow}\mathcal{B}$ be a bijective and satisfies $${\Phi}(A{\bullet}B{\bullet}A)={\Phi}(A){\bullet}{\Phi}(B){\bullet}{\Phi}(A)$$, for all $A,B{\in}{\mathcal{A}}$ where $A{\bullet}B=A^{\ast}B+BA^{\ast}$. Then, ${\Phi}$ is additive. Moreover, if ${\Phi}(I)$ is idempotent then we show that ${\Phi}$ is ${\mathbb{R}}$-linear ${\ast}$-isomorphism.